the cost of capital for the water sector at pr19...the cost of capital for the water sector at pr19...
TRANSCRIPT
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The Cost of Capital for the
Water Sector at PR19
17 July 2019
Europe Economics is registered in England No. 3477100. Registered offices at Chancery House, 53-64 Chancery Lane, London WC2A 1QU.
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© Europe Economics. All rights reserved. Except for the quotation of short passages for the purpose of criticism or review, no part may be used or
reproduced without permission.
Introduction
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Contents
1 Introduction .................................................................................................................................................................... 3
2 Inflation .......................................................................................................................................................................... 12
2.2 The CPI-CPIH wedge......................................................................................................................................... 13
2.3 The RPI-CPI wedge ............................................................................................................................................ 15
2.4 Overall conclusion .............................................................................................................................................. 19
3 The risk-free rate ........................................................................................................................................................ 20
3.1 Introduction ......................................................................................................................................................... 20
3.2 Market evidence of nominal gilts and index-linked gilts ............................................................................ 20
3.3 Is it better to base “observable asset” estimates of the risk-free rate on nominal gilts or RPI-index-
linked gilts? ......................................................................................................................................................................... 21
3.4 Market-implied rate change in AMP7 ............................................................................................................. 23
3.5 Conclusions on the risk-free rate ................................................................................................................... 25
4 Total Market Return .................................................................................................................................................. 27
4.1 Introduction ......................................................................................................................................................... 27
4.2 The TMR and the alternative approaches available for its estimation ................................................... 27
4.3 Ex-post approaches to the TMR ..................................................................................................................... 28
4.4 Ex-ante approaches to the TMR ..................................................................................................................... 32
4.5 Forward-looking approaches based on practitioners’ estimates ............................................................. 34
4.6 Forward-looking approaches based on Dividend Growth Models (DGM) and Dividend Discount
Models (DDM) .................................................................................................................................................................. 35
4.7 Conclusions on TMR ......................................................................................................................................... 37
5 Beta and the cost of equity ....................................................................................................................................... 38
5.1 Introduction ......................................................................................................................................................... 38
5.2 What a beta is an how an asset beta and its components are estimated ............................................. 38
5.3 Specific methodology for raw equity beta estimation ................................................................................ 45
5.4 Beta evidence based on OLS............................................................................................................................ 45
5.5 Cross-checks based on ARCH/GARCH estimates .................................................................................... 50
5.6 Unlevered betas .................................................................................................................................................. 54
5.7 Debt betas ............................................................................................................................................................ 56
5.8 Summary of findings on asset beta.................................................................................................................. 62
5.9 Re-levering to obtain the notional equity beta ............................................................................................ 62
5.10 Overall cost of equity ........................................................................................................................................ 64
6 Cost of debt ................................................................................................................................................................. 66
6.1 Introduction ......................................................................................................................................................... 66
6.2 Cost of embedded debt .................................................................................................................................... 66
6.3 Ratio of new to total debt ................................................................................................................................ 74
Introduction
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6.4 Cost of new debt ................................................................................................................................................ 75
6.5 Overall cost of debt ........................................................................................................................................... 77
7 Overall WACC ............................................................................................................................................................ 78
7.1 Appointee vanilla WACC ................................................................................................................................. 78
7.2 Retail margin and wholesale WACC ............................................................................................................. 78
8 Appendix ....................................................................................................................................................................... 80
8.1 Methodological issues when estimating raw equity betas ......................................................................... 80
8.2 ARCH/GARCH estimation .............................................................................................................................. 89
8.3 Derivation of the debt beta equation used for the decomposition approach ..................................... 89
8.4 Regulatory fair value gearing ............................................................................................................................ 90
Introduction
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1 Introduction
This document sets out our view on the appropriate WACC for PR19. The main drivers of changes in our
WACC estimates compared to the recommendations we made in 20171 arise from:
Changes in market data (the cut-off date used to produce estimates in this report is 28 February 2019,
whist the cut-off date used in our early view analysis was 31 July 20172)
Methodological changes (these are summarised in Table 1.2).
We start by comparing our current WACC recommendations (“EE’s current recommendation 2019”) to
the figures we proposed in 2017 (“EE’s early view 2017”) and to the WACC estimates chosen by Ofwat in
its Final Methodology paper3 (“Ofwat’s early view 2017”).
Table 1.1: Europe Economics’ current recommendation — comparison with EE and Ofwat early views
Ofwat’s
early view
(2017)
EE’s early
view (2017)
EE’s current
view (2019)
Change
relative to
Ofwat’s early
view
Change
relative to
EE’s early
view
Risk-free rate 2.10% 2.00% 1.81% -29 bps -19 bps
Total Market Return 8.60% 8.88% 8.63% +3 bps -25 bps
Raw equity beta 0.63 0.59 0.62 -0.01 +0.03
Market gearing 49% 49% 54.7% +6.70% +6.70%
Unlevered beta 0.32 0.30 0.28 -0.04 -0.02
Debt beta 0.10 0.125 0.15 +0.05 +0.025
Asset beta 0.37 0.36 0.36 -0.01 Unchanged
Notional gearing 60% 60% 60% Unchanged Unchanged
Notional equity beta 0.77 0.72 0.68 -0.09 -0.04
Cost of equity 7.13% 6.96% 6.45% -68 bps -51 bps
Cost of new debt 3.40% 3.60% 3.36% -4 bps -24 bps
Cost of embedded debt 4.64% 4.90% 4.52% -12 bps -38 bps
Share of new debt 30% 30% 20% -10% -10%
Issuance cost 0.10%* 0.10%* 0.10% Unchanged Unchanged
Cost of debt 4.36% 4.51% 4.39% +3 bps -12 bps
Vanilla WACC 5.47% 5.49% 5.21% -26 bps -28 bps
Retail margin adjustment 0.10% 0.10% 0.11% +1bps +1bps
1 Europe Econmics (2017) “PR19 — Initial Assessment of the Cost of Capita”, available at:
https://www.ofwat.gov.uk/publication/europe-economics-pr19-initial-assessment-cost-capital/ 2 We note that, in order to determine its initial view on the risk-free rate Europe Economics used spot yields at March
2017, adjusted with forward yield curve data covering the period April 2017, July-2017. 3 Ofwat (Dec 2017): “Delivering Water 2020: Our methodology for the 2019 price review - Appendix 12 Aligning
risk and Return”.
Introduction
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Ofwat’s
early view
(2017)
EE’s early
view (2017)
EE’s current
view (2019)
Change
relative to
Ofwat’s early
view
Change
relative to
EE’s early
view
Wholesale WACC 5.37% 5.39% 5.10% -27bps -29bps
* In Ofwat’ s early view issuance and liquidity costs are added to the overall cost of debt, whilst in EE’s initial view they are added only to the cost of
new debt. The 3.60 per cent figure for the cost of new debt recommended in EE’s initial view includes already a 10 bps allowance cost issuance and
liquidity costs.
The table below summarise the methodologies adopted by Europe Economics in 2017, and sets out the
methodology underpinning the proposals presented in this report and explained in the corresponding
sections.
Table 1.2: Methodologies underpinning the proposals
EE early view EE current view
Risk-free rate Range: 1.70%-2.51%
Point estimate: 2.00%
Range: 1.54%-1.92%
Point estimate: 1.81%
The lower end is based on the observed yield on
10-year nominal gilts (1.21%), adjusted for the
lower end of the expected rise in interest rates
in 2020-25 period (0.49%).
The upper end is based on the observed yield on
20-year nominal gilts (1.92%), adjusted for the
upper end of the expected rise in interest rates
in 2020-25 period (0.59%).
We placed more weight on the 10-year gilts,
hence our point estimate was towards the lower
end of the range.
ILG data available now that was temporarily
unavailable in 2017 allows some use of ILG data
this time.
Reflecting the view that both nominal and ILG
series are relevant, we calculate the lower bound
from average spot values of 10/20-year ILGs gilts
(-1.70% RPI-deflated value), and upper bound
based on average spot values (1.62%) of 10/20-
year nominal gilts. Both values are adjusted for
the average expected rise in interest in the 2020-
25 period (i.e. +0.28% added to the RPI-deflated
value of -1.70%, which results in a RPI-deflated
value of -1.42%, and thus 1.54% in nominal terms,
and +0.31% added to the nominal rate of 1.62%
so as to obtain a nominal rate of 1.92%)
Reflecting our analysis of differences in the
relative distortions of the nominal and ILG series
at different maturities (described in Section 3),
the point estimate is the average between 10-
year nominal gilts (adjusted for rate change
expectations) and the average between 20-year
nominal gilts and ILGs (also adjusted to reflect
rate change expectations).
Total market
return Range: 8.38%-9.14%
Point estimate: 8.88%
Range: 8.12%-9.14%
Point estimate: 8.63%
Range based on judgment using a wide range of
evidence. Significant weight was placed on EE’s
DGM estimates to inform a plausible range of
8.4-9.1%. Point estimate slightly above the mid-
point of the range to reflect estimate of EE’s
preferred DGM model.
Historical approaches based on the latest DMS
data are consistent with CPI-deflated TMR
estimate of ~6.5-7%, with a non-recession point
estimate likely to be of the order of 0.2% below
this.
DGM and DDM models produce similar CPI-
deflated TMR estimates broadly within the
similar 6-7% range.
Introduction
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EE early view EE current view
Adjusted historical approaches suggest a CPI-
deflated value for the TMR towards the lower
end of that range of around 6%.
Although the average across practitioners’
estimates is materially below 6 per cent, we
place more weight upon the first three factors,
producing a real (CPIH-deflated) range of 6-7%.
When inflated by our assumed 2.0% CPIH rate,
we obtain 8.12%-9.14% for the nominal TMR.
Raw equity
beta Range: N/A
Point estimate: 0.59
Range: 0.57-0.66
Point estimate: 0.62
The value is imputed from the unlevered beta
point estimate and the market gearing value.
The ranges are imputed from the unlevered beta
ranges and the market gearing value. The point
estimate is imputed from the unlevered beta
point estimate and the market gearing value.
Market gearing Range: N/A
Point estimate: 49%
Range: N/A
Point estimate: 54.7%
The 49% value is determined by the 2-year
trailing average of net debt to enterprise value
for SVT/UU.
The 54.7% value is determined by the 2-year
trailing average of net debt to enterprise value
for SVT/UU.
Unlevered
beta Range: N/A
Point estimate: 0.30
Range: 0.26-0.30
Point estimate: 0.28
Point estimate slightly below the 2-year daily
OLS beta for SVT/UU to reflect regulatory
precedents and the fact, at the time, there was
not sufficiently strong evidence to justify change
in beta from the PR14 value. Therefore the
unlevered beta value chosen is the same as the
PR14 asset beta value based on zero debt beta.
Point estimate based on 2-year OLS beta for
SVT/UU using daily data. The range is a judgment
call based on the fact that beta estimates are
intrinsically subject to some degree of
uncertainty.
Debt beta Range: 0.10-0.15
Point estimate: 0.125
Range: 0.10-0.17
Point estimate: 0.15
Decomposition approach suggests a debt beta
value of 0.2 but regulatory precedents suggest a
range of 0.1-0.15. The point estimate chosen
was the mid-point of the range.
Debt beta range of 0.1-0.17, with upper bound
based on spot value from the decomposition
approach and lower bound based on regulatory
precedents. The point estimate of 0.15 is
consistent with 2-year trailing average debt beta
obtained from the decomposition approach.
Cost of new
debt Range: 3.35-3.83%
Point estimate: 3.60%
Range: N/A
Point estimate: 3.36%
The lower bound is based on the sum of the spot
yield for the iBoxx 10+non-financial A (2.91%),
plus the lower end of the expected rise in
interest rates (49bps) minus 15bps for
outperformance. The upper bound is based on
the spot yields for the iBoxx 10+ non-financial
BBB plus (3.14%), and the upper end of the
expected rise in interest rates (59bps). Note that
we do not make any outperformance adjustment
The point estimate is based on the spot yield of
the iBoxx non-financials 10+ A/BBB index
(3.30%) adjusted to account for expected rise in
interest rate (+31bps), minus 25bps to account
for companies’ historical outperformance against
the index.
Introduction
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EE early view EE current view
to the upper end of the range. Finally, we added
10bps to both ends to account for issuance and
liquidity costs. The point estimate is the mid-
point of the range.
Cost of
embedded
debt
Range: 4.37%-5.25%
Point estimate: 4.90%
Range: 4.25%-4.65%
Point estimate: 4.52%
The bottom end of the range is the company-
level average cost of embedded debt (based on
standard debt only, i.e. excluding exotic swaps).
The top end of the range is the 10-year trailing
average of the average 15+ index for non-
financials A/BBB iBoxx index. The mid-point is
the average cost of debt based on all debt
instruments excluding only particularly
expensive swaps and one amortising loan.
The point estimate is the 15-year trailing average
of the iBoxx average A/BBB index (forecasted up
to April 2020), minus 25bps to account for
companies’ outperformance against the index.
The bottom end of the range is the sector
weighted average cost of embedded debt (based
on companies’ balance and accounting only for
pure-debt instruments). The top end of the
range is the sector’s median cost of embedded
debt (again, based on companies’ balance and
accounting only for pure-debt instruments).
Share of new
debt Range: N/A
Point estimate: 30%
Range: N/A
Point estimate: 20%
Estimate based on Europe Economics’ analysis of
company debt data and extrapolation of RCV
growth rates from the current control period.
Estimate based on business plan submissions.
We now discuss the main drivers behind the change in parameters from our ‘early view’, distinguishing —
where possible — the extent to which such changes are attributable to changes in market data as opposed
to being driven by changes in methodology. .
Risk-free rate
Compared to Europe Economics early view the risk-free rate we recommend in this report is 19bps lower.
This difference is due to the following factors:
Increase in spot yields — gilt yields have increased since 2017: the average yield of 10-year and 20-year
nominal gilts in March 2017 (the cut-off date to determine the risk-free rate in our initial view) was 1.57
per cent, whilst the average yield of 10-year and 20-year nominal gilts in February 2019 was 1.61 per
cent. This implies that, if we were to place equal weight to 10-year and 20-year nominal gilts we would
expect an increase of around 4bps since March 2017.
Lower interest rate rise expectations — the average uplift to nominal (10-year and 20-year) gilt yields
used in 2017 was 54 bps, whilst, as of February 2019 the average expected rise in nominal across 10-year
and 20-year nominal gilts is 31bps. This implies a decrease of around 23bps since March 2017.
Evidence placed on index-linked gilts — by contrast with the approach taken by Europe Economics in
2017 we now place some weight on index-linked gilts (ILGs) as well as nominal gilts.4 In terms of basis
point, this methodological change has the same impact as our decision, in 2017, to place more weight on
the 10-year gilts (and which resulted in our point estimate being towards the lower end of the range).
4 It is perhaps worth noting that at the time of the Europe Economics 2017 study and the Ofwat Final Methodology,
the Bank of England had removed some of its index-linked gilts data for potential revision, which was a factor in our
dependence on nominal data at that time. The use of ILGs is also in line with recommendations made by the UKRN
Study which was published after Ofwat’s early view publication.
Introduction
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Therefore, compared to the overall methodology adopted in 2017, placing weight on evidence from
index-linked gilts versus the 2017 approach of using nominal bonds but placing more weight on 10 year
bonds (which had lower yields) has a 0bps impact (ie no net change) on the 2017 risk-free rate figure.
Total market return
The TMR figure we recommend in this report is 25bps lower than that recommended in Europe Economics
initial view. This reflect our assessment of a new market evidence (e.g. ex-post historical approaches, ex-
ante approaches, forward-looking approaches, and practitioners’ estimates).
Unlevered beta
Compared to the unlevered beta figure of 0.30 used in Europe Economics early view, the figure recommended
here is 0.28 i.e. 2bps lower. This change is entirely attributable to an increase in market gearing since 2017.
In fact, as we can see from Table 1.1 the raw equity beta value implied by Europe Economics in its early view
(i.e. 0.59) is lower than the one we use here (i.e. 0.62), however the market gearing has increased materially
from 49 per cent (the value in Europe Economics’ early view) to 54.7 per cent. Thus one way to think about
the reduction in the unlevered beta is that the raw beta has not risen as much as it would have done, given
the gearing rise we have seen, had the unlevered beta been stable. Hence the implication of the raw beta and
gearing shifts, together, is that the unlevered beta has fallen.
Debt beta
Compared to the debt beta figure of 0.125 used by Europe Economics in 2017, we recommend here a higher
figure of 0.15. This change is attributable to there now being a longer history of market evidence that
supports a debt beta in the range of 0.10 to 0.20.
Cost of new debt
Our recommended point estimate is approximately 24bps lower than the figure adopted by Europe
Economics in its early view. As of February 2019, the spot yield of the iBoxx A/BBB index (3.30 per cent) is
28bps higher than the yield at March 2017 (3.02 per cent). This rise is, however, more-than-offset by the
following reductions:
Issuance and liquidity cost — the cost of new debt figure of 2017 was inclusive of a 10bps uplift to account
for issuance and liquidity costs. However the cost of new debt figure we report is net of any issuance
cost allowance as this is provided as an uplift to the overall cost of debt. This is responsible for a decrease
of 10bps.
Decrease in interest rate rise expectations — this was 54bps in 2017, compared to the 31bps increase
we assume here. Thus this is responsible for a decrease of around 23bps.
Assumptions on outperformance wedge — in Europe Economics early view we adopted a conservative
assumption about companies’ ability to outperform the iBoxx index and chose an outperformance wedge
of 15bps. Furthermore we applied such wedge only to the lower end of the range (effectively decreasing
the impact of the wedge to 7.5bps) However, having conducted more extensive analysis, our view is
that an outperformance wedge of 25bps is more appropriate. This results in further reduction of 18bps.
So the net effect is +28-10-23-18 -24bps (difference due to rounding).
Cost of embedded debt
The cost of embedded debt we recommend is 38bps lower than that adopted in Europe Economics’ early
view. The difference reflects a methodological change. In this report we have based our estimate on the
historical yield (15-years average) of the iBoxx A/BBB benchmark (minus 25bps to account for companies’
outperformance) instead of the company-level sector average (based on all debt instruments excluding only
particularly expensive swaps and one amortising loan).
Introduction
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This methodological change from the early view is justified on the grounds that the sector average value
based on companies balance sheet is skewed towards the higher costs incurred by WoCs and would
therefore result in significant overcompensation for WaSCs and large WoCs. With regards to the decision
of using a 15-years trailing average, we note that around 50 per cent of embedded debt was issued over 10
years ago, and over 80 per cent of embedded debt was issued within the last 15 years. Therefore, we
consider that a 15-years trailing is representative of the sectors issuance profile and the interest costs that
prevailed at the time of issuance.
A potential issue associated with benchmarking the cost of embedded debt to an index (as opposed to
estimating it based on companies’ balance sheet) is that it does not account for the possibility of companies’
systematic outperformance or underperformance against the benchmark. For this reason, we have
conducted an assessment of companies’ outperformance/underperformance relative to the iBoxx A/BBB
index, and concluded that, on average that on average companies have outperformed the index by around
25bps.
Share of new debt
This has decreased from 30 per cent to 20 per cent as a result of more accurate data from actual company
submissions on stock and flows of new and embedded debt being made available. The data underpinning the
new share of new debt figure, was sourced directly from companies’ business plan submissions, and indicates
that averages of new-to-embedded debt ratio range between 17-22 per cent.
Overall impact of parameters changes on the WACC
We can see that the figures recommended here represent a drop from those proposed by Europe Economics
in its early view. It is of interest to account for the drivers of change. The table and figure below illustrate
what contribution of the total 28bps reduction WACC is accounted for by changes in the risk-free rate, total
market return, beta, gearing, cost of embedded debt, cost of new debt, and ratio of new debt to total debt.
The impact attributable to a particular WACC component is illustrated in the chart below and was calculated
by keeping all other WACC components at the Europe Economics’ early view level, and changing the value
of the component under consideration to the level proposed in this report.
Introduction
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Figure 1.1: Impact of parameters on the vanilla WACC
Source: Europe Economics
1.1.1 Remark on developments in the WACC evidence since the data window for this
report
The WACC estimates produced in this report, used market data up to the end of February — the data
window relevant for Ofwat’s Draft Determinations. We note that since that time there have been further
market movements, in particular a significant drop in gilt yields. There could be further market movements
before Final Determinations that either take returns down further or raise them. But, as matters stand, the
expectation should be that Final Determination figures will be lower than those presented here.
For illustrative purposes only, we provide below the evolution of gilts and unlevered beta of SVT/UU beta
since February 2019.
5.49%
5.21%
-0.02%-0.07% -0.18%
-0.02% -0.04%
-0.16%
0.09%
0.08%
0.06%
4.80%
4.90%
5.00%
5.10%
5.20%
5.30%
5.40%
5.50%
5.60%
EE (2017) RFR
impact
TMR
impact
Raw
equity
beta
impact
Market
gearing
impact
Debt beta
impact
New debt
impact
Embedded
debt
impact
Ratio of
new debt
impact
Issuance
cost
impact
EE (2019)
Introduction
- 10 -
Figure 1.2: Evolution of nominal gilts yield in 2019
Source: Thomson Reuters, Europe Economics calculations
Figure 1.3: Evolution of index-linked gilts yield in 2019
Source: Thomson Reuters, Europe Economics calculations
28-Feb-19, 1.35
28-Jun-19, 0.89
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
02-Jan-19 02-Feb-19 02-Mar-19 02-Apr-19 02-May-19 02-Jun-19
Nominal gilts yield (10yr)
28-Feb-19, -1.78
28-Jun-19, -2.42
-2.60
-2.50
-2.40
-2.30
-2.20
-2.10
-2.00
-1.90
-1.80
-1.70
02-Jan-19 02-Feb-19 02-Mar-19 02-Apr-19 02-May-19 02-Jun-19
Index-linked gilts yield (10yr)
Introduction
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Figure 1.4: Evolution of unlevered beta of SVT/UU in 2019
Source: Thomson Reuters, Europe Economics calculations
As we can see from the charts below, since February 2019, the yields on 10-year nominal gilts has decreased
by 46 bps, the yields on 10-year index-linked gilts yield has decreased by 64bps, and the value of the unlevered
beta for SVT/UU has decreased by 0.2.
In order to provide a sense of the scale of the impact that that such market changes might imply for the
WACC, we have done a back-of-the-envelope calculation to determine what the WACC would be under
the following scenarios:
A decrease in the risk-free rate of 50bps (i.e. broadly in line with the average change in yields across
nominal gilts and index-linked gilts) whilst keeping all other WACC components constant.
A decrease in the unlevered beta from 0.28 to 0.26 whilst keeping all other WACC components constant.
A simultaneous decrease in the risk-free rate of 50bps and a decrease in unlevered beta from 0.28 to
0.26, again, whilst keeping all other WACC components constant.
Table 1.3: Potential impact of changes in WACC parameters on Vanilla WACC
Change in parameter Vanilla
WACC
Change relative to our
Vanilla WACC
recommendation
Decrease in risk-free rate of 50bps 5.15% -6bps
Unlevered beta is 0.26 5.08% -13bps
Decrease in risk free rate of 50bps and unlevered beta is 0.26 5.00% -21bps
Source: Europe Economics calculations
28-Feb-19, 0.28
28-Jun-19, 0.26
0.25
0.25
0.26
0.26
0.27
0.27
0.28
0.28
0.29
0.29
01-Jan-19 01-Feb-19 01-Mar-19 01-Apr-19 01-May-19 01-Jun-19
Inflation
- 12 -
2 Inflation
In this section we consider the inflation rate it is appropriate to assume and our view of the wedges Ofwat
should assume, for the purposes of the PR19 price review, between the annual percentage rates of change in
the Consumer Prices Index including owner occupiers’ housing costs (CPIH) and in the Consumer Prices
Index (CPI), and between the annual percentage rates of change in CPI and in the Retail Prices Index (RPI).
The sum of these two wedges is the RPI-CPIH wedge.
This is of particular importance to Ofwat at PR19 because the transition to CPIH means that, from 2020,
part of the Regulatory Capital Value (RCV) will be indexed to CPIH and part to RPI. The Ofwat methodology
said that it will assume a fixed wedge above CPIH for the portion of the RCV that is indexed by RPI. This is
important for setting the real WACC that applies to that portion of the RCV.
Our real WACC (i.e. our WACC deflated by CPIH, the Office for National Statistics’ official measure of
inflation) forms the basis for our WACC calculation, with the nominal WACC being the real WACC inflated
by our CPIH assumption and the RPI-deflated WACC being derived by deflating the nominal WACC by the
RPI assumption. Hence, if we assume our real WACC is estimated correctly, if our RPI-CPIH wedge is
incorrect, that will mean our RPI-deflated WACC is either too low or too high.
As we set out below, Ofwat’s Final Methodology includes a truing-up process that will in due course correct
for any discrepancy between the actual RPI-CPIH wedge and the assumed wedge. But if the assumed wedge
is incorrect there will still be certain consequences — especially cash-flow consequences. Let us focus on the
case in which our assumed wedge is too high, so the RPI-deflated WACC, before truing up, is too low. Then
in the initial period, before truing-up, the revenues that firms receive are too low, consumers will be paying
too little, and firms’ financeability will be too weak. There may also be distortions to firms’ incentives to hold
RPI-index-linked debt versus nominal debt, with potential mis-matches between revenues and costs. The
extent of these various issues should not be exaggerated, but they do mean that it is appropriate for Ofwat
to attempt to forecast the RPI-CPIH wedge correctly even though it is committed to truing up for
discrepancies later.
2.1.1 Ofwat’s position in its Final Methodology
For the final methodology Ofwat argued that:
Over the long-term, the rate of CPI inflation can be assumed to be 2 per cent, in line with the Bank of
England’s inflation target.
CPI can be treated as roughly equivalent, over time to CPIH, with there being no obvious tendency of
one to be consistently higher than the other — so the CPI-CPIH “wedge” can be assumed to be zero.
The RPI-CPI wedge, and hence (by the above reasoning) the RPI-CPIH wedge, can be assumed to be
100bps.5
There will a truing up to take account of the actual RPI-CPIH wedge.6
5 This was supported by the Office for Budget Responsibility’s estimate. 6 See p99ff, Appendix 12 of the Final Methodology https://www.ofwat.gov.uk/wp-content/uploads/2017/12/Appendix-
12-Risk-and-return-CLEAN-12.12.2017-002.pdf.
Inflation
- 13 -
2.2 The CPI-CPIH wedge
The following graph compares CPIH and CPI over time. The left-hand panel compares the two indices. The
right-hand panel compares their annual range of change and illustrates the wedge between them.
Figure 2.1: CPIH vs CPI series (Jan 1988 = 100)
In the following table, we compare the annual rates of CPI and CPIH inflation over various time periods.
Table 2.1: Differences between CPI and CPIH inflation over various time periods
Arithmetic CAGRs
5 years -0.080% -0.082%
10 years 0.193% 0.189%
20 years 0.016% 0.014%
30 years -0.090% -0.089% Notes: The periods are up to and including December 2018. The “Arithmetic” column is the mean of the differences between the annual December
to December percentages rates of change. The “CAGRs” column is the difference between the compound average growth rates of the indices over
the time periods in each row.
Source: ONS, Europe Economics
In the 5 years to December 2018, the rate of CPIH inflation has exceeded that of CPI inflation, by 0.08
percentage points. But over the 10 years to December 2018 the opposite is true — CPI inflation has exceeded
CPIH inflation over that period. We see a similar inconsistency of pattern over longer time periods, also —
over 20 years it is CPI inflation that has been greater, whilst over 30 years it is CPIH inflation that was greater.
The difference between the two series arises from any differences between the rate of inflation in owner
occupiers’ housing costs7 and that in inflation more generally. When owner occupiers’ housing costs rise at
a faster rate than inflation more broadly, CPIH exceeds CPI, and when the opposite is true CPI inflation is
7 ONS defines owner occupiers’ housing costs as follows: “Owner occupiers’ housing costs (OOH) are the costs of housing
services associated with owning, maintaining and living in one’s own home. This is distinct from the cost of purchasing a house,
which is partly for the accumulation of wealth and partly for housing services.”
https://www.ons.gov.uk/economy/inflationandpriceindices/articles/understandingthedifferentapproachesofmeasuring
owneroccupiershousingcosts/januarytomarch2018 Thus, OOH are affected by movements in house prices only
insofar as such movements arise from changes in the cost of housing services as opposed to accumulated wealth
effects.
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
Jan-8
9
Dec-
90
Nov-
92
Oct
-94
Sep-9
6
Aug-
98
Jul-00
Jun-0
2
May
-04
Apr-
06
Mar
-08
Feb-1
0
Jan-1
2
Dec-
13
Nov-
15
Oct
-17
CPI-CPIH CPIH CPI
Inflation
- 14 -
higher. There appears to be no consistent pattern over the long-term, suggesting that a long-term assumption
about the wedge being zero is appropriate.
Given variance is low (less than 0.1 per cent for most of the series) and one series not consistently above
the other, on average, an assumption of zero wedge is the most defensible unless good evidence arises to
the contrary.
We are doubtful that such a robust basis is available. As noted above, if there were to be a short-term wedge
it would arise from deviations between the ratio of owner occupiers’ housing costs and broader inflation.
Over time, such deviations appear to be relatively low, on average (rather less than 0.1 percentage points),
and to vary through time.
This may be surprising given that it is well-known that house price inflation varies very materially from
broader inflation and that house prices are subject to significant cycles. It is worth emphasizing that, though
there is a very broad-brush relationship, the rate of growth in owner occupiers’ housing costs is (as noted
above in Footnote 7) not straightforwardly a reflection of changes in house prices. We can see that by
comparing house price inflation with the CPI-CPIH wedge, as in the figure below.
Figure 2.2: UK house price inflation versus the CPI-CPIH wedge
Source: ONS data, Europe Economics analysis
We can see that, in a very broad sense, there is a relationship in that the periods when the wedge is highest,
in the early 1990s and in the late 2000s / early 2010s, correspond roughly to the periods of the early 1990s
and 2001-2011 house price crashes. But we can also see that the wedge only went modestly negative as
house price growth accelerated in the late 1990s and indeed the wedge was frequently positive in the 2003-
2007 period despite house price growth often exceeding 10 per cent and reaching almost 30 per cent at
peak.
Nonetheless, if we foresaw a large deviation from historic norms (either up or down) in house prices over
the forthcoming review period, we might need to reflect upon the implications for the CPI-CPIH wedge (i.e.
the extent to which these might reflect changes in the cost of housing services).
As we can see from the following figure, the Office for Budget Responsibility (OBR) forecasts that house
price inflation will be a little slower than in recent years, though not dramatically so. We interpret that as
implying that expected deviations in house prices are not so dramatic that we need to review the possibility
that the short-term CPI-CPIH wedge differs from its long-term level, and hence the appropriate assumption
is zero.
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
-20%
-10%
0%
10%
20%
30%
40%
Jan-8
9
Jan-9
0
Jan-9
1
Jan-9
2
Jan-9
3
Jan-9
4
Jan-9
5
Jan-9
6
Jan-9
7
Jan-9
8
Jan-9
9
Jan-0
0
Jan-0
1
Jan-0
2
Jan-0
3
Jan-0
4
Jan-0
5
Jan-0
6
Jan-0
7
Jan-0
8
Jan-0
9
Jan-1
0
Jan-1
1
Jan-1
2
Jan-1
3
Jan-1
4
Jan-1
5
Jan-1
6
Jan-1
7
Jan-1
8
House price inflation (LH axis) CPI-CPIH wedge (RH axis)
Inflation
- 15 -
Figure 2.3: OBR forecasts for house price growth
Source: https://obr.uk/forecasts-in-depth/the-economy-forecast/housing-market/ Uploaded 3/1/2019 at 1200.
2.3 The RPI-CPI wedge
2.3.1 Evolution of the RPI-CPI wedge over time
The following graph compares the evolution of RPI and CPI over the period January 1988 to December 2018.
The left-hand panel compares the two indices over time. The right-hand panel compares their annual rate of
change and the wedge between them.
Inflation
- 16 -
Figure 2.4: RPI vs CPI series (Jan 1988 = 100)
In the following table, we compare the annual rates of RPI and CPI inflation over various time periods.
Table 2.2: Differences between RPI and CPI inflation over various time periods
RPI/CPI Arithmetic CAGRs
5 years 0.959% 0.959%
9 years 0.839% 0.840%
20 years 0.782% 0.780%
30 years 0.692% 0.691% Notes: The periods are up to and including December 2018. The “Arithmetic” column is the mean of the differences between the annual December
to December percentages rates of change. The “CAGRs” column is the difference between the compound average growth rates of the indices over
the time periods in each row.
Source: ONS, Europe Economics
We can see that over the past five years, the wedge has been just under 1 percentage point. In the second
row we compare over the past 9 years since the start of 2010, rather than 10 years, because it was in 2010
that there was the notorious change in the RPI methodology regarding the estimation of clothing inflation
that led to RPI materially accelerating relative to CPI — as indeed we can see by comparing the shorter-term
inflation periods with those further back in time.8
2.3.2 Other expectations and estimates of the long-term RPI-CPI wedge
The OBR’s forecast of the long-term RPI-CPI wedge is 1.0 per cent.9 That is actually a reduction from its
previous (2011) forecast of 1.4 percentage points. The OBR breaks down its estimate of the wedge as
follows.
Table 2.3: OBR breakdown of its RPI-CPI wedge estimate
Contribution to RPI-
CPI wedge (percentage points)
8 Looking forward, it is also likely that ONS changes to the calculation of telecoms sector prices will also mean the
wedge is higher than was the case pre-2010 — see https://www.ft.com/content/abc14c66-fb78-11e7-a492-
2c9be7f3120a 9 https://obr.uk/box/revised-assumption-for-the-long-run-wedge-between-rpi-and-cpi-inflation/
-6.0%
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
Jan-8
9
Dec-
90
Nov-
92
Oct
-94
Sep-9
6
Aug-
98
Jul-00
Jun-0
2
May
-04
Apr-
06
Mar
-08
Feb-1
0
Jan-1
2
Dec-
13
Nov-
15
Oct
-17
RPI-CPI RPI CPI
Inflation
- 17 -
Formula effect 0.9
Housing 0.5
Coverage 0.0
Weights -0.4
Total 1.0 Source: https://obr.uk/box/revised-assumption-for-the-long-run-wedge-between-rpi-and-cpi-inflation/
KPMG’s survey of pension professionals showed that the median assumption was 1.0 per cent.10 That
was from the following distribution of assumptions, illustrating that 1.1 percentage points was favoured
by a non-trivial minority.
Figure 2.5: Distribution of RPI-CPI wedge assumptions amongst KPMG survey respondents
Source: p19 of https://assets.kpmg/content/dam/kpmg/uk/pdf/2017/04/pensions-survey-2017.pdf
The Hymans Robertson IAS19 Assumptions Report of July 2018 assumes an RPI-CPI wedge of 1.0
percentage points11, as does the presentation of Prof Wass of September 2018 on the indexation of
periodical payments for care.12
The 1.0 percentage point wedge figure has also become standard in financial markets commentary.13
2.3.3 Our interpretation of the longer-term RPI-CPI wedge
Noting that the wedge appears to have risen to just under 1 percentage point over the past five years, that
the OBR estimates the long-term wedge at about 1 percentage point, that that is also the median view of
KPMG survey respondents, standard in other analyses of pensions and cost indexation, and standard in
financial markets commentary, our view is that 1.0 percentage points is an appropriate long-term assumption.
In principle, there could be some deviation from this assumption over shorter time periods such as the period
of a price control. But as with the CPI-CPIH wedge, the best assumption for the wedge may well be that
10 https://assets.kpmg/content/dam/kpmg/uk/pdf/2017/04/pensions-survey-2017.pdf 11 https://www.hymans.co.uk/media/uploads/180629_2_IAS19_Pensions_Assumption_Report_final.pdf 12 https://ampersandadvocates.com/wp-content/uploads/2018/09/Victoria-Wass-Indexation-of-Periodical-Payments-
for-Care.pdf 13 For some examples, see:
https://www.ftadviser.com/pensions/2018/06/26/first-cpi-linked-bonds-bring-hope-for-pension-schemes/
https://www.bondvigilantes.com/blog/2019/01/18/war-indices-inflation-measure-use/
Inflation
- 18 -
long-term level, with any deviation from that assumption requiring quite a robust evidential basis. In the case
of the RPI-CPI wedge it is arguable that, given the nature of the drivers of the wedge (as we discuss below)
there could be more cyclicality, so that it could more often be appropriate to consider the possibility of a
short-term deviation here than was the case for the CPI-CPIH wedge — for example in a period in which
mortgage interest rates were expected to be well above the historic norm of recent years, or in which house
prices were expected to crash.
2.3.4 Factors affecting the wedge in the shorter-term
In the RPI, housing costs include housing depreciation (which changes with house prices) and the costs of
servicing mortgages (which change with mortgage interest rates), neither of which appears in CPI. Hence, the
key factors affecting short- to medium-term deviations in the RPI-CPI wedge from its long-term average are
movements in house prices and in interest rates.
We note that house price movements feed more directly into the RPI-CPI wedge than into the CPI-CPIH
wedge, through the impact of house prices on housing depreciation and on mortgage interest payments. We
can see that effect if we compare the RPI-CPI wedge to changes in house prices.
Figure 2.6: House prices vs the RPI-CPI wedge
Source: ONS data, Europe Economics analysis
The correlation has been particularly close in recent years when there were not movements in interest rates
creating an additional factor, but similarities of pattern are visible in earlier periods, also.
2.3.5 House price movements over the forthcoming price control period.
As noted in the previous section, house prices are expected to grow more slowly over that period than in
recent years, as we have seen from the OBR’s latest forecast, which would tend to reduce the wedge relative
to that of recent years, but perhaps only modestly.
On the other hand, the OBR expects interest rates to rise, which would tend to imply a higher wedge than
in recent years. This effect could be larger than the house price effect itself.
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
-20%
-10%
0%
10%
20%
30%
40%
Jan-8
9
Jan-9
0
Jan-9
1
Jan-9
2
Jan-9
3
Jan-9
4
Jan-9
5
Jan-9
6
Jan-9
7
Jan-9
8
Jan-9
9
Jan-0
0
Jan-0
1
Jan-0
2
Jan-0
3
Jan-0
4
Jan-0
5
Jan-0
6
Jan-0
7
Jan-0
8
Jan-0
9
Jan-1
0
Jan-1
1
Jan-1
2
Jan-1
3
Jan-1
4
Jan-1
5
Jan-1
6
Jan-1
7
Jan-1
8
House price inflation (LH axis) RPI-CPI wedge (RH axis)
Inflation
- 19 -
Figure 2.7: OBR expectations for movements in Bank Rate
Source: Chart 3.7, https://obr.uk/download/economic-and-fiscal-outlook-october-2018/
The OBR forecast wedge, from its October 2018 Economic and Fiscal Outlook (Table 3.10) is as follows:
2018 2019 2020 2021 2022 2023
CPI 2.6 2 2 2.1 2.1 2
RPI 3.5 3.1 3.1 3.2 3.1 3.1
Wedge 0.9 1.1 1.1 1.1 1 1.1
The compound average wedge over this period is 1.05 per cent. For the four-year period 2020-2023 (2019
base), the forecast average is 1.075 per cent.
Our interpretation of this evidence is that there could be a case for a shorter-term wedge assumption slightly
above the long-term level of 1.0 (perhaps in line with the OBR’s forecast), but not as high as 1.1 percentage
points. In the context of Ofwat’s truing approach we suggest that such a modest variation is probably
unnecessary and that the long-term assumption of 1.0 percentage points is sufficient.
2.4 Overall conclusion
It continues to be the case that over the long-term, the rate of CPI inflation can be assumed to be 2 per cent,
in line with the Bank of England’s inflation target. Given that we have argued that the CPI-CPIH wedge should
be assumed to be zero, that implies that CPIH inflation should be assumed to be 2.0 per cent. Given that we
have argued that the RPI-CPI wedge should be considered to be 1.0 per cent, that implies that RPI inflation
should be assumed to be 3.0 per cent.
The risk-free rate
- 20 -
3 The risk-free rate
3.1 Introduction
This section provides our view on the appropriate risk-free rate to be used in PR19. The section is structured
as follows:
In Section 3.2 we present market evidence on nominal gilts and index-linked gilts.
In Section 3.3 we provide a recommendation as to which instrument is more relevant when assessing
the risk-free rate of return.
In section 3.4 we set out our approach to infer the market implied rate change over AMP7.
We conclude in Section 3.5 with our recommended range and point estimate for the risk-free rate.
3.2 Market evidence of nominal gilts and index-linked gilts
The evolution of 10-year and 20-year nominal gilts and 10-year and 20-year index-linked gilts since 2010 (i.e.
after the significant market turbulence caused by the great financial crisis of 2008/09) is presented in Error!
Reference source not found.
Figure 3.1: 10-year and 20-year nominal gilt yields
Source: Thomson Reuters, Europe Economics’ calculations.
0.00
1.00
2.00
3.00
4.00
5.00
6.00
Nominal gilts yield (10yr) Nominal gilts yield (20yr)
The risk-free rate
- 21 -
Figure 3.2: 10-year and 20-year index-linked gilt yields
Source: Thomson Reuters, Europe Economics’ calculations.
We can see that yields have decreased considerably since 2010, with both 10-year and 20-year index-linked
gilts yields being consistently negative since mid-2014. Since January 2017, the interest rates on gilts have
been relatively stable. The spot values of gilts yield at 28-February-2019 together with the trailing averages
for the previous three months and six months are reported in the table below.
Table 3.1: Summary of evidence on gilts
Instrument Spot at 28-
February-2019
Trailing average
(previous 3
months)
Trailing average
(previous 6
months)
Nominal gilts yield (10yr) 1.35% 1.28% 1.40%
Nominal gilts yield (20yr) 1.88% 1.82% 1.91%
Nominal gilts yield (average 10yr & 20yr) 1.61% 1.55% 1.65%
Index-linked gilts yield (10yr) -1.78% -2.06% -1.92%
Index-linked gilts yield (20yr) -1.62% -1.80% -1.69%
Index-linked l gilts yield (average 10yr & 20yr) -1.70% -1.93% -1.80%
Source: Thomson Reuters, Europe Economics’ calculations.
3.3 Is it better to base “observable asset” estimates of the risk-free rate on
nominal gilts or RPI-index-linked gilts?
In our 2017 study, Europe Economics used nominal gilts as the basis for what we term the “observable asset”
approach to estimating a risk-free rate of return.14 At the time of the 2017 report, data availability limitations
14 We contrast two kinds of approach to risk-free rate estimation. In one, the risk-free rate (and indeed the cost of
capital more generally) is regarded as a discount rate or other such parameter that is a feature of economic market
equilibrium. There may or may not be any single asset in the economy at any point in time that has a return of or
close to the risk-free rate. Rather, the risk-free rate is to be regarded as a parameter akin to the “sustainable growth
rate” or the “output gap” — an equilibrium parameter that economic data can be used to infer but which may not
be directly observable. In the UK regulators such as Ofcom take this “equilibrium parameter” approach to the risk-
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
Index-linked gilt yield (10yr) Index-linked gilts yield (20yr)
The risk-free rate
- 22 -
meant that only the zero-coupon nominal gilts series was feasible.15 In its 2018 study, the academic study on
cost of capital for regulators through UKRN16 (which we will refer to as URKN Study) recommended the
use of RPI index-linked gilts (ILGs)17, which is also the approach Europe Economics has adopted in a number
of previous WACC studies.18
A further argument for using RPI-linked bonds has been advanced in previous price controls where RCV
indexation and pricing indexation were based upon the RPI, namely that the use of RPI bonds was the natural
counterpart to the use of RPI in the control — so even if RPI inflation and RPI-indexed yields were distorted,
the effects of such distortions might cancel out across the control. We shall not consider the merits of that
case in detail, but note that in any event the argument is weaker in PR19, given that the control is partially
on a CPIH basis.
Outwith a price regulation context, if there were a CPIH-linked (or even CPI-linked) gilts series, we would
certainly favour its use for estimating real yields. The case for using RPI-linked gilts to estimate an RPI-
discounted yield, as versus using nominal gilts to estimate a nominal yield, is less straightforward. In the past
we certainly would have favoured the use of RPI-linked gilts (and indeed did use such gilts in many regulatory
WACC analyses). As RPI diverges more and more from CPIH and does so in ways that have not been stable
over time (as was discussed at length in our 2017 report), the case for placing sole reliance upon RPI-linked
gilts as versus nominal gilts, has become weaker.
The approach we adopt here is to use both nominal and RPI-linked gilts to generate a range. We do not
consider that there is a strong basis for favouring either the nominal or RPI-linked ends of that range, and we
recognise that UKRN Study recommends the use of ILGs. Nonetheless, we have a mild preference for the
nominal gilts at the shorter end of the horizon where, given how entrenched inflation targeting is as a
framework, it seems both unlikely to us that there will be large systematic deviations of inflation from target
(limited systematic risk) and that it is more consistent with the overall assumption that CPIH inflation will be
2 per cent and the RPI-CPIH wedge will be 1 per cent (hence that RPI inflation will be 3 per cent) that, in
fact, we use the 2 per cent assumption (in combination with the nominal yield) rather than using some other
assumption implicit in market yields.19 For the longer horizon, we acknowledge that there is at least some
tail risk of larger inflation deviations (e.g. associated with a switch away from inflation targeting) and we adopt
the expedient of taking the simple average of the (CPIH-deflated) nominal and (RPI-CPIH wedge-inflated) ILG
free rate, assuming that the best means to estimate the equilibrium value of the risk-free rate is as an average that
the yields on gilts will tend to cycle around, over time. Across Europe, many other regulators (e.g. those following
the advice of the Body of European Regulators for Electronic Communications, BEREC) take this same version of
the equilibrium parameter approach, using long-term average to estimate the risk-free rate. In Ireland and France,
some regulators that take the equilibrium parameter approach do not use averages to estimate its value, but instead
use macroeconomic forecasts plus models of the relationship between medium-term economic growth and the risk-
free rate.
The form of equilibrium parameter approach that is based on long-run averages was strongly criticised by the UKRN
Study and Ofwat, Ofgem and the CAA now favour an approach that treats the risk-free rate as an observable spot
(or quasi-spot) yield on a risk-free or near-risk-free asset, government bonds. We term this the “observable asset”
approach. The pros and cons of these two approaches were debated at length in our 2017 report and we do not
rehearse the arguments here. 15 The Bank of England had suspended and withdrawn certain of its index-linked yields data series and we understood
that there was some risk of figures being revised. 16 See http://www.ukrn.org.uk/wp-content/uploads/2018/03/2018-CoE-Study.pdf 17 “Estimating the cost of capital for implementation of price controls by UK Regulators” (2018) available at
https://www.ukrn.org.uk/estimating-the-cost-of-capital-for-implementation-of-price-controls-by-uk-regulators/,
especially Section D. 18 e.g. see http://www.europe-economics.com/publications/20100204eecostcapital.pdf esp paragraph 2.31. 19 If we assumed there were no distortions in ILG yields and that the inflation risk premium is nugatory, the wedge
between ILGs and nominal bonds would imply that inflation is materially higher than 3 per cent at between the 10
and 20 years horizons.
The risk-free rate
- 23 -
yield at the 20 year horizon. Hence, overall we use a range from the (CPIH-deflated) nominal yields to the
(RPI-CPIH wedge-inflated) ILG yields, and our point estimate is derived in the following way.
Use nominal gilts at the 10 year horizon
Use an average of real yields obtained from nominal and index-linked gilts at the 20 year horizon.
Take the average of the first two steps as a 15 year risk-free rate.
We freely acknowledge that other judgements are possible.20
3.4 Market-implied rate change in AMP7
To determine future movements in the risk free rate we can make use of the yields on different maturity gilts
so as to estimate the forward rates for relevant length gilts. The forward rate captures the implied future
yield on an investment made in a certain number of years’ time. In this case, we are interested in the yield on
10-year and 20-year year gilts arising from investments made during the AMP7 period, or more specifically:
At the beginning of AMP7, i.e. April 2020.
In the middle of AMP7, i.e. October 2022.
At the end of AMP7, i.e. April 2025.
The forward rates are calculated using the following formula:
𝑓𝑡.𝑇 = ((1 + 𝑟𝑇)𝑇
(1 + 𝑟𝑡)𝑡 )
1𝑇−𝑡
− 1
where t is the time from present to the date at which the risk-free rate is being estimated (eg three years),
and T is that timeframe plus the duration of the gilts of interest (e.g. for a ten year gilt, T = 3 + 10 = 13). Thus
in the case of the forward rate for a ten-year gilt, the formula solves for the forward rate (𝑓𝑡.𝑇) that would
equalise the yield (𝑟𝑡) on a gilt taken out today with three years to maturity (and then reinvested in a gilt, in
three years’ time, with ten years to maturity), and the yield (𝑟𝑇) on a gilt taken out today with thirteen years
to maturity.
To account for any potential day-to-day volatility, we consider data over a predetermined period, namely
one month of daily data. We then analyse the average spot yield for gilts with time to maturities of 3, 13 and
23 years, thus enabling the estimation of forward rates for 10 and 20 year gilts three years ahead of that
period. One can then either use those rates directly or estimate changes relative to spot rates now.
We have used the Bank of England daily spot rates for February 2019 and used the formula above to
determine the forward rates at the beginning, in the middle and at the end of AMP7. We have then used the
forward rates to determine the average market implied change in rates relative to the daily spot rates of
February 2019. These are reported in the table below.
20 For example, if the risk-free rate estimate was based entirely on 10-years ILGs (and the market-implied rate change
on these gilts), the nominal risk-free rate figure we would obtain is 1.5 per cent, as opposed to the nominal risk-free
rate figure of 1.81 that — as we shall see at the end of this Section — we obtain under our preferred approach. A
nominal risk-free rate of 1.5 per cent would result in an overall WACC figure which is 4bps lower than the one we
recommend here (i.e. a nominal 5.17 per cent WACC of as opposed to 5.21 per cent).
The risk-free rate
- 24 -
Table 3.2: Market implied rate change for 10yr and 20yr nominal gilts, February 2019
Nominal(10yr) Nominal(20yr)
Average
10yr &
20yr
nominal
Implied
change in
Apr-2020
Implied
change in
Oct-2022
Implied
change in
Apr-2025
Average
across
AMP7
Implied
change in
Apr-2020
Implied
change in
Oct-2022
Implied
change in
Apr-2025
Average
across
AMP7
Average
across
AMP7
Average 0.13 0.49 0.79 0.47 -0.08 0.18 0.31 0.14 0.31
Max 0.48 0.14 0.31
Min 0.46 0.13 0.30
Source: Bank of England, Europe Economics’ calculations.
Table 3.3: Market implied rate change for 10yr and 20yr index-linked gilts, February 2019
ILG (10yr) ILG (20yr)
Average
10yr &
20yr
ILGl
Implied
change
in Apr-
2020
Implied
change
in Oct-
2022
Implied
change
in Apr-
2025
Average
across
AMP7
Implied
change
in Apr-
2020
Implied
change
in Oct-
2022
Implied
change
in Apr-
2025
Average
across
AMP7
Average
across
AMP7
Average 0.28 0.36 0.32 0.21 0.28 0.24 0.28
Max 0.35 0.26 0.31
Min 0.26 0.21 0.24
Source: Bank of England, Europe Economics’ calculations.
As we can see from Table 3.2 in February 2019, the average market implied rate increase across the AMP7
period for (average) 10-year and 20-year nominal gilts was 31bps with the highest increase recorded in that
month being also 31bps, and the lowest being 30bps.
Since the Bank of England’s forward rate curves data for index-linked gilts is more limited,21 for index-linked
gilts the average rate increase across the AMP7 period is calculated considering only the middle and the end
of AMP7. For the (average) 10-year and 20-year index-line gilts, the average rate increase implied by February
2019 data was 28bps, the maximum rate increase was 31bps, and the minimum rate increase was 24bps.
Perhaps the most striking difference between the implied changes for the two series is that for the index-
linked gilts the likely path for 10 year and 20 year bonds is more similar than for nominal bonds. So, for
example, by October 2022 10 year ILGs are expected to rise 28bps and 20 year ILGs by 21bps, whereas 10
year nominal gilts are expected to rise 49bps versus just 18bps for 10 year nominal gilts. Could we, perhaps,
infer which of these series appears more likely to be distorted from this?
To answer that question, we need to begin by understanding what a rise in yields implies for these different
series. Both 10 and 20 year gilts already embody assumptions about changes in interest rates over the next
10 and 20 years. If 10 year gilts have higher implied yields in 3 years’ time than today, that implies that interest
rates between 3 and 13 years ahead are expected to be higher than interest rates between 0 and 10 years
ahead, or to express the same point another way, that average rates between 10 and 13 years ahead are
expected to be higher than average rates between 0 and 3 years ahead. Similarly, if yields on 20 year bonds
21 The data provide rates for bonds with at least four years of maturity, hence we cannot use the forward rate formula
to calculate the market implied rate for April 2020.
The risk-free rate
- 25 -
are expected to rise over the next three years, than implies that average rates between 20 and 23 years
ahead are expected to be higher than average rates between 0 and 3 years ahead.
But now suppose that, within the next ten years, interest rates are expected to reach a “normal” level, that
they then sustain indefinitely thereafter. In that case we would expect interest rates between 10 and 13 years
ahead to be about the same as those between 20 and 23 years ahead. The implication of that, in turn, would
be that the rise in 20 year gilt yields should only be around half that of the rise in 10 year gilts. We can see
why with a concrete example.
Suppose that yields on 10 year gilts were simply the product of yields on 1 year gilts for each of the next 10
years (and similarly with 20 year gilts). And suppose that yields were currently 0.5 per cent, and expected to
rise 0.5 per cent each year until they reached 3.5 per cent, whereafter they were constant forever. Then
yields on 10 year bonds would currently be 2.75 per cent and yields on 20 year bonds would currently be
3.12 per cent. But yields on 10 year bonds would be expected to rise over the next three years to 3.35 per
cent — a rise of 60bps. Yet yields on 20 year bonds would be expected to rise by just 30bps, to 3.42 per
cent. The effect of the rise in rates over the next few years is spread over twice as many years for 20 year
as 10 year gilts, so the impact should be half as much, under the assumption that a long-term average is
reached within the next ten years.
In order for the rise in the 10 year bond to match that in the 20 year bond, we would need a different
assumption. For example, suppose that one-year bond yields were expected to rise by half a per cent for
each of the next 23 years. Then 10 year bonds would currently be 3.24 per cent and expected to rise to 4.74
per cent over the next three years (a rise of 150bps), whilst 20 year bonds would currently yield 5.71 per
cent and be expected to rise to 7.21 per cent over the next three years (again, a rise of 150bps).
When we compare the paths for nominal and index-linked gilts, we see that each lies somewhere between
these two kinds of cases. At 49 bps in 3 years for 10 year gilts versus 18bps for 20 year gilts, the nominal
series seems, if anything, to imply that short-term gilt yields will fall back a little, somewhere between 10 and
20 years ahead, relative to their level after 10 years. By contrast at 28 bps in 3 years for 10 year gilts versus
21bps for 20 year gilts, the index-linked series seems to imply that short-term gilt yields will continue to rise,
a little, beyond 10 years ahead.
One possibility here, that might help to explain the difference, could be that investors expect that distortions
associated with the RPI series, relative to the CPI, will change in the medium-term future, distorting ILG
yields upwards even as undistorted real gilt yields fell back, slightly.
3.5 Conclusions on the risk-free rate
Table 3.4: Summary of evidence on risk-free rate
Spot yield at
28-Feb-2019
Market
implied rate
change in
AMP7
Risk-free rate
(Nominal /
RPI-linked)
Nominal risk-
free rate
CPI-deflated
risk-free rate
Nominal 10yr 1.35% 0.47% 1.82% 1.82% -0.18%
Nominal 20yr 1.88% 0.14% 2.02% 2.02% 0.02%
Average Nominal 1.62% 0.31% 1.92% 1.92% -0.08%
RPI-linked 10yr -1.78% 0.32% -1.46% 1.50% -0.49%
RPI-linked 20yr -1.62% 0.24% -1.38% 1.58% -0.41%
Average RPI-linked -1.70% 0.28% -1.42% 1.54% -0.45%
Source: Bank of England, Thomson Reuters and Europe Economics’ calculations.
The risk-free rate
- 26 -
Based on the evidence presented above the nominal risk-free rate we recommend is 1.54 (based on index-
linked gilts) and 1.92 per cent (based on nominal gilts), which corresponds to a range of -0.45 to -0.08 per
cent in CPI-deflated terms.
For our preferred point estimate we suggest the following methodology:
Use nominal gilts at the 10 year horizon. This gives a (nominal) value of 1.82 per cent
Use an average between 20-year nominal gilts (2.02 per cent) and 20-year ILGs (1.58 per cent). This
gives a value of 1.80 per cent
Take the average of the first two steps. This results in a nominal value of 1.81 per cent, and -0.19 per
cent in CPI-deflated terms.
Therefore our recommendation is as follows:
A nominal risk-free rate range of 1.54-1.92 per cent, with a point estimate of 1.81 per cent.
A CPI-deflated risk-free rate range of -0.45 to -0.08 per cent, with a point estimate of -0.19
per cent.
Total Market Return
- 27 -
4 Total Market Return
4.1 Introduction
This section sets out our view on the appropriate Total Market Return (TMR) value to be used in PR19. The
section is structured as follows:
In Section 4.2 we provide an overview of the different approached that can be used to estimate the TMR.
In Section 4.3 we presents TMR estimates obtained under the historical “ex-post” approach.
In Section 4.4 we presents TMR estimates obtained under the adjusted historical “ex-ante” approach.
In Section 4.5 we provide an overview of TMR estimates sourced from finance professionals and
practitioners.
In Section 4.6 we present the result of our dividend growth (DGM) model and dividend discount model
(DDM).
Section 4.7 provides our TMR recommendation.
4.2 The TMR and the alternative approaches available for its estimation
The Total Market Return (TMR) is the return that would be delivered by a notional perfectly diversified
portfolio consisting of all assets (“the whole market”). The Market Risk Premium (MRP) is the difference
between the TMR and the risk-free rate. The usual proxy for the TMR is the Total Equity Market Return and
the usual proxy for the Market Risk Premium is the Equity Risk Premium (ERP).
One important decision in TMR analysis is whether it should be assumed that the TMR is more stable or the
ERP is more stable. When fluctuations in the risk-free rate were small, it was often assumed that fluctuations
in the ERP tended to offset risk-free rate fluctuations, such that the TMR was more stable than its
components. When movements in the risk-free rate became larger, from the late 2000s onwards, there was
a period of assuming that the ERP should be considered fairly constant over time (perhaps subject to some
temporary and specific upwards adjustment in periods of recession) with the TMR varying largely in line the
risk-free rate. Some regulators around Europe continue to take the view that the ERP should be considered
stable over time, even when movements in the risk-free rate are large.22 By contrast, a number of UK
regulators have taken the approach of estimating the TMR directly on the basis that the ERP and the risk-
free rate have an inverse relationship, and therefore are more volatile over time than TMR. The TMR can
be estimated on the basis of a range of approaches.
In its early view Ofwat grouped such approaches into three board categories:
“Ex-post” approaches – TMRs are derived from long-run averages of historically realised equity returns
which are then used as a proxy for expected future returns (treating past returns as a proxy distribution
of possible future returns), potentially adjusted upwards in periods of recession and downwards in non-
recession periods.23
“Ex-ante” approaches – these approaches attempt to decompose data on historically realised equity
returns into investor expectations of return and returns that are related to non-repeatable (i.e. “good
luck” or “bad luck”) events.
22 For example, this is the stance adopted by BEREC. 23 See https://www.bankofengland.co.uk/-/media/boe/files/working-paper/2009/why-do-risk-premia-vary-over-time-a-
theoretical-investigation-under.pdf
Total Market Return
- 28 -
“Forward-looking” approaches – these approaches use recent market data to estimate a forward-looking
TMR (e.g. though the use of dividend discount and dividend growth models (DDM and DGM)), or use
finance practitioners’ surveys and forecasts.
We present below the main evidence for each of the approaches listed above.
4.3 Ex-post approaches to the TMR
A commonly quoted source for long-term historic market returns is the analysis published by Dimson, Marsh,
and Staunton (DMS) in the Credit Suisse Global Investment Returns Yearbook24, which provides returns
figures based on over a century of annual data25.
The rationale for using this long time period (as long a time period as possible) is that it maximises the amount
of information available on which to form a forward-looking estimate, i.e. expectation, about future market
returns. The benefit of having as much information as possible is that the total market return, by definition,
includes risky assets, and therefore the actual outturn in any one year is a poor indicator of expected returns
in the future. By the same logic, even a sample of returns over one or two decades may provide a relatively
inaccurate estimate of expected future market returns.
There are various ways that historic data could be used to form a view about the future. Two particularly
important ones are the following.
Using past returns (perhaps adjusted in various ways) to inform a model of the distribution of future
returns. We might term this a “sample distribution” approach.
Using some form of average of past returns to inform a view as to what a reasonable average expectation
might be for the future, for example if an investor deployed “adaptive expectations”.
Each of these approaches is sometimes termed a “historical ex-post approach”, but that is arguably better as
a term when applied to the adaptive expectations variant than to the sample distribution form. Let us consider
the sample distribution approach first, then the adaptive expectations variant.
When we are using very long-run series of returns in the sample distribution approach, we aim to capture a
significant portion of the total probability distribution of returns that an investor today might account for in
decisions about the future. The approach does not “look backwards”. Instead what is happening is that the
approach makes use of historical data as a basis for estimating the future. In effect, we are treating each
historical data point as an independent, random draw from the probability distribution of returns. (This is in
line with the assumption of weak market efficiency26 which underlies the CAPM, which implies that returns
24 The latest publication is the Credit Suisse Global Investment Returns Yearbook (2019). Another, albeit somewhat
less frequently used, source is the Barclays Equity Gilt Study. We note the results from this alternative source below. 25 The 2019 edition of the Credit Suisse Global Investment Returns Yearbook provides returns data for the period
1900-2018. 26 A market is defined as “weakly efficient” if past price and volume movements do not predict future movements, with
the consequence that stock price movements are completely independent of each other, and hence processes such
as price momentum (future price movements tending to be in the same direction as past price movements) or mean
reversion (future price movements tending to be in the opposite direction to past price movements) do not exist.
The corporate finance theory underlying the Capital Asset Pricing Model assumes that markets are what is called
“weakly efficient”. A consequence of markets achieving weak efficiency is that so-called “technical analysis”,
attempting to identify and then trade from patterns in pricing data, cannot be effective. Since highly elaborate
arbitrage pricing systems, operating at very frequency, devote considerable resources to trading from technical
patterns and arbitrage opportunities, it seems likely that market inefficiencies exist at the timescales upon which they
operate (often markedly less than a second). On the other hand, precisely because such systems exist, it is also likely
that they arbitrage away weak market inefficiencies if given sufficient time to do so, so that markets eventually must
become weakly efficient, at least to the scale at which remaining anomalies are so low as to be impossible to make
money by trading against. If weak market inefficiencies persisted over all timescales that would imply that markets
fail to find and exploit enduring opportunities for infinite near-riskless returns, which seems implausible.
Total Market Return
- 29 -
in different time periods will not be serially correlated.) Thus, assuming the future distribution of potential
returns is the same as in the past (an assumption which is inherent in using ex post returns to estimate the
TMR, but which we shall challenge below), then the larger the sample of independent draws from an identical
distribution (i.e. historical data points) that we have, the more accurate a model we can form of the true
underlying distribution, which can in turn be used to model the future.
When using historical data in this “sample distribution” way to create a proxy sample distribution for
expected future returns, the unambiguously correct way to calculate the single-period expected return from
past data, when it is used to construct a probability distribution of the future (we consider possible alternative
uses of that data below), is by using the arithmetic mean (rather than the geometric mean), since the expected
return of a given probability distribution is the arithmetic mean. The use of geometric averaging would be
straightforwardly inconsistent with the concept we have set out for how historical data are being used — i.e.
as a sample from which to construct a distribution of possible future out-turns.27
If, on the other hand, we are using the adaptive expectations approach, it is less clear whether the arithmetic
or geometric mean should be preferred. Some analysts use historical data as a basis for producing a broad-
brush average for past equity returns to inform adaptive expectations about future equity returns — so
investors are taken as, in some sense, assuming that future returns will match those in the past, adapting that
expectation as past returns change. If agents are simply applying a future expectation that matches past
performance, the question becomes: past performance by what measure? That could be the geometric mean.
It could be the arithmetic mean. It could be something in between, or above or below either. The best way
to use historic data to form an adaptive expectation will be a matter of evidence (eg on what past measures
have best predicted future returns) and judgement.28
Many regulators and competition authorities have placed some weight upon geometric means, including in
particular the Competition Commission. In particular the Competition Commission argued in 2007 and 2008
that neither the arithmetic nor geometric mean is likely to provide “a good guide to what will happen in the
future”.29 The reasoning it offered was as follows.
“The reason for this is that one tends to have data only from a sample of observations and does not know the
underlying distribution from which these observations are drawn. If one assumes that Rm is drawn from a normal
distribution with mean μ and variance σ2, it can be shown that the arithmetic mean return from a sample of
historical annual data is an unbiased estimator of Rm after one year. However, after N years the arithmetic
mean is biased upwards (ie it overstates the expected value of Rm after N years), while the geometric mean is
biased downwards for so long as N<T.
“If one further allows for the possibility that stock market returns in any given year are not independently
distributed, and in particular for negative serial correlation or mean reversion over time, it can also be shown
that the upward bias in the arithmetic average grows still further.
27 Even if one believed that holding periods were longer than one year, the correct calculation would be to take the
arithmetic average of the geometric average across holding periods. So if holding periods were two years and one
had a century of data, the answer would be to take fifty two-year period returns, then take the arithmetic average
of that set of fifty points. That the arithmetic mean is the correct concept is simply a mathematical point about how
an expected value is obtained from a sample distribution rather than any point of debate in finance theory. 28 Indeed, in some cases even the geometric average will overstate the return. For example, Jacquier E., Kane A. &
Markus A.J. (2005) (“Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of
Compounded Estimation Risk”, Journal of Financial Econometrics, 3(1), pp37–55.) argue that both the arithmetic and
geometric measures are biased estimates and that even the geometric average will overstate expected returns if the
investment horizon is sufficiently long relative to the historical period considered (specifically, if the horizon is more
than a third of the historical period). 29 See Annex 2, page L31 of https://webarchive.nationalarchives.gov.uk/20140403005111/http:/www.competition-
commission.org.uk/assets/competitioncommission/docs/pdf/non-inquiry/rep_pub/reports/2008/fulltext/539al.pdf
Total Market Return
- 30 -
“This means that the expected return on the market portfolio over the longer run (ie the sort of timescale in
which we are interested when setting price limits for a regulated company) will lie somewhere between the
arithmetic mean and the geometric mean obtained from historical data. Different experts have different views
on which of the two measures is the least biased or, alternatively, how the arithmetic and geometric means
should be weighted. Because there is no obvious consensus on the matter, we did not seek to prefer one type
of Rm estimate over another but instead took account of both arithmetic and geometric means in our cost of
equity calculation.”
We present in Table 4.1 below the average historical real TMR (real returns on equities) for different
geographies and averaging methods (geometric and arithmetic). These results are based on long-run historical
returns data from 1900 to 2017, and, are CPI-deflated.
Table 4.1: Real (NB CPI-deflated) TMR estimates by geography and by averaging method, based on data
1900 to 2018
Geometric mean Arithmetic mean
UK 5.4 7.2
Europe 4.2 6.0
World 5.0 6.5
Source: Dimson, Marsh and Staunton (2019), “Credit Suisse Global Investment Returns Yearbook 2019”.
We can see here that historical arithmetic means for Europe and the World lie in the region of 6.0-6.5 per
cent. With the UK capital market being increasingly heavily integrated into world markets, so the UK market
is becoming more like a part of a world capital market rather than a segmented market on its own, we should
expect convergence between the UK and world return over time, meaning that it is arguable that the World
figure might provide a better forwards-looking view than the UK figure.
It is important to stress that the “real” TMR returns of Table 4.1 are deflated on the basis of measures of
consumer prices. They are not RPI-deflated. However, they are not exactly the same as the CPI series,
either.
The following graph compares inflation between 1900 and 2018 under the DMS inflation series (which uses
the Cost of Living Index (COLI) up to 1949, ONS’s backcast measure of CPI since 1949, and CPI from 1988
onwards) with the inflation series produced by the Bank of England in its “Millennium dataset” (which uses
ONS’s Consumption Expenditure Deflator (CED) up to 1949, the ONS’s backcast measure of CPI since
1949, and CPI from 1988 onwards).30
30 This is the ‘original’ version of the Millennium dataset series. There is also a Millennium dataset ‘preferred’ CPI
inflation: This is the same as the ‘original’ Millenimum dataset apart from the period 1900-1914, which replaces the
O’Donoghue et al. (2004) series with a series from a paper by Feinstein (1991). The distinctions between the ‘original’
and ‘preferred” series are not relevant to us for our purposes here.
Total Market Return
- 31 -
Figure 4.1: Comparison of DMS and Bank of England Millennium dataset inflation series
Source: Ofwat analysis of Bank of England, Credit Suisse Equity Returns Yearbook 2019 data
We see that there are some distinctions between these series. For example the DMS series assumes more
deflation in certain years in the 1920s and less inflation in the 1940s, but more inflation in certain years in the
1950s and 1970s. Overall, for the purpose of obtain a CPI-deflated figures, both inflation series are
appropriate. We note that the ONS has expressed a preference for the CED over the COLI, because the
latter has relatively more limited coverage in terms of both products and population and because there are
some concerns about the quality of the weights. That would tend to favour the BoE’s CPI series based on
the “Millennium dataset”.31
For the sake of comprehensiveness, we have calculated “real” UK TMR figures based on the two alternative
inflation measures (the DMS series and the BoE’s ‘original’ CPI series). TMR estimates have been calculated
also under different assumptions concerning the investment holding period (e.g. 1-year, 5-year holding period,
etc.), and under two different averaging methods (arithmetic mean and geometric mean). These are reported
below
Table 4.2: Historical TMR estimates based on DMS annual data32 (1899-2018)
Holding period BoE original CPI series DMS inflation series
Arithmetic mean Geometric mean Arithmetic mean Geometric mean
1-year 6.89% 5.14% 7.25% 5.44%
5-year 6.77% 5.34% 7.06% 5.65%
10-year 6.72% 5.39% 7.00% 5.71%
15-year 6.85% 5.48% 7.12% 5.83%
20-year 6.81% 5.71% 7.08% 6.10%
Min. 6.72% 5.14% 7.00% 5.44%
Max. 6.89% 5.71% 7.25% 6.10%
Source: 2019 Credit Suisse Equity Returns Yearbook and Bank of England data, Ofwat and Europe Economics calculations
We can see from the table above that (depending on the investment horizon chosen), the real TMR estimates
based on the arithmetic mean range between 7.00-7.25 per cent under the DMS inflation series, and 6.72-
31 Office for National Statistics, ‘Consumer Price Indices Technical Manual, 2007 edition’, p73 32 Source: Credit Suisse Global Investment Returns Yearbook (2019), ONS
Total Market Return
- 32 -
6.89 per cent under the BoE series. Estimates based on the geometric mean range between 5.44-6.10 per
cent (under the DMS inflation series), and 5.14-5.7 per cent (under the BoE series).
We note that the UKRN Study relies on DMS data for the period 1900-2016 to estimate the TMR, and its
estimation methodology applies two important adjustments:
First, real returns are calculated on the basis of the Millennium Dataset and not on the basis of the
consumer price inflation measure that was used by DMS.
Second, rather than using an arithmetic mean, the estimate is based on a geometric average, which is
then uplifted by of 100-200pbs to reflect an adjustment from geometric to arithmetic returns.
Based on this the UKRN Study finds that the appropriate range for the CPI-deflated TMR is 6-7 per cent.
Drawing together these various sources, and placing particular weight upon the World TMR estimate of 6.5
and the BoE-CPI value of the UK series of 6.89 per cent, we interpret this historical data as suggesting a
figure in the range of 6.5-6.9 per cent.
Furthermore, we note the following, by way of reinforcement of the idea that the current TMR might
potentially face downward pressure relative to the historic TMR. The UK is not currently in recession and is
not expected to enter recession over AMP7. In periods of recession, Europe Economics has previously
advised that the ERP be temporarily elevated by around 20 per cent33 and some degree of temporary
elevation has been an approach a number of regulators have adopted, including regulators not advised by
Europe Economics.34 If the ERP is 20 per cent higher in recession periods, then in order for a long-term
average to be unaffected, the ERP must be lower than that long-term average in non-recession periods. The
UK economy has contracted in around 17 per cent of quarters since 1955. Let us assume that the ERP is
elevated by 1 percentage point in recession periods (as was assumed to be the case by Ofwat at PR09). Then
in non-recession periods the ERP would need to be discounted by around 0.2 percentage points.35
The TMR in a sustained recession might vary with the risk-free rate as well as with the ERP (potentially with
offsetting impacts such that the overall effect is stability in the TMR), so there is not straightforward
translation from this ERP effect to a TMR effect, but the key point for our purposes here is that the
counterpart of elevating the ERP in a recession (which we have recommended in the past) is to discount it
in a non-recessionary period (e.g. now). Not to do so would result in a systematic overstatement of the TMR
when considered over multiple reviews. Hence this is a further reason the TMR might be expected to be
lower at present.
We adopt 7 as our upper bound estimate and take account of the need to recognise some form of non-
recession discount in our recommendation of point estimate.
4.4 Ex-ante approaches to the TMR
One key potential disadvantage of the use of historical data to create a proxy expectations distribution, even
after adjusting for recession versus non-recession periods, is that there could be structural changes in the
distribution of returns over time. The use of a latest-data-driven estimate of the risk-free rate and latest data-
driven estimates of betas and the debt premium allow for a forwards-looking view including the possibility of
33 For example, this was our advice to Ofwat in 2009 (see p56 of https://www.ofwat.gov.uk/wp-
content/uploads/2015/11/rpt_com_20091126fdcoc.pdf) and to the CAA in 2010 (see p61 of http://www.europe-
economics.com/publications/20100204eecostcapital.pdf). 34 For example, this was done by Ofcom in its May 2009 WACC judgement on Openreach, of which it stated “we
believed that the volatility we observed in equity markets at the time suggested that investors required a higher level of return
in exchange for holding risky equity assets, and an increase of 0.5% in our ERP estimate did not seem unreasonable in this
context” — see paragraph 6.92 of https://www.ofcom.org.uk/__data/assets/pdf_file/0021/34239/condoc.pdf. 35 For example if the ERP were 5 on average and 6 in recessions, hence 6 around 17 percent of the time, then in non-
recession periods the ERP would be (5 – 0.17 x 6) / (1 – 0.17) = 4.79.
Total Market Return
- 33 -
structural change. There seems a potential paradox in basing these other parameters on data up to some
data cut-off close to the determination yet allowing the TMR to be set on the basis of data that is a century
and more old. The other three approaches to the TMR seek to incorporate close to up-to-date information
into the estimate.
In its Final Methodology Ofwat provided evidence from a number of studies that use an ex-ante approach,
and noted that the TMR estimates obtained under this approach tend to be lower than those obtained under
the traditional historical ex-post approach. For example:
Gregory (2007)36 applies a Fama-French Dividend Growth Model (DGM) approach to UK data ranging
from 1927 to 2007 and finds that a plausible forward-looking range for the TMR is likely to be between
4.30 per cent and 6.18 per cent in RPI-deflated terms. The RPI-CPIH wedge has changed materially since
2007, but purely for reference, applying the current RPI-CPIH wedge means these figures would
correspond to a TMR range of 5.32-7.22 per cent in CPIH deflated terms.
Vivian (2007) argues that the expected returns implied by a Fama-French DGM approach since 1966 have
been much lower than average stock returns for the UK stock market as a whole and that the appropriate
estimate of the expected equity risk premium for UK investors over the period 1966-2002 was around
3.0 per cent in real terms. This implies an RPI-deflated TMR of 5.09 per cent (based on the author’s use
of a risk-free rate of 2.09 per cent). We note that, of course, there is no good reason to expect the RPI-
deflated yield to be stable over time, since that is not the real yield.
Furthermore, as discussed in Section 2.3 of the 2017 Europe Economics report, there is some reason to
question to what extent historical data gives an unbiased sample of the distribution of expected returns and,
even if it were an unbiased sample, to what extent certain of the returns periods in the past might be repeated
in the future. The 2017 DMS sourcebook and its accompanying slide pack attempted to estimate what
proportion of long-term global returns were the product of such unanticipated or non-repeatable events.
DMS contended that from the average geometric return of 5.1 per cent one should subtract around one per
cent to account for real dividend growth and changes in P/E ratio. Insofar as a similar downwards adjustment
were justified for the UK, that would suggest a forward-looking total market return of around 6.5 per cent
in real (i.e. CPIH-deflated) terms.
Three further issues are as follows. First, as noted above, the UK return may in the future be more similar
to the world return than was the case in the past, because the UK may be more integrated into international
capital markets.
Second, other markets may become more integrated so TMRs across the world may become more similar
and also international diversification may become more efficient, reducing the global risk premium and hence
(for any given risk-free rate) reducing the TMR.
Third, there may be reason to question to what extent volatility of returns in the future will match volatility
in the past. If future volatility is lower than in the past (eg mirroring the well-documented reduction in GDP
volatility in modern economies compared with those in past decades), then even if future geometric returns
were the same as historic returns, future arithmetic returns would be lower than in the past. Conversely, if
there were reason to believe future volatility might be higher (eg if algorithmic trading, the more extensive
use of tracker funds, or greater globalisation of markets led to destabilisation rather than stabilisation), then
even if geometric returns were stable, arithmetic returns could rise.37
36 A. Gregory, (2007) “How Low is the UK Equity Risk Premium?” 37 On this point, we note that Smithers & Co (2003), “A Study into Certain Aspects of the Cost of Capital for Regulated
Utilities in the UK”, state (p39) “There is indeed a reasonable amount of evidence that macroeconomic aggregates like
GDP became more stable in the second half of the twentieth century. But, at least in mature markets, the evidence that stock
markets, as opposed to the rest of the economy, have got much safer, is distinctly weaker. In economies that escaped major
disruption, such as the UK or the US, there is little or no evidence of a decline in stock return volatility.” And since Smithers
and Co were writing, there has been the considerable volatility of the lead-up to and period of the Great Recession.
Total Market Return
- 34 -
Suppose, for example, we were to decompose the UK’s historic TMR into three components (quoting the
2019 DMS estimate in brackets after each component):
The World geometric TMR (5 per cent)
The World volatility premium, ie the wedge between arithmetic and geometric returns (1.5 per cent)
The premium of the UK arithmetic TMR over the World arithmetic TMR (0.7 per cent)
By the arguments above, each of these components might rise or fall. For example, the World geometric
TMR was 5.6 in 2000 and is only 5.0 now. The World premium of arithmetic over geometric returns, on the
DMS series, was 1.1 in 2003 and is 1.5 now. The UK premium over the World premium was about 0.4 in
2000 and is about 0.7 now. Let us assume, for illustrative purposes, that each of these changes were halved
again in the future — i.e. the world geometric TMR falls to 4.7 per cent, the world premium of arithmetic
over geometric returns rises to 1.7 per cent, and the UK premium over the World premium rises to 0.8 per
cent. That would imply a total UK arithmetic TMR of 7.2 per cent — unchanged compared with the current
value. This illustrates that it is by no means clear how these different factors might net out. We therefore
stick with our core estimates.
4.5 Forward-looking approaches based on practitioners’ estimates
A view on a plausible forward-looking TMR values also be can formed also by taking into consideration the
views of finance practitioners. We review these below.
Fernandez Survey – the paper by Fernandez et al. (2019)38 presents the results of a survey about the risk-
free rate and the Market Risk Premium (MRP) for 69 countries. The survey is composed by emails from
economic professors, analysts and companies’ managers who provide their points of view about the RFR
and the MRP used to calculate the return to equity in their specific country. The survey results suggest
that the TMR for the United Kingdom was on average 8.3 per cent in nominal term. This corresponds to
a CPI-deflated TMR of 6.18 per cent
Practitioners’ forecasts – In its recent methodology paper for RIIO-2, Ofgem provides an overview of
asset managers’ estimates of medium-term and long-term nominal UK TMR.39 These are reported in the
table below and indicate that, on average the nominal TMR is 7.19 per cent. Ofgem notes that TMR
figures provided by Wills Tower Watson and Vanguard are likely to underestimate actual equity returns
because the former is based on a portfolio with a significant bond component (around 40 per cent), and
the latter refers to hedged return. If Wills Towers Waterson and Vanguard figures are excluded, the
average nominal TMR is 7.66 per cent, which corresponds to a CPI-deflated TMR of 5.55 per cent. The
highest TMR estimate from Schroders (8.9 per cent in nominal terms), corresponds to a CPI-deflated
TMR of 6.8 per cent.
Table 4.3: Summary of asset managers’ views on the UK TMR
Asset Manager Description Nominal TMR
Schroders 30yr UK expected returns (Jan 2019) 8.9%
BlackRock 10yr return, Europe large cap, GDP, median (Dec 2018) 8.5%
Old Mutual LT UK equity (Dec 2018) 8.0%
Nutmeg 10yr+ UK equity (Sept 2017) 7.8%
38 Fernandez, Martinez, and Acin (2019) “Market Risk Premium and Risk-Free Rate used for 69 countries in 2019: a
survey” 39 The original investment managers’ figures are expressed in geometric terms, and Ofgem applied a 1 per cent uplift
to translate the geometric means in in arithmetic means.
Total Market Return
- 35 -
Asset Manager Description Nominal TMR
FCA 10-15yr UK projected equity returns (Sep 2017) 7.6%
Aon Hewitt 10yr UK projected nominal equity returns (June 2018) 7.4%
[REDACTED] 10yr horizon (Nov 2018) 7.2%
Aberdeen AM UK expected equity returns, 10yr (Dec 2017) 6.9%
JP Morgan Long Term UK expected returns (Sept 2018) 6.6%
Wills Towers Watson 10yr UK equity, median “lower for longer” (Dec 2018) 5.2%
Vanguard 10yr UK expected equity returns (Nov 2018) 5.0%
AVERAGE 7.19%
AVERAGE (excluding Wills Towers Waterson and Vanguard) 7.66%
Source: Ofgem, (24 May 2019) “RIIO-2 Sector Specific Methodology Decision – Finance”
Although surveys can be a useful reality check on, or challenge to, the evidence gathered from historical or
contemporaneous market data, it has been standard in regulatory WACC analysis to place relatively little
weight on such surveys, as they tend to be subjective in nature and to involve wide ranges. Their key
importance here is that their (fairly consistent) message appears to be that the TMRs in historical analyses of
World or UK returns (of order 8.5 per cent to above 9 per cent in nominal terms) are materially higher than
these analyst opinions of the future. That could be seen to justify at least considering a lower end estimate
that lay below the historical range — perhaps something closer to (or even lower than) the European range
(closer to 8 per cent in nominal terms).
4.6 Forward-looking approaches based on Dividend Growth Models (DGM)
and Dividend Discount Models (DDM)40
In December 2017, we concluded that our preferred model was a Dividend Growth Model based on GDP.
This model produced a 6.89 estimate for the TMR, lying within Europe Economics’ recommended range of
6.25-7.0 per cent. Europe Economics recommended 6.75 per cent as its point estimate. Ofwat chose a value
of 6.47 per cent. We have updated this model using a blended dataset41 with data up to February 2019. The
results are presented below.
40 What we term the “DGM model” here uses recent historic dividend (and buyback) yields and then uses projections
of GDP growth as a predictor of dividend returns. What we term the “DDM” model uses recent historic dividend
(and buyback) yields and then uses analyst predictions of dividend yields for future dividend returns, potentially with
a volatility adjustment (though we argued in our 2017 report that that volatility adjustment might be nugatory in
practice). 41 The “blended dataset” includes data from Bloomberg and Thomson Reuters.
Total Market Return
- 36 -
Figure 4.2: Multi-stage DGM based on GDP growth
Source: Bloomberg, Thomson Reuters and Europe Economics calculations.
The spot value of the updated DGM based on GDP growth at February 2019 is 6.26 per cent, whilst the 5-
year trailing average is 6.12 per cent. The preferred rolling 5 year average-based forecast42 from our DGM
model implies there has been a reduction in the TMR since 2017 of around 0.8 per cent, but in recent months
(e.g. since July 2018) the spot value estimates of TMR has risen sharply.
In 2017 we also presented a DGM model based on growth in dividends and buybacks. This model has also
been updated with data up to February 2019.
Figure 4.3: Multi-stage DGM based on Dividend and buy-backs growth
Source: Bloomberg, Thomson Reuters and Europe Economics calculations.
42 In our 2017 report we demonstrated quantitatively that the 5 year average was a better predictors of future returns
than the spot return. This was in line with the conclusions of previous academic studies on the same point.
0
0.02
0.04
0.06
0.08
0.1
0.12
Jan-0
0
Aug-
00
Mar
-01
Oct
-01
May
-02
Dec-
02
Jul-03
Feb-0
4
Sep-0
4
Apr-
05
Nov-
05
Jun-0
6
Jan-0
7
Aug-
07
Mar
-08
Oct
-08
May
-09
Dec-
09
Jul-10
Feb-1
1
Sep-1
1
Apr-
12
Nov-
12
Jun-1
3
Jan-1
4
Aug-
14
Mar
-15
Oct
-15
May
-16
Dec-
16
Jul-17
Feb-1
8
Sep-1
8
Spot 5yr trailing average
0%
2%
4%
6%
8%
10%
12%
14%
Jan-0
0
Aug-
00
Mar
-01
Oct
-01
May
-02
Dec-
02
Jul-03
Feb-0
4
Sep-0
4
Apr-
05
Nov-
05
Jun-0
6
Jan-0
7
Aug-
07
Mar
-08
Oct
-08
May
-09
Dec-
09
Jul-10
Feb-1
1
Sep-1
1
Apr-
12
Nov-
12
Jun-1
3
Jan-1
4
Aug-
14
Mar
-15
Oct
-15
May
-16
Dec-
16
Jul-17
Feb-1
8
Sep-1
8
Spot 5yr trailing average
Total Market Return
- 37 -
The spot value of the DGM model at March 2019 is 7.47 per cent, whilst the 5-year trailing average is 6.51
per cent.
We note that, considering both spot value and 5-years trailing average values, our DGM models produce a
CPI-deflated TMR estimate range of 6.12-7.47 per cent.
4.7 Conclusions on TMR
We note that:
Ex-post and ex ante approaches based on the latest DMS data, subject to appropriate adjustments, are
consistent with CPI-deflated TMR estimate of around 6.5-7.0 per cent, with a non-recession point
estimate likely to be of the order of 0.2 per cent below this.
DGM and DDM models produce similar CPI-deflated TMR estimates broadly within the similar 6-7 per
cent range.
Ex-ante approaches suggest a CPI-deflated value for the TMR towards the lower end of that range of
around 6 per cent.
Practitioners’ estimates are consistently materially below 6.8 per cent (in CPI-deflated terms).
The preponderance of this evidence is consistent with a CPI-deflated TMR range of 6.0-7.0 per cent,
i.e. implying a drop at the lower end compare with our 2017 recommendation. That would be consistent
with a point estimate for the CPI-deflated TMR 6.50 per cent. At 2 per cent assumed CPIH that
would imply a nominal TMR range of 8.12-9.14 per cent with a nominal TMR point estimate of
8.63 per cent.
Beta and the cost of equity
- 38 -
5 Beta and the cost of equity
5.1 Introduction
This section provides our view on the appropriate beta estimate for the UK water sector in PR19. The
section is structured as follows:
In Section Error! Reference source not found. we provide a formal description of different beta
concepts and how these are calculated in practice.
In Section 5.3 we provide an in-depth discussion of methodological issues concerning beta estimation.
More specifically we provide here responses of certain issues raised by the UKRN Study and set out
our preferred approach.
In Section 5.4 we provide the main raw equity beta evidence based on OLS estimation method.
In Section 5.5 w provide a number of cross-checks on raw equity betas obtained following the
ARCH/GARCH estimation methodology proposed by the UKRN Study.
In Section Error! Reference source not found. we set up the gearing measure used to unlevered
beta and provide evidence on the unlevered betas.
In Section 5.6 we provide evidence and our recommendation on unlevered beta.
In Section 5.6.1 we provide evidence and our recommendation on debt beta.
In Section 5.8 we present evidence and recommendations on asset betas and equity beta at the notional
gating level.
In Section 0 we conclude with our recommended range and point estimate for the cost of equity.
5.2 What a beta is an how an asset beta and its components are estimated
5.2.1 What is the “beta” of an asset?
The beta of an asset is a measure of the systematic riskiness of the cashflows that it generates. In mathematical
terms, the beta of any asset 𝑖 generating returns 𝑅𝑖 is defined as follows.
𝛽𝑖 =𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑅𝑖, 𝑅𝑚)
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑅𝑚)
where 𝑅𝑚 is the return on the market as a whole.
This expression applies to the returns on any asset — a car; a patent; a water firm’s pipes, taps, reservoirs,
staff, staff networks, intellectual property, etc; or some financial claim on the returns of a water firm, such as
bonds or shares.
It is important to emphasize that the water firm’s assets themselves and the equity of a water firm are two
distinct assets, not simply two ways of looking at the same asset, and they will have their own distinct (and
typically different) betas. When shares are traded publicly on a stock exchange their beta at any point in time
can be measured directly. But betas at different points in time and betas for different scenarios (eg different
levels of gearing) cannot meaningfully be compared without various adjustments (which we shall discuss
below). Hence the unadjusted betas are referred to as “raw” equity betas.
Beta and the cost of equity
- 39 -
5.2.2 Why does the equity beta change with gearing?
A firm does not have an equity beta per se. It has an equity beta at a given level of gearing. The equity beta
will rise as gearing rises and fall as gearing falls. One straightforward way to understand intuitively why equity
beta is higher at a higher level of gearing is to see that when gearing is higher, a larger proportion of the firm’s
revenues, in any given period, will be required to fund committed payments. So if matters turn out badly,
there is a smaller equity buffer to cover losses, and thus a larger risk that equity is wiped out altogether in
bankruptcy. Conversely, if matters go well, that smaller slice of equity has fewer other equity-holders (or less
other equity) to share the gains with. So when gearing is higher, losses have a greater impact and gains created
greater rewards. So any given business risk is leveraged (multiplied).
Hence, when comparing the systematic risk of two firms with different gearing, it is necessary to convert raw
equity betas to take account of gearing and also to take account of the beta on debt. The Modigliani-Miller
Theorems tell us both why this is so and how the relevant adjustment should be made.
The reason why this is so is as follows. A firm consists of some capital equipment, some intellectual property,
networks of contacts, staff with various human capital and internal traditions. It has customers, competitors,
a current level of market technology, potential new entrants, and so on. These factors come together to
produce cash-flows out of the firm (costs) and cash flows in (revenues). These cash flows are subject to risks,
some diversifiable and some non-diversifiable. In combination these produce net cash flows — the firm’s
earnings.
The earnings are then split between different debt and equity claimants according to the capital structure
(the gearing). But unless something about how they are split up changes the management of the business, it
is only a division. A division in itself cannot change how much earnings there is or the riskiness of that earnings
any more than the size of a cake can be changed by how many pieces we cut it into.
That means that the riskiness of the business — the asset beta — will not be affected by the gearing. But
since the betas of debt and equity are almost always different for any firm, that means that one or both of
them must change with gearing — otherwise any change in the shares of them would change the asset beta,
as we can see below.
First, we note that the asset beta is, as one would expect, the weighted average of the betas of debt and
equity.
𝛽𝐴 = (1 − 𝑔)𝛽𝐸𝑟𝑎𝑤+ 𝑔𝛽𝐷,
where 𝛽𝐸𝑟𝑎𝑤 is the “raw” equity beta”, 𝛽𝐷 is the debt beta, 𝑔 is the proportion of debt and equity that is
debt.
Suppose 𝛽𝐷,= 0.1, 𝛽𝐸𝑟𝑎𝑤= 1 and g = 60 per cent. Then 𝛽𝐴 = 0.6 x 0.1 + 0.4 x 1 = 0.46. Suppose, instead that
g = 0.5 but 𝛽𝐷, and 𝛽𝐸𝑟𝑎𝑤 were still as before. Then 𝛽𝐴 = 0.5 x 0.1 + 0.5 x 1 = 0.55 — i.e. higher. Suppose,
alternatively, that g = 0.7 but again 𝛽𝐷, and 𝛽𝐸𝑟𝑎𝑤 were as before. Then 𝛽𝐴 = 0.7 x 0.1 + 0.3 x 1 = 0.37 — i.e.
lower.
So if the asset beta is to remain unaffected by gearing — if gearing merely cuts up the cake of earnings without
changing the size of that cake — then when gearing changes, one or both of the costs of debt and equity
must change. Normally it is assumed that, at intermediate levels of gearing, even fairly significant changes up
or down in gearing levels are unlikely to have a large impact on the debt beta. So the equity beta changes
with gearing. We can see how by re-expressing the formula above in terms of the equity beta.
𝛽𝐸𝑟𝑎𝑤=
𝛽𝐴 − 𝑔𝛽𝐷
1 − 𝑔
Beta and the cost of equity
- 40 -
So, revisiting the examples above, if 𝛽𝐷= 0.1, 𝛽𝐸𝑟𝑎𝑤 = 1 and 𝛽A= 0.46 when g = 60 per cent, then when g =
50 per cent, 𝛽𝐸𝑟𝑎𝑤 = (0.46 – 0.5 x 0.1) / (1 - 0.5) = 0.82.
5.2.3 What is the correct concept of gearing to use when estimating the asset beta?
The raw equity beta is a measure of the systematic riskiness of the firm’s equity (at the given level of gearing),
not a measure of the risk of the firm’s assets. If we are seeking to infer the firm’s actual systematic risks we
need to use the actual gearing over the relevant time horizon used in the estimation when we de-leverage
the actual raw equity beta. If we were to use something other than the firm’s actual gearing we would not be
assessing the firm’s actual systematic risks.
The most straightforward actual gearing concept (and that with the most frequently available data) is what
we term the “enterprise value gearing”, define as the book value of net debt over the sum of the market
value of equity and the book value of debt. In standard financial data sources this is available at high frequency
(at least daily and sometimes with higher frequency).
In our 2017 report we set out how one might adjust the enterprise value gearing to take account of shifts in
market interest rates and debt premiums that affect the mark-to-market fair value of debt — i.e. the amount
of debt the firm would need to raise to refinance its debt, “today” (i.e. at the relevant point in the regulatory
period), with the same maturity profile. We also noted that because Ofwat’s policy approach to the cost of
capital assumes an amount for embedded debt of the notional company”, such “fair value gearing” would not
be the correct concept for such an adjustment, since embedded debt shields the firm from market movements
subsequent to debt being raised, for that portion of debt that is embedded. We termed the fair value gearing,
after adjusting for the effects of embedded debt, the “regulatory fair value gearing”. We also noted that there
are drawbacks with using fair value gearing (regulatory or otherwise) in that the adjustments are not available
on a daily basis (unlike yields), so there would need to be a sufficiently significant difference between
regulatory fair value gearing and enterprise value gearing for the use of regulatory fair value gearing to actually
be a methodological improvement.
In 2017, when we conducted the analysis, we found that the impact on gearing and asset beta of using
regulatory fair value adjustments to enterprise value was so small that it did not outweigh the losses from
being unable to use up-to-the-day data.
For this analysis, we have, once again, explored the implications of the use of regulatory fair value adjustments.
In the Appendix in Section 8.4 we explain the calculations in some detail. In the graph below we report the
key chart, setting out the enterprise value and regulatory fair value gearings for UU and SVT over recent
years.
In respect of UU we can see that there is almost no difference between fair value and enterprise value
gearing.
In respect of SVT we can see that it has not been unusual for fair value gearing to be rather higher than
enterprise value gearing. At higher gearing, any given SVT raw equity beta would be associated with a
lower unlevered beta. As of 28 February 2019 this effect makes about 1bps difference to unlevered beta
for a given raw equity beta.
There is thus no difference in respect of UU and the difference in respect of SVT is modest. Hence hereafter
we focus solely upon enterprise value gearing in all our calculations. However, in interpreting our results we
note that SVT unlevered betas may be overstated by a basis point or so.
Beta and the cost of equity
- 41 -
Figure 5.1: Regulatory fair value gearing (RFVg) vs Enterprise value gearing (ENTg)
Source: Thomson Reuters, companies’ financial statements, Europe Economics’ calculations.
5.2.4 Gearing measure used to un-lever raw equity betas
For the purpose of un-levering raw beta the gearing measure used is net debt over enterprise value (ND/EV)
as available from Thomson Reuters. Net Debt is defined by Thomson Reuters as the sum of:
Total debt.
Redeemable preferred stock.
Preferred stock – von redeemable, net.
Minority interest.
minus:
Cash.
Cash & equivalents.
Short term investments.
In order to un-lever the average raw equity beta of SVT/UU and the average raw equity beta of PNN/SVT/UU,
we calculate a weighted average ND/EV with weights proportional to the companies’ market capitalisation.
When un-levering raw equity betas we use a rolling average of ND/EV over the same time horizon of the
raw equity beta that we un-lever. So for example, in order to unlever a 2-years raw equity beta we use a 2-
years trailing average of ND/EV.
We provide below the evolution of ND/EV for Severn Trent, and United Utilities, together with the 1-year,
2-year and 5-years trailing averages. We also report the average gearing measures (ND/EV and trailing
averages) for SVT/UU.
30.00%
35.00%
40.00%
45.00%
50.00%
55.00%
60.00%
65.00%
03/0
1/2
017
03/0
2/2
017
03/0
3/2
017
03/0
4/2
017
03/0
5/2
017
03/0
6/2
017
03/0
7/2
017
03/0
8/2
017
03/0
9/2
017
03/1
0/2
017
03/1
1/2
017
03/1
2/2
017
03/0
1/2
018
03/0
2/2
018
03/0
3/2
018
03/0
4/2
018
03/0
5/2
018
03/0
6/2
018
03/0
7/2
018
03/0
8/2
018
03/0
9/2
018
03/1
0/2
018
03/1
1/2
018
03/1
2/2
018
03/0
1/2
019
03/0
2/2
019
03/0
3/2
019
03/0
4/2
019
UU RFVg SVT RFVg UU ENTg SVT ENTg
Beta and the cost of equity
- 42 -
Figure 5.2: Gearing measures for Severn Trent (%)
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.3: Gearing measures for United Utilities (%)
Source: Thomson Reuters, Europe Economics’ calculations.
30
35
40
45
50
55
60
65
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (ND/EV) Severn Trent (1yr trailing average ND/EV)
Severn Trent (2yr trailing average ND/EV) Severn Trent (5yr trailing average ND/EV)
30
35
40
45
50
55
60
65
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
United Utilities (ND/EV) United Utilities (1yr trailing average ND/EV)
United Utilities (2yr trailing average ND/EV) United Utilities (5yr trailing average ND/EV)
Beta and the cost of equity
- 43 -
Figure 5.4: Average gearing measures for SVT/UU (%)
Source: Thomson Reuters, Europe Economics’ calculations.
A summary of the various gearing measures (including, for completeness, also that of the PNN/SVT/UU
portfolio) is reported in the table below.
Table 5.1: Summary of gearing measures
Company ND/EV 1-yr trailing
average of ND/EV
2-yr trailing
average of ND/EV
5-yr trailing
average of ND/EV
Pennon 48.2% 49.1% 47.2% 43.9%
Severn Trent 53.8% 54.7% 52.2% 49.6%
United Utilities 56.4% 59.2% 56.9% 53.1%
SVT/UU 55.2% 57.1% 54.7% 51.4%
PNN/SVT/UU 53.6% 55.2% 52.9% 49.7%
Source: Thomson Reuters, Europe Economics’ calculations.
5.2.5 De-levering equity betas into asset betas
When comparing the betas of different firms, one has to take into account the different gearing levels that
firms choose since (other things being equal) a firm with higher gearing will exhibit a higher equity beta and
there is a difference here between the gearings of the firms we are considering and between their gearing
and the notional gearing. Asset betas are calculated in order to control for the effect of differing levels of
gearing. An asset beta is a hypothetical measure of the beta that a firm would have if it were financed entirely
by equity. Another useful concept is the “unlevered beta”, which is simply the equity beta multiplied by the
portion of total capital that is equity.43 Asset betas are calculated using the following formula:
43 The term “unlevered beta” is often used as a synonym for asset beta. In Europe Economics’ December 2017 cost of
capital report we used the term “unlevered beta” to refer more narrowly to the equity beta adjusted for gearing
with no allowance for debt beta, and the term “asset beta” to refer to the asset beta including debt beta. We follow
that convention here also.
30
35
40
45
50
55
60
65
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (ND/EV) SVT/UU (1yr trailing average ND/EV)
SVT/UU (2yr trailing average ND/EV) SVT/UU (5yr trailing average ND/EV)
Beta and the cost of equity
- 44 -
𝛽𝐴 = (1 − 𝑔)𝛽𝐸𝑟𝑎𝑤+ 𝑔𝛽𝐷,
where 𝛽𝐸𝑟𝑎𝑤 is the “raw” equity beta, (1 − 𝑔)𝛽𝐸 is the “unlevered beta”, 𝛽𝐷 is the debt beta, 𝑔 is the actual
enterprise gearing.
When the debt beta is assumed, for calculation purposes, to be zero, the role of the asset beta is instead
played by the unlevered beta, 𝛽𝑈:
𝛽𝑈 = (1 − 𝑔)𝛽𝐸𝑟𝑎𝑤
5.2.6 Calculating debt beta
For most utilities, the cost of new debt is higher than the risk-free rate — there is a “debt premium" that
means, by definition, that market participants (rightly or wrongly) believe there is some probability of utility
companies defaulting on their debts.44 Such defaults create a wedge between the risk-free rate and the cost
of new debt in two ways. First, a default probability creates a wedge between the promised return on debt
and the expected return on debt: because the amount promised might sometimes not be paid, the expected
return of debt45 must (by definition) be lower than the promised return of debt.
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡
= 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡) ⋅ % 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 + (1 — 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡))
⋅ 𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡.
Secondly, if there is a correlation between when defaults are most likely to occur, or the losses on default
when defaults occur, and the broader returns cycle, there will be a yield cost reflecting the systematic risk
borne — i.e. a debt beta.
The CAPM applies to any asset — an electricity grid, a plastics bottle-making machine, an equity claim on a
telecoms firm or a debt claim on a water network. So the expected cost of debt can be expressed, in the
CAPM, as46
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡 = 𝑅𝐹𝑅 + 𝛽𝐷 ⋅ 𝐸𝑅𝑃,
It is worth observing the relationship between the probability of default, the loss given default and the debt
beta. In an accounting sense, the debt beta arises from the residual debt premium that is not explained by
the probability of default and loss given default, so for any given debt premium, the lower the probability of
default and loss given default, the higher the debt beta must be. Conversely, the lower the debt beta, the
higher the probability of default and loss given default must be. The assumption of a zero debt beta is
equivalent to the assumption that all of the debt premium is to be accounted for by the probability of default
and loss given default and that no default risk has a systematic component. That will not typically be correct.
When adjusting for small differences in gearing, it is often mathematically convenient to assume a debt beta
of zero because even with a debt beta of 0.1 or 0.2, the mathematical impact would only arise at the second
44 We note that defaults have been very rare in developed economy utilities sectors. Nonetheless, the market data
indicates that market participants do perceive some risk of default. As we shall explain later, we calibrate from
market data what the market-implied rate of default is. 45 The “expected return on debt” here is not the same as the cost of debt. The expected return on debt is the
(promised) cost of debt adjusted for the probability of default and loss given default. 46 Note that this means the debt beta is equal to the ratio of the difference between the expected return on debt and
the risk-free rate. Insofar as we can ignore the risk of default, that means the debt beta is roughly equal to the ratio
of the spread to the ERP. In what follows we shall derive a formula that is simply a more precise variant of this basic
insight, with a small adjustment for the risk of default.
Beta and the cost of equity
- 45 -
or third significant figure. However, if the enterprise value gearing of listed comparator company differs
materially from the notional gearing, then unlevered betas must be re-levered at a materially different gearing.
In such a situation it is inappropriate to assume a zero debt beta in order to determine the asset beta unless
one really believes the debt beta is zero.
In practical terms, it can be shown that the debt beta can be calculated according to the following
mathematical formula (we refer to the Appendix for the technical details of how the formula is derived).
𝛽𝐷 = (1— 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡)) ⋅ 𝑑𝑒𝑏𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 — 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡) ⋅ (𝑅𝐹𝑅 + % 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡)
𝐸𝑅𝑃
A debt beta estimation approach based on the formula above is known as a disaggregation approach. An
alternative method to estimate debt beta is a regression approach where the returns on a company’s bonds,
(or an appropriate bond index) are regressed against the returns of a broad market index in the same way
equity betas are estimated. The estimation results obtained following these two approached are illustrated
in Section 5.6.
5.3 Specific methodology for raw equity beta estimation
In the Appendix we set out various methodological issues when estimating raw equity betas. Based on that
discussion, our preferred approach is to estimate raw equity beta based on the OLS estimations applied to
years of daily data. However, as a cross check, we provide also beta estimates obtained on different time
horizons (one-year, and five-years), different data frequency (weekly and monthly returns data), and using the
ARCH/GARCH estimation framework.
In addition to data frequency, and estimation method used, beta estimates can also be affected by two
additional features:
the choice of the market index used in the regression; and
the specific time/date at which stock price used to calculate returns are recorded.
With regards to the choice of the market index, our preference of to use the FTSE All Share Total Market
Return index. We are estimating a beta for a UK enterprise, based on a UK risk-free rate estimate (derived
from gilts) and a UK TMR estimate, so for consistency we require a UK equities index. The FTSE All Share
index is the standard all-share benchmark for the UK.
With regards to the time/date at which prices are calculated, we follow the convention of using closing trading
prices. This means: closing daily prices for daily data, closing prices on Fridays for weekly return data, and
closing prices on the last day of the month for monthly data.
5.4 Beta evidence based on OLS
In this section we provide the main evidence regarding raw equity betas. We show the evolution of raw
equity betas using data of different frequencies and different trailing windows for the analysis. In particular:
Figure 5.5-Figure 5.10 shows raw equity betas for Severn Trent, United Utilities, and a portfolio47 of
two water companies (denoted as SVT/UU) based on data with different frequencies and different
trailing windows;
Figure 5.11 and Figure 5.12 compares raw equity betas of the portfolio obtained using the same trailing
windows, but data of different frequencies.
47 The portfolio’s beta is estimated using weighted average returns of the portfolio’s constitutents, where the weights
are proportional to the companies’ market capitalisations.
Beta and the cost of equity
- 46 -
It is worth noticing that the beta estimates presented in this section do not include Pennon. This choice is
justified on the grounds that, whilst, Severn Trent and United Utilities are pure-play water companies, Pennon
is a multiline utility with a significant portion of revenues generated from unregulated activities. However, as
a cross-check we have estimated betas including Pennon and the results are not particularly sensitive its
inclusion (adding around 1bp to the beta estimate).
The cut-off date used for this analysis is 28-February-2019, and we recall that the cut-off date used in our
initial assessment of the cost of capital was the 31-July-2017 (this is indicated as a dotted vertical line in the
charts below).
Figure 5.5: Daily raw equity betas — 1yr trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.2
0.4
0.6
0.8
1
1.2
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (1yr Daily - OLS) United Utilities (1yr Daily - OLS) SVT/UU (1yr Daily - OLS)
July 2017
Beta and the cost of equity
- 47 -
Figure 5.6: Daily raw equity betas — 2yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.7: Daily unlevered betas — 5yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (2yr Daily - OLS) United Utilities (2yr Daily - OLS) SVT/UU (2yr Daily - OLS)
July 2017
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (5yr Daily - OLS) United Utilities (5yr Daily - OLS) SVT/UU (5yr Daily - OLS)
July 2017
Beta and the cost of equity
- 48 -
Figure 5.8: Weekly raw equity betas — 2yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.9: Weekly raw equity betas — 5yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (2yr Weekly - OLS) United Utilities (2yr Weekly - OLS) SVT/UU (2yr Weekly - OLS)
July 2017
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
Severn Trent (5yr Weekly - OLS) United Utilities (5yr Weekly - OLS) SVT/UU (5yr Weekly - OLS)
July 2017
Beta and the cost of equity
- 49 -
Figure 5.10: Monthly raw equity betas — 5yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations
Figure 5.11: Daily and weekly SVT/UU raw equity betas — 2yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
2010M
01
2010M
04
2010M
07
2010M
10
2011M
01
2011M
04
2011M
07
2011M
10
2012M
01
2012M
04
2012M
07
2012M
10
2013M
01
2013M
04
2013M
07
2013M
10
2014M
01
2014M
04
2014M
07
2014M
10
2015M
01
2015M
04
2015M
07
2015M
10
2016M
01
2016M
04
2016M
07
2016M
10
2017M
01
2017M
04
2017M
07
2017M
10
2018M
01
2018M
04
2018M
07
2018M
10
2019M
01
Severn Trent (5yr Monthly - OLS) United Utilities (5yr Monthly - OLS)
SVT/UU (5yr Monthly - OLS)
July 2017
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (2yr Daily -OLS) SVT/UU (2yr Weekly -OLS)
Beta and the cost of equity
- 50 -
Figure 5.12: Daily, weekly and monthly SVT/UU raw equity betas — 5yrs trailing window (OLS)
Source: Thomson Reuters, Europe Economics’ calculations.
The table below compares the spot beta estimates at 28-February-2019 obtained over different time horizons
and data frequencies. For completeness we report also the estimates of the portfolio which includes Pennon
(denoted below as PNN/SVT/UU).
Table 5.2: Summary of raw beta estimates (spot at 28-February-2019) based on OLS
Company Data frequency 1-yr trailing
average
2-yr trailing
average
5-yr trailing
average
Severn Trent Daily 0.53 0.60 0.67
Weekly - 0.58 0.66
Monthly - - 0.76
United Utilities Daily 0.58 0.64 0.70
Weekly - 0.60 0.67
Monthly - - 0.78
SVT/UU Daily 0.56 0.62 0.68
Weekly - 0.59 0.67
Monthly - - 0.77
PNN/SVT/UU Daily 0.55 0.62 0.68
Weekly - 0.62 0.67
Monthly - - 0.77 Source: Thomson Reuters, Europe Economics calculations.
5.5 Cross-checks based on ARCH/GARCH estimates
Some of the authors of the recent UKRN Study expressed the view that, since high-frequency financial data
display heteroscedasticity, caution should be applied in the use of OLS estimates based on daily return data.
Instead, they claim, other statistical techniques, such as the ARCH/GARCH framework, might be preferable
0
0.2
0.4
0.6
0.8
1
1.2
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (5yr Daily -OLS) SVT/UU (5yr Weekly -OLS) SVT/UU (5yr Monthly -OLS)
Beta and the cost of equity
- 51 -
as they are better equipped to deal with heteroscedastic data. Although we dispute this reasoning (see
Appendix 8 for a detailed response to the methodological issues raised by the UKRN Study), we see some
merit in cross-checking our judgements drawn from OLS results with ARCH/GARCH framework results,
and report these below for various trailing windows and data frequencies (details on the specific model
specification used are reported in the appendix).
Figure 5.13: Daily SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 1yr trailing window
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.14: Daily SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 2yr trailing window
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (1yr Daily -ARCH/GARCH) SVT/UU (1yr Daily -OLS)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (2yr Daily -ARCH/GARCH) SVT/UU (2yr Daily -OLS)
Beta and the cost of equity
- 52 -
Figure 5.15: Daily SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 5yr trailing window
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.16: Weekly SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 2yr trailing window
Source: Thomson Reuters, Europe Economics’ calculations.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (5yr Daily -ARCH/GARCH) SVT/UU (5yr Daily -OLS)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (2yr Weekly -ARCH/GARCH) SVT/UU (2yr Weekly -OLS)
Beta and the cost of equity
- 53 -
Figure 5.17: Weekly SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 5yr trailing window
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.18: Monthly SVT/UU average raw equity beta (OLS vs ARCH/GARCH) — 5yr trailing
window
Source: Thomson Reuters, Europe Economics’ calculations.
As we can see from the table below, although the ARCH/GARCH graphs above exhibit lower volatility, as
one would expect, the results as of 28 February 2019 are very similar for the OLS and ARCH/GARCH
methods and provide very similar estimates across all trailing windows and data frequencies. We also notice
that, compared to OLS estimates ARCH/GARCH estimates produce trailing betas that are somewhat less
volatile.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
SVT/UU (5yr Weekly -ARCH/GARCH) SVT/UU (5yr Weekly -OLS)
0
0.2
0.4
0.6
0.8
1
1.2
Jan-1
0
May
-10
Sep-1
0
Jan-1
1
May
-11
Sep-1
1
Jan-1
2
May
-12
Sep-1
2
Jan-1
3
May
-13
Sep-1
3
Jan-1
4
May
-14
Sep-1
4
Jan-1
5
May
-15
Sep-1
5
Jan-1
6
May
-16
Sep-1
6
Jan-1
7
May
-17
Sep-1
7
Jan-1
8
May
-18
Sep-1
8
Jan-1
9
SVT/UU (5yr Monthly -ARCH/GARCH) SVT/UU (5yr Monthly -OLS)
Beta and the cost of equity
- 54 -
Table 5.3: Summary of raw equity beta estimates (spot at 28-February-2019) based on ARCH/GARCH
Company Data frequency 1-yr trailing
average
2-yr trailing
average
5-yr trailing
average
Severn Trent Daily 0.60 0.64 0.66
Weekly - 0.58 0.59
Monthly - - 0.72
United Utilities Daily 0.60 0.62 0.67
Weekly - 0.64 0.65
Monthly - - 0.65
SVT/UU Daily 0.60 0.63 0.67
Weekly - 0.64 0.64
Monthly - - 0.67
PNN/SVT/UU Daily 0.60 0.64 0.66
Weekly - 0.64 0.64
Monthly - - 0.70 Source: Thomson Reuters, Europe Economics’ calculations.
5.6 Unlevered betas
Based on the raw equity betas provided in Table 5.2 and Table 5.3, and the gearing measures of Error!
Reference source not found., we provide below the overall evidence on unlevered betas.
Table 5.4: Summary of unlevered beta estimates (spot at 28-February-2019) based on OLS
Company Data frequency 1-yr trailing
average
2-yr trailing
average
5-yr trailing
average
Severn Trent Daily 0.24 0.29 0.34
Weekly - 0.28 0.33
Monthly - - 0.39
United Utilities Daily 0.24 0.28 0.33
Weekly - 0.26 0.32
Monthly - 0.37
SVT/UU Daily 0.24 0.28 0.33
Weekly - 0.27 0.32
Monthly - - 0.38
PNN/SVT/UU Daily 0.25 0.29 0.34
Weekly - 0.29 0.34
Monthly - - 0.39 Source: Thomson Reuters, Europe Economics’ calculations.
Beta and the cost of equity
- 55 -
Table 5.5: Summary of unlevered beta estimates (spot at 28-February-2019) based on ARCH/GARCH
Company Data frequency 1-yr trailing
average
2-yr trailing
average
5-yr trailing
average
Severn Trent Daily 0.27 0.31 0.33
Weekly - 0.28 0.30
Monthly - - 0.36
United Utilities Daily 0.24 0.27 0.31
Weekly - 0.28 0.31
Monthly - 0.31
SVT/UU Daily 0.26 0.29 0.32
Weekly - 0.29 0.31
Monthly - - 0.33
PNN/SVT/UU Daily 0.27 0.30 0.33
Weekly - 0.30 0.32
Monthly - - 0.35 Source: Thomson Reuters, Europe Economics’ calculations.
5.6.1 Conclusions on unlevered betas
Having estimated betas based on data of different frequency and time windows of different length, we note
that:
Betas based on shorter windows (e.g. 1-year) are more responsive to information from the recent events
but — being based on relatively small sample sizes — they run the risk introducing uninformative
volatility.
Betas based on longer time windows (e.g. 5-years) are less prone to uninformative volatility but contain
a higher proportion of relatively old information and therefore have a higher risk of being obsolete and
not appropriate for the purpose of forming a forward looking view on systemic risk.
There is no mechanistic way to determine a precise optimal window. Our preference, based on past
experience and the considerations above, is for daily betas obtained on two year trailing windows as they
provide a good trade-off between the need of reflecting up-to-date information whilst minimising the risk of
uninformative volatility. Daily data has a clear advantage in terms of the number of data points, and utilities
stocks tend to be traded sufficiently frequently that thin-trading liquidity issues biasing values down at daily
frequencies tend to be limited. We have found that one-year asset betas can move up and down in ways that
appear uninformative, since movements in one direction are frequently not sustained but, instead reversed.
Nonetheless, one-year betas do provide some indication as to the mathematical tendency for future two-
year beta shifts (if the one-year beta is above the two-year beta the two-year beta may tend to rise48). Betas
of more than two years include rather old data, of increasingly diminishing relevance the longer the data used.
Indeed, five-year daily data will include data from the previous price control period, and both the evolving
nature of risk through time and changes in the regulatory framework49 imply that it is preferable to focus on
more recent data. Whole-year data reduces the potential that sub-yearly data windows could introduce
some form of seasonal or date-based bias.
We are not persuaded by arguments that utilities betas should be expected to be invariant over the very
long-run (see Appendix 8.1.2, for details). We suggest placing the most weight upon the most recent data,
48 This is not quite mathematically certain, since it is possible that the one-year beta more than one year ago was higher
than the two-year beta is now. But there is at least some broad tendency of this sort, since the one-year equity beta
is based on half of the two year equity beta data. 49 For example, since PR14 there have been two key changes in Ofwat’ s regulatory policy, i.e. a movement from a
price control to a revenue control (with revenue reconciliation adjustment), and the introduction of totex control.
Beta and the cost of equity
- 56 -
subject to some common-sense consideration of whether data on any particular day immediately prior to
the decision exhibits some unusual volatility.
Although data is available for Pennon, Pennon includes a large proportion of non-regulated water assets.
Consequently we place most weight on the betas of the portfolio composed of Severn Trent and United
Utilities (i.e. SVT/UU). We have nonetheless cross-checked our results adding in Pennon in proportion to
its asset size and doing so would not fundamentally change our results (i.e. the betas for PNN/SVT/UU are
fairly similar to those for SVT/UU).
Therefore, based on the discussion above, we place most weight on the 2-year OLS daily beta estimates of
SVT/UU, with some weight on the OLS 1-year and some consideration of the OLS 5-year along with GARCH
figures as cross-checks. We also note the point raised in Section Error! Reference source not found.
that because the SVT regulatory fair value gearings are higher than the enterprise value gearings, the SVT
unlevered betas may be overstated by perhaps up to 1bps.
These give:
An unlevered beta of 0.28 based on OLS as our preferred estimate.
Cross-checks of 0.24 for 1-year and 0.33 for 5-year.
Crosschecks based on GARCH of 0.29 for 2-year, 0.26 for 1-year and 0.32 for 5 year.
Crosscheck based on regulatory fair value gearing
The evidence from the cross-checks is strongly consistent with our preferred estimate. Indeed, if we had
used the average from amongst our cross-checks we would obtain a value of 0.288. Accordingly, we use
0.28 as our unlevered beta point estimate. We propose an unlevered beta range of 0.26-0.30.
5.7 Debt betas
5.7.1 Evidence based on decomposition approach
The decomposition approach is based on the formula presented in Section 5.2.6, and which we report again
below.50
βD = (1— prob(default)) ⋅ (debt premium − liquidity risk premium) — prob(default) ⋅ (RFR + % loss given default)
ERP
The values of the inputs used to populate the formula above are as described below:
Risk-free rate — average yields between of 10-years and 20-years nominal gilts (consistently with our
risk-free rate analysis).
ERP — the difference between 5-years trailing average of the returns produced by our DGM of Section
4.6 (expressed in nominal terms) and the nominal risk-free rate.
Debt premium — this is calculated as the spread between the average nominal yield of A/BBB 10-year+
iBoxx non-financial indices (this is the same index we use to estimate the cost of debt, see Section 6) and
the nominal risk free rate. Consistent with the methodology used for the cost of debt, the spread has
been also adjusted by subtracting 25bps to account for water companies’ outperformance (see Section
6.2.2).
Liquidity risk premium — is assumed to be 30bps as per estimates by the Bank of England.51
50 It is worth noting that the approach used by the Competition Commission (CC) in 2007 included an allowance for
a “liquidity premium”. Consistently with the approach used by the CC in 2007 we have also added a liquidity premium
to the formula. 51 https://www.bankofengland.co.uk/-/media/boe/files/financial-stability-report/2014/june-2014.pdf
Beta and the cost of equity
- 57 -
Percentage loss given default — this is assumed to be 20 per cent.52
The probability of default — this is 0.2 per cent and is based on the (rounded) median value of default
probability in the utilities sector as per S&P 2018 Global Corporate Default Study.53
The resulting debt beta series is reported in the chart below.
Figure 5.19: Debt beta obtained through the decomposition approach
Source: Thomson Reuters, and Europe Economics’ calculations.
As we can see from the figure above, since 2010 the debt beta we obtained through the calibrated
decomposition approach ranges broadly between 0.10 and 0.25 and, as of 28 February 2019, has a value of
0.18. The two-years trailing average ranges broadly between 0.125 and 0.175, and as of 28-February-2019
has a value of 0.15 (i.e. in the middle of the 0.125-0.175 range).
5.7.2 Evidence based on regression approach
We start by providing evidence on the debt beta obtained through the regression approach. First, for a
general insight into the developments in debt betas on UK investment-grade corporate sector bonds (below
we consider water sector bonds in particular) we have regressed the average returns of the iBoxx Non-
financial 10-year+ A/BBB index54 on the total returns on the UK FTSE All Share index. As we did for raw
equity betas, we have estimated debt betas for different time horizons (1-year, 2-year and 5-year) and for
different data frequencies (daily, weekly and monthly). The results are reported in the charts below.
52 The 20 per cent is a typical estimate of “costs of bankruptcy” across many sectors. There would be almost no
difference to the results if, for example, loss given default were to be 10 per cent. 53 S&P Global (2019), "2018 Annual Global Corporate Default Study And Rating Transitions" available at:
https://www.spratings.com/documents/20184/774196/2018AnnualGlobalCorporateDefaultAndRatingTransitionStud
y.pdf 54 This is calculated as the average between the returns of the iBoxx A 10-year+ non-financial index and the returns of
the iBoxx BBB 10-year+ non-financial index. Placing equal weight on the two indices is consistent with the approach
we take for estimating the cost of debt (see relevant Section on the cost of debt).
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Debt beta Debt beta (2yr trailing average)
Beta and the cost of equity
- 58 -
Figure 5.20: iBoxx A/BBB debt betas based on daily data regressions
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.21: iBoxx A/BBB debt betas based on weekly data regressions
Source: Thomson Reuters, Europe Economics’ calculations.
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Debt beta iBoxx A/BBB index (5yr Daily)
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Beta and the cost of equity
- 59 -
Figure 5.22: iBoxx A/BBB debt beta based on monthly data regression
Source: Thomson Reuters, Europe Economics’ calculations.
As we can see from the charts above, the values of debt beta vary considerably across the different charts,
and are often negative. This is not surprising since a well-known weakness of the regression approach is that
it produces estimates that are very sensitive to the time horizon and data frequency chosen.
We have also applied the regression approach to water bonds. We have selected 21 water bonds55 based
on the following criteria.
They have more than ten years to maturity (so as to ensure comparability with the iBoxx analysis
conducted before).
They have been traded for at least 1500 days since January 2012 (this ensures that the instrument are
traded frequently and that betas can be estimated also on a time horizon of five years).
They are sterling denominated.
They are plain vanilla fixed-coupon bonds.
They have an investment-grade credit rating.
The average debt beta across all water bonds considered are reported below, again for different time
horizons and data frequencies.
55 These water bonds are distributed across water companies as follows: Affinity Water (2 bonds), Northumbrian
Water (1 bond), Severn Trent (1 bond), South East Water (2 bonds), Southern Water (5 bonds), Sutton and East
Surrey Water (1 bond), Thames Water (3 bonds), Wessex Water (1 bond), Yorkshire Water (5 bonds).
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Jan-1
9
Beta and the cost of equity
- 60 -
Figure 5.23: Average water bonds’ debt beta based on daily data regressions
Source: Thomson Reuters, Europe Economics’ calculations.
Figure 5.24: Average water bonds’ debt beta based on weekly data regressions
Source: Thomson Reuters, Europe Economics’ calculations.
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Beta and the cost of equity
- 61 -
Figure 5.25: Average water bonds’ debt beta based on monthly data regressions
Source: Thomson Reuters, Europe Economics’ calculations.
Table 5.6: Summary of debt beta estimates (spot at 29-February-2019)
Instruments Data frequency 1-yr trailing
average
2-yr trailing
average
5-yr trailing
average
iBoxx A/BBB Daily -0.06 -0.01 -0.08
Weekly 0.08 0.03
Monthly 0.4
Water bonds Daily -0.05 -0.03 -0.11
Weekly 0.01 -0.04
Monthly 0.28 Source: Thomson Reuters, Europe Economics’ calculations.
If we calculate the average across all debt beta estimates of Table 5.6 we obtain a debt beta value of 0.04.
However, the average across all non-negative debt beta (excluding negative debt beta on the grounds that
the true values of debt betas are unlikely to be negative) estimates of Table 5.6 is 0.16.
It is worth noting that the regression approach has been subject to a range of criticisms. These include:
Concerns about the high level of volatility of results — for example, we see here that even for the iBoxx-
based data the regressions are fairly often negative and exhibit quite a large range given what one would
expect to be the fairly stable nature of utilities bonds;
Inability to distinguish robustly from zero — as well as point estimates being volatile, confidence intervals
tend to encompass zero.56
To these poor statistical properties of the regressions, the Competition Commission, when it considered
debt betas in its key recommendation of 200757, added the following:
56 The importance of this criticism is easy to overstate. If we observed 100 point estimates, independently observed,
each of which had a 95 per cent confidence interval of -0.1 to +0.2, and each has a point estimate of +0.05, the
probability of the true value being zero or below would be less than 10-18 per cent. Of course, the first criticism tells
us that it is not true that we always obtain a positive regression debt beta — so thus far we have merely repeated
the point about volatility of observations in a more technical form. But by itself, all this criticism really adds is that
one should be circumspect in placing high weight on simply the latest point estimate. 57 See p F24, paragraph 92, of https://webarchive.nationalarchives.gov.uk/20140402235745/http:/www.competition-
commission.org.uk/assets/competitioncommission/docs/pdf/non-inquiry/rep_pub/reports/2007/fulltext/532af.pdf
This judgement was particularly influential since it was the first time the CC had considered the question of whether
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Average (5yr Monthly)
Beta and the cost of equity
- 62 -
“the relatively poor quality of the data that we have on returns to debt holders”
“the difference between historical and assumed [regulatory period] gearing levels”
“thin trading… [which] affect[s] debt beta estimates more seriously than equity beta estimates even for
large firms”.
The Competition Commission stated “These factors have led us to favour the indirect, decomposition
method, where we can be much more confident that we are correctly observing how much compensation
lenders are asking for in exchange for bearing systematic risk.” It went on to recommend a decomposition
approach.
5.7.3 Conclusions on debt beta
The regression approach we have carried out suggest that, on average, debt beta estimates range between
0.04 (this is the average across all debt beta estimates) and 0.16 (this is the average across all non-negative
debt beta estimates). The decomposition approach indicates that daily debt beta tend to range between 0.1
and 0.25, whilst the two-years trailing average falls within a narrower band of around 0.125-0.175. As of 28-
February-2019 the value of the debt beta obtained with the decomposition approach is 0.18, whilst the value
of the two-years trailing average value is 0.15. Taking this evidence altogether, we recommend a debt beta
range of 0.1-0.17, with a point estimate of 0.15.
5.8 Summary of findings on asset beta
Based on the unlevered beta recommendations set out in 5.6.1, the debt beta recommendations set out in
5.7.3, and the market gearing (i.e. the 2-year trailing average ND/EV for SVT/UU) presented in Error!
Reference source not found., the asset beta range we propose is 0.31-0.39 with a point estimate
of 0.36 (see table below).
Table 5.7: Asset beta range and point estimate
Low High Point estimate
Unlevered beta 0.26 0.30 0.28
Market gearing 54.7% 54.7% 54.7%
Debt beta 0.10 0.17 0.15
Asset beta 0.31 0.39 0.36
Thomson Reuters, Europe Economics’ calculations.
5.9 Re-levering to obtain the notional equity beta
5.9.1 Re-levering asset beta into equity beta
Now the appropriate asset beta value, 𝛽𝐴, has been determined, we need to use it to obtain a notional equity
beta, 𝛽𝐸𝑁, through a re-levering exercise which makes use of a notional gearing level. That uses the following
formula:
it was appropriate to use a non-zero debt beta and the first full debate about whether the debt beta should be non-
zero in UK regulation. It is also key in that all subsequent UK regulatory analyses of debt beta have appealed to it as
an authority.
Beta and the cost of equity
- 63 -
𝛽𝐸𝑁 =𝛽𝐴 − 𝑔𝑁𝛽𝐷
(1 − 𝑔𝑁),
where 𝑔𝑁 is the notional gearing for the regulated entity. The value of debt beta will directly affect the asset
betas and the re-levered equity betas. Gearing is denoted 𝑔, and is calculated on the basis of companies’ net
debt to enterprise value. The notional gearing level, used to re-lever asset betas into notional equity beta, is
denoted by 𝑔𝑁. These steps required to calculate the notional equity beta starting from the raw equity beta
are summarised in the diagram below.
Figure 5.26: Calculations to obtain notional equity beta from raw equity beta
Source: Europe Economics
5.9.2 Notional enterprise value gearing — an RCV premium?
The notional gearing should be understood as the enterprise value gearing58 of the notional entity. Typically
regulators operate on the basis that the enterprise value of the notional entity is equal to the regulated asset
value / regulatory capital value (RCV). That means that for the notional entity there is no distinction between
its regulatory book value and its enterprise value — they are identical by definition.
One reason that is important to recognise is because when the notional entity is re-levered at a level of
gearing expressed in terms of net debt to RCV, that does not mean the entity’s equity beta, having been de-
levered at an enterprise value, is then re-levered according to a book value instead — introducing a potential
source of inconsistency into the process. Rather, it is de-levered at an actual enterprise value gearing and re-
levered at a notional enterprise value gearing.
58 Or perhaps more strictly, the regulatory fair value gearing. But hereafter we shall elide this distinction for the
purposes of the present discussion.
Beta and the cost of equity
- 64 -
A second reason that is important to recognise is that a regulator might not choose to assume that the
notional entity’s enterprise value is equal to its RCV. For example, one option would be to assume some
level of totex outperformance or the meeting of other incentive thresholds, producing an enterprise value
premium to the RCV. That would imply a lower level of enterprise value gearing. There might be implications
for depreciation and for the aggregate allowance for debt costs under such a model, but let us focus here
upon the implications for the notional equity beta. Because the notional gearing level would be lower, the
notional equity beta at that lower notional gearing would be likewise lower. Below we shall illustrate the
quantitative impact on the equity beta of this approach under two illustrative cases: one in which the assumed
RCV premium is 5 per cent and one in which it is 10 per cent.
5.9.3 Equity beta at the notional gearing level
Consistently with the view expressed by Ofwat in its Final Methodology, we calculate the equity beta at a
notional gearing level of 60 per cent. This results in a notional equity beta range of 0.64-0.73 with a
point estimate of 0.68.
Table 5.8: Notional equity beta range and point estimate
Low High Point estimate
Asset beta 0.31 0.39 0.36
Notional gearing 60% 60% 60%
Debt beta 0.10 0.17 0.15
Notional Equity beta 0.64 0.73 0.68
Source: Thomson Reuters, Europe Economics calculations.
We note that this point estimate of notional equity beta in the table above (0.68) is higher than the raw
equity beta for (0.62 i.e. the two-year daily beta of SVT/UU). This reflects the fact that the notional gearing
value of 60 per cent is higher than the market value gearing (54.7 per cent) used to calculate the unlevered
beta. In fact, if we assumed a zero debt beta, the difference between the raw equity beta and the notional
equity beta would be even larger.59 The presence of non-zero debt beta partially offset the impact of gearing
and decreases the gap between the value of raw and notional equity beta.60
5.10 Overall cost of equity
Based on the risk-free rate recommendation set out in Section 3.5, the TMR recommendation set out in
Section 4.7, and the gearing and beta figures presented in Table 5.7 and Table 5.8:
The post-tax nominal cost of equity range is 5.73-7.17 per cent, with a point estimate of 6.45
per cent.
The post-tax CPI-deflated cost of equity range is 3.66-5.07 per cent, with a point estimate of
4.36 per cent.
59 If debt beta was zero, then the asset beta would be identical to the unlevered beta (i.e. the asset beta would be 0.28),
and the notional-equity beta would be 0.7 (0.7=0.28/(1-60%)). 60 By way of illustration, if we assumed an RCV premium of 5 per cent, the notional gearing would fall from 60 per cent
to 57.1 per cent and the point estimate for the notional equity beta at a gearing of 57.1 per cent would be 0.64. If
we assumed an RCV premium of 10 per cent, the notional gearing would fall from 60 per cent to 54.5 per cent and
the notional equity beta at 54.5 per cent gearing would be 0.62.
Beta and the cost of equity
- 65 -
Table 5.9: Post-tax cost of equity
Nominal CPI-deflated
Low High Point
estimate Low High
Point
estimate
Risk-free rate 1.54% 1.92% 1.81% -0.45% -0.08% -0.19%
TMR 8.12% 9.14% 8.63% 6.00% 7.00% 6.50%
ERP 6.58% 7.22% 6.82% 6.45% 7.08% 6.69%
Raw equity beta 0.57 0.66 0.62 0.57 0.66 0.62
Market gearing 54.70% 54.70% 54.70% 54.70% 54.70% 54.70%
Unlevered beta 0.26 0.30 0.28 0.26 0.30 0.28
Debt beta 0.10 0.17 0.15 0.10 0.17 0.15
Asset beta 0.31 0.39 0.36 0.31 0.39 0.36
Notional gearing 60% 60% 60% 60.0% 60.0% 60.0%
Notional equity beta 0.64 0.73 0.68 0.64 0.73 0.68
Cost of equity (post tax) 5.73% 7.17% 6.45% 3.66% 5.07% 4.36%
Cost of debt
- 66 -
6 Cost of debt
6.1 Introduction
Ofwat’ cost of debt is estimated as a weighted average between the cost of embedded debt and the cost of
new debt. In its Final Methodology Ofwat assumed the ratio of embedded to new debt being 70:30.
Embedded debt and new debt are calculated through two separate approaches.
Embedded debt — Ofwat applies a fixed approach (i.e. without indexation) to embedded debt. In its
Final Methodology the cost of embedded debt was estimated based on debt instruments contained in
the companies’ balance sheets, and its value was determined by the company-level median value within
the water sector.
New debt — the approach to new debt includes an indexation mechanism where the value of new debt
is referenced to the evolution of the non-financial iBoxx indices. The benchmark index proposed in
Final Methodology was a 50:50 mix of A and BBB non-financial iBoxx indices with a tenor of 10 years or
more. In its Final Methodology Ofwat deducted 15bps to the average yield value of this benchmark to
reflect the evidence that, on average, water companies tend to outperform against the index.
This document sets out an updated view on the cost of debt and is organised as follows:
Section 6.2 sets out sets out our proposed methodology for estimating the cost of embedded debt.
Section 6.3 provides evidence on the appropriate ratio of new debt to embedded debt.
Section 6.4 sets out the methodology for the cost of new debt and its estimation.
Section 6.5 sets out the overall cost of debt.
6.2 Cost of embedded debt
The main objective when estimating the cost of embedded debt is to determine the allowance for debt that
is on the balance sheet at the start of the 5 year period and is expected to still be there in 2025. This can be
done following two alternative approaches:
Balance sheet approach — the estimation is based on the cost of debt instruments contained in the
companies’ balance sheets. Since companies have access to a variety of debt instruments, under this
approach it is necessary to review debt instruments in order to so as to include only ‘pure debt’ which
a notionally geared company might issue. This implies excluding, for example, swaps (as these are part
of company risk management activity and should not be reflected into a notional structure), liquidity
facilities, and instruments with equity like characteristics (e.g. preferred shares). Therefore, whilst this
approach has the merit of reflecting companies’ actual financing costs, it is inevitably prone to judgment
errors (e.g. erroneous exclusion/inclusion of debt instruments that do not reflect a notional pure-debt
structure).
Benchmark index approach — the estimation is based on an external benchmark index. The comparative
advantage of this approach relative to the balance sheet approach is that it is less reliant on sector
efficiency to derive a stretching benchmark. Furthermore, it allows a more transparent estimation and
assessment of companies’ potential outperformance or underperformance against the benchmark.
We present cost of embedded debt estimates based on both approaches.
Cost of debt
- 67 -
6.2.1 Cost of embedded debt based on the balance sheet approach
While we agree in principle that some non-standard instruments might be inefficiently acquired, identifying
debt that was not efficient at the time of issuance is not a straightforward task. However, we decided to
exclude all non-standard instruments as it is not possible to compare such instruments against a benchmark
and to form a view on whether these have been acquired efficiently.
The balance sheet approach requires some judgment in relation to the debt instruments to include for the
assessment of a notional debt structure. A notional company will have a range of instruments but some of
these will might have been under circumstances that are unique to individual companies under their actual
structure. Therefore, we have only pure-debt instruments and the average interest rate has been calculate
after excluding the following:
Swaps (apart from cross-currency swaps);
Credit facilities;
Overdrafts;
Irredeemable debentures;
Debenture stocks;
Preference shares;
Callable debt.
Other non-standard debt’ which includes class B debt and collateral borrowing.
In addition to excluding the instruments listed above, modifications were applied to the cost of borrowing
though the Artesian facility. The Artesian Finance facility was set up by the Royal Bank of Scotland in 2002
and was designed to serve the financing needs of small water companies. As a result, a significant portion of
WoCs financing is comprised of long term Artesian debt. As was done in PR14, we adjust downwards the
nominal cost of Artesian debt and calculate the effective cost of debt in relation to the proceeds received,
because the nominal cost of Artesian debt (which is typically higher than other more traditional debt
instruments) does not reflect the effective cost of debt incurred, as the proceeds received from issuance (i.e.
the cash made available to companies) for such schemes tend to be higher than the par value (i.e. amount of
money that companies agree to repay) and therefore the nominal rate tends to overestimate the effective
cost of debt. A similar modification (in which we reinstated the instruments effective interest cost) was
applied also to instruments that were issued materially above or below par value.
Finally, for debt instruments maturing prior to the start of PR19 (i.e. prior to 1 April 2020), and thus
embedded by the time the price control will begin, a refinancing assumption was applied, with the refinancing
cost of debt calculated on the basis of the spot value of the average yields of the iBoxx non-financial A/BBB
index (see Section 6.2.2 and Section 6.4 for details on how the index is constructed) and the market-implied
increase in interest rates.61
The company-level nominal cost of debt at 31 March 2020 for pure-debt debt instruments (i.e. after the
exclusion of the debt instruments listed above, and after effective interest costs adjustments) that will remain
embedded at 31 March 2025, is provided in the chart below.
61 The market implied increase in interest rate used is 3pbs and is calculated as the average between the rate increase
implied on10-year nominal gilts yields at April 2020 (which is 13bps as per Table 3.2) and the rate increase implied
on 20-year nominal gilts yield at April 2020 (which is -8bps as per Table 3.2).
Cost of debt
- 68 -
Figure 6.1: Assessment of the nominal cost of embedded
Source: Ofwat, and Europe Economics’ calculations.
In the table below we report the median cost of debt embedded across companies, the arithmetic average
cost of embedded debt across companies62, and the debt-instruments weighted average cost of embedded
debt within the water sector, where the average is weighted by the principal issue amount.
Table 6.1: Weighted average, average and median cost of embedded
Weighted average Arithmetic average Median
Water sector 4.25% 4.63% 4.65%
WaSCs & Large WoCs 4.23% 4.25% 4.45%
Small WoCs 5.60% 5.76% 5.47%
Source: Analysis of PR19 Business Plan data.
6.2.2 Cost of embedded debt based on the benchmark index approach
The key methodological aspects to be considered here are:
The choice of the benchmark index
The time horizon over which historical costs are estimated
How to assess of any potential outperformance or underperformance against the chosen index
With regard to the choice of the index, we propose using the same index used for determining the cost of
new debt, i.e. 50:50 mix of A-rated and BBB-rated UK non-financial iBoxx indices with a tenor of 10 years or
more. We refer to the index so constructed as iBoxx Non-Financials A/BBB index. With regard to the time-
62 This is the arithmetic average across companies, with the cost of embedded debt of each company being calculated
as a weighted average with weights proportional to the debt instruments’ amounts.
6.8%
5.5% 5.4% 5.3%
4.9% 4.8% 4.7% 4.7% 4.6% 4.5%4.4% 4.4% 4.3%
3.8% 3.8%
2.2%
0%
1%
2%
3%
4%
5%
6%
7%
8%
PRT BRL SES SSC SRN SEW WSH YKY ANH AFW TMS NES WSX SVH UUW SWB
Cost of debt
- 69 -
horizon to estimate historical costs, it is important to choose a trailing average that is representative of the
sector’s issuance profile. As we can see from the chart below, around 80 per cent of the water sector’s
embedded debt was issued over the past 15 years, and the largest increase in debt issuance (around 36 per
cent of all debt issued) took place between 2005-2010. The conclusions we draw from this is that a 20-years
trailing average would be too long — as it would reflect interest cost paid on a relatively small proportion
(20 per cent) of debt issued — and a 10-year trailing average would be too short — because it would account
for only 50 per cent of the debt issued and it would not cover the period 2005-2010 in which debt issuance
was more prevalent. Based on these considerations, we think that a 15-years trailing average is sufficiently
representative of the sector’s issuance profile, and the interest costs that prevailed at the time of issuance.
Therefore we propose using 15-year trailing average (with a 10-year trailing average used as a cross-check).
Figure 6.2: Cumulative debt issuance by year in the water sector
Source: Analysis of PR19 Business Plan data.
When assessing water companies’ financing performance against the benchmark index, we decided to focus
on bonds instruments, making a distinction between bonds with short tenure (maturity at issuance of less
than 10 years) and bonds with a longer tenure (maturity at issuance of more than 10 years).
We start by reporting below the evolution of the iBoxx non-Financials A/BBB index together with the 10-
year and 15-year trailing averages. Since the cut-off date for this report is 28 February 2019, the iBoxx
A/BBB index values for the period 1-March-2019 to 31-March-2020 have been forecasted as follows:
The spot value of the iBoxx average A/BBB index at 28-February is around 3.30 per cent.
The average market implied increase in interest rate on 10-year nominal gilts yields in April 2020, as
recorded in February 2019, is 13bps (see Table 3.2), whilst the average market implied increase in
interest rate on 20-year nominal gilts yields in April 2020, is -8bps (see Table 3.2). Thus, the average
market implied increase in interest rate between 10-year and 20-year nominal gilts is 2.5bps.
We have then added 2.5bps to the iBoxx A/BBB index spot value at 28-February-2019 to infer the
value of the index in April 2020 (i.e. 3.33 per cent), and we have interpolated linearly the values in
between these dates.
0%
20%
40%
60%
80%
100%
120%
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
Cost of debt
- 70 -
Figure 6.3: Evolution of the iBoxx A/BBB index (with values forecasted up to April 2020)
Source: Thomson Reuters, Band of England, and Europe Economics’ calculations.
The forecasted values of the iBoxx A/BBB index and the 10-year and 15-years trailing averages as of April
2020 are reported in the table below.
Table 6.2: IBoxx A/BBB values in April 2020
Values at 1 April 2020
iBoxx A/BBB spot value (forecast) 3.33%
iBoxx 10yr trailing average 4.10%
iBoxx 15yr trailing average 4.77%
Source: Thomson Reuters, Bank of England, and Europe Economics’ calculations.
We conclude this section with an assessment of companies’ outperformance/underperformance relative to
the iBoxx A/BBB index. We report below the values of water bonds’ nominal yield-at-issuance in relation to
the nominal yield of the iBoxx A/BBB index. Figure 6.4 and Figure 6.5 exclude index-linked bonds, and
floating-rate bonds.
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
iBoxx Non-Financials 10+ A/BBB iBoxx Non-Financials 10+ A/BBB (Forecast)
iBoxx Non-Financials 10+ A/BBB (10yr trailing average) iBoxx Non-Financials 10+ A/BBB (15yr trailing average)
Cost of debt
- 71 -
Figure 6.4: Water bonds’ performance relative to iBoxx A/BBB index (2000-2019)
Source: Ofwat analysis of IHS Markit data
Figure 6.5: Water bonds’ performance relative to iBoxx A/BBB index (2015-2019)
Source: Ofwat analysis of IHS Markit data
We can see from the charts above that, on average, water companies’ bonds have outperformed the iBoxx
A/BBB index. Unsurprisingly the outperformance is higher for bonds with less than 10 years of maturity (this
is likely to be due to the fact that shorter maturities are associated with lower yields). The average
outperformance relative to the iBoxx index is summarised in the table below where (for the period 2000-
2019, the period 2010-2019 and the period 2015-2019) we report the average outperformance across bonds,
the median outperformance, and the weighted average performance with weights proportional to the
amounts issued.
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
7.00%
8.00%
9.00%
iBoXX A/BBB Bonds <10yrs Bonds >10yrs
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
4.50%
5.00%
iBoXX A/BBB Bonds <10yrs Bonds >10yrs
Cost of debt
- 72 -
Table 6.3: Summary of nominal water bonds’ outperformance relative to the iBoxx A/BBB index
Tenor of debt Period Arithmetic
average Median Weighted average
Whole sample 2000-2019 -0.55% -0.49% -0.54%
Less than 10yr 2000-2019 -1.23% -1.22% -1.28%
More than 10yr 2000-2019 -0.50% -0.43% -0.46%
Whole sample 2010-2019 -0.36% -0.41% -0.46%
Less than 10yr 2010-2019 -1.15% -1.22% -1.16%
More than 10yr 2010-2019 -0.21% -0.30% -0.27%
Whole sample 2015-2019 -0.54% -0.49% -0.69%
Less than 10yr 2015-2019 -1.22% -1.24% -1.21%
More than 10yr 2015-2019 -0.37% -0.43% -0.43%
Source: Ofwat analysis of IHS Markit data.
We place most weight on bonds with maturity of more than 10 years as this is consistent with our use of
the iBoxx 10+ year benchmark, with the risk-free rate evidence based on the average yield of 10-year and
15-years gilts, and moreover it decreases the potential for refinancing risk arising as a result of companies
issuing debt at excessively short horizons. There is a case for excluding index-linked debt because, due to
the potential presence of a liquidity premium in index-linked debt (as discussed in Section 2), there is a risk
of obtaining distorted outperformance estimates. In the table below we therefore report the historical wedge
for nominal fixed-rate bonds with a tenor greater than ten years.
Table 6.4: Historical outperformance of water sector bonds against the iBoxx (fixed rate debt, >10yrs
tenor at issuance)
Year No. of instruments Average wedge vs iBoXX A/BBB at
issuance (bps)
2000 2 6
2001 3 34
2002 4 46
2003 6 32
2004 4 35
2005 5 44
2006 4 29
2007 3 60
2008 n/a n/a
2009 8 61
2010 1 -51
2011 1 8
2012 5 27
2013 4 13
2014 1 48
2015 n/a n/a
Cost of debt
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Year No. of instruments Average wedge vs iBoXX A/BBB at
issuance (bps)
2016 8 44
2017 5 39
2018 1 50
2019 1 65
Average 33
Source: Thomson Reuters, Ofwat.
The average outperformance wedge for the class of debt providing the most robust indication (i.e. fixed-rate
debt), when such debt is of over 10 years tenor at issuance, has been 33 bps. The average across over-ten-
year bonds since 2010 (arguably the most relevant period since it cover the period after the 2008/09 financial
crisis and that of the two most recent price control periods) is 27 bps on a weighted average basis and a
lower 21bps on an arithmetic average basis.63 Overall, 25 bps appears to be a reasonable conservative
estimate.
6.2.3 Conclusion on the cost of embedded debt
We summarise the evidence on the cost of embedded debt obtained using different approaches in the table
below.
Table 6.5: Nominal cost of embedded debt
Estimation approach Nominal cost of embedded debt
Companies’ balance sheet (water sector)
- Weighted average 4.25%
- Arithmetic average 4.63%
- Median 4.65%
Benchmark with outperformance adjustment of 25bps
- 10yr trailing average 3.85%
- 15yr trailing average 4.52%
Source: Thomson Reuters, Ofwat, Bank of England, and Europe Economics’ calculations.
As we can see the 15-years trailing average of the iBoxx A/BBB index (adjusted for companies’
outperformance) gives a value which is consistent with the cost observed from the companies’ balance sheets.
More specifically, the value of 15-year iBoxx trailing average (4.52 per cent) sits broadly between the weighted
average value (4.25 per cent) and the median value (4.65 per cent) obtained under the balance sheet approach,
and is only slightly lower that the companies’ average value (4.63 per cent) under the balance sheet approach.
We recommend using a value of 4.52 per cent for the nominal cost of embedded debt, with a range
of between 4.25 per cent (the weighted average under the balance sheet approach) and 4.65 per cent
(the median under the balance sheet approach).
63 One interpretation of the wedge is that it is a tenor effect. The average tenor for actual debt costs in the water
sector is now around 15 years. By contrast, the tenor of iBoxx A/BBB, as of February 2019, is around 21 years.
Therefore it is possible that, at least a portion of the wedge we observe might be due to differences in debt tenor.
Cost of debt
- 74 -
6.3 Ratio of new to total debt
The ratio of new to total debt has been calculated based on business plan submissions for each year of the
PR19 price control (from 2020/21 to 2024/25) as the ratio of new debt stock over total debt stock where:
New debt stock is the cumulative amount of new debt issued from 2020/21 onwards.
Total debt is the sum of new debt stock and embedded debt stock, where embedded debt stock is the
previous year figure of embedded debt plus indexation for index-linked debt instruments minus debt
repaid.
The ratio of new debt to total debt for each company across the 2020/21 to 2024/25 period is reported in
the chart below.
Figure 6.6: Ratio of new to total debt (average across the PR19 period)
Source: Ofwat, and Europe Economics’ calculations.
The simple average ratio of new debt to total debt across the companies (i.e. the average across the figures
reported in the chart above) is 17 per cent. The industry average split (across the PR19 period) is 22 per
cent. In the chart below we report also the industry weighted average split for each year of the price control.
28% 28%26%
25%24% 24%
22%
16%15%
14%12%
11%9%
8%
5%
2%
0%
5%
10%
15%
20%
25%
30%
SWB SVH WSX TMS ANH WSH YKY UUW NES SSC SRN SES SEW PRT AFW BRL
Cost of debt
- 75 -
Figure 6.7: Evolution of the industry weighted average ratio of new to total debt over the price control
period.
Source: Ofwat, and Europe Economics’ calculations.
For the purpose of calculating the overall cost of debt we propose a split of new debt to embedded debt
of 20:80.
6.4 Cost of new debt
In its Final Methodology, Ofwat’s approach to new debt includes an indexation mechanism whereby the value
of new debt is referenced to the evolution of non-financial iBoxx indices, and then there is a truing-up
reconciliation at PR24. More specifically, as a draft for the assumption that will be required in setting the
PR19 determination, the Final Methodology uses a benchmark index which is calculated as the simple average
between the following indices:
The iBoxx 10+ Non-financial index A — an index based on A-rated bonds of non-financial companies with
maturity of at least 10 years.
The iBoxx 10+ Non-financial BBB index — an index based on BBB-rated bonds of non-financial companies
with maturity of at least 10 years.
We refer to the synthetic index calculated as the simple average between the two indices listed above as
iBoxx non-Financial A/BBB index. We propose calculating the cost of new debt using the same synthetic
index. The evolution of the yields of the two iBoxx indices listed above, and that of the synthetic A/BBB
index (are reported below.
0%
5%
10%
15%
20%
25%
30%
35%
40%
2020-21 2021-22 2022-23 2023-24 2024-25
Cost of debt
- 76 -
Figure 6.8: Evolution of the iBoxx non-Financials indices
Source: Thomson Reuters and Europe Economics’ calculations.
The table below provides the spot values of the indices at 28-February-2019 and some summary statistics
(i.e. the average, minimum, and maximum values recorded of over the previous six months).
Table 6.6: Summary of evidence from iBoxx non-financial indices
Spot at 28-
Feb- 2019
Average over
the previous 6
months
Min. over the
previous 6
months
Max. over the
previous 6
months
iBoxx 10+ Non-financial, A 3.12% 3.26% 3.01% 3.49%
iBoxx 10+ Non-financial, BBB 3.48% 3.58% 3.35% 3.82%
iBoxx 10+ Non-financial, A/BBB 3.30% 3.42% 3.19% 3.65%
Source: Thomson Reuters and Europe Economics’ calculations.
For the cost of new debt, given the indexation mechanism and the truing process, there is no need for a
range — only a point estimate is required. For the purpose of determining that point estimate we place most
weight on the spot value of 3.30 per cent, then apply the following adjustments. Since future movements in
the yields of the iBoxx A/BBB index are likely to match movements in gilts yields very closely, we uplift the
spot yield by 31bps, i.e. the same market-implied rate increase in AMP7 that we used for the risk-free rate
(see Section 3.4). Finally, we deduct 25bps to reflect the evidence that water companies tend to outperform
the iBoxx index (as set out in Section 6.2.2). 3.30 + 0.31 – 0.25 = 3.36. Accordingly, our estimate for the
nominal cost of new debt is 3.36 per cent.
Table 6.7: Nominal cost of new debt
Spot value of iBoxx A/BBB 3.30%
Market implied rate change in
AMP7 0.31%
Outperformance wedge -0.25%
Cost of new debt 3.36%
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
01-Jan-10 01-Jan-11 01-Jan-12 01-Jan-13 01-Jan-14 01-Jan-15 01-Jan-16 01-Jan-17 01-Jan-18 01-Jan-19
iBoxx Non-Financials 10+ BBB iBoxx Non-Financials 10+ A iBoxx Non-Financials 10+ A/BBB
Cost of debt
- 77 -
6.5 Overall cost of debt
In its Final Methodology, Ofwat proposed a 10bps allowance for issuance and liquidity costs. We consider
this value still appropriate and therefore we apply an uplift of 10bps to the overall cost of debt. Therefore
Based on evidence presented above we propose:
A nominal cost of debt of 4.39 per cent, with a range of 4.17-4.49 per cent.
A CPI-deflated cost of debt of 2.34 per cent, with a range of 2.13-2.45 per cent.
Table 6.8: Overall cost of debt ranges and point estimate
Nominal CPI-deflated
Low High Point
estimate Low High
Point
estimate
Cost of new debt 3.36% 3.36% 3.36% 1.33% 1.33% 1.33%
Cost of embedded debt 4.25% 4.65% 4.52% 2.21% 2.60% 2.47%
Ratio of new to embedded debt 20% 20% 20% 20% 20% 20%
Issuance and liquidity costs 0.10% 0.10% 0.10% 0.10% 0.10% 0.10%
Overall cost of debt 4.17% 4.49% 4.39% 2.13% 2.45% 2.34%
Overall WACC
- 78 -
7 Overall WACC
7.1 Appointee vanilla WACC
Based on the cost of equity recommendations provided in Section 0, the cost of debt recommendations
provided in Section 6.5 and the notional gearing level of 60 per cent, our proposed range and point estimate
for the overall vanilla WACC are as follows:
A nominal appointee WACC of 5.12 per cent, with a range of 4.80-5.56 per cent.
A CPIH-deflated appointee WACC of 3.15 per cent, with a range of 2.74-3.50 per cent.
Table 7.1: Vanilla WACC ranges and point estimate
Nominal CPI-deflated
Low High Point
estimate Low High
Point
estimate
Risk-free rate 1.54% 1.92% 1.81% -0.45% -0.08% -0.19%
TMR 8.12% 9.14% 8.63% 6.00% 7.00% 6.50%
ERP 6.58% 7.22% 6.82% 6.45% 7.08% 6.69%
Raw equity beta 0.57 0.66 0.62 0.57 0.66 0.62
Market gearing 54.70% 54.70% 54.70% 54.70% 54.70% 54.70%
Unlevered beta 0.26 0.30 0.28 0.26 0.30 0.28
Debt beta 0.10 0.17 0.15 0.10 0.17 0.15
Asset beta 0.31 0.39 0.36 0.31 0.39 0.36
Notional gearing 60% 60% 60% 60.0% 60.0% 60.0%
Notional equity beta 0.64 0.73 0.68 0.64 0.73 0.68
Cost of equity (post tax) 5.73% 7.17% 6.45% 3.66% 5.07% 4.36%
Cost of new debt 3.36% 3.36% 3.36% 1.33% 1.33% 1.33%
Cost of embedded debt 4.25% 4.65% 4.52% 2.21% 2.60% 2.47%
Ratio of new to embedded
debt
20.00% 20.00% 20.00% 20.00% 20.00% 20.00%
Issuance and liquidity costs 0.10% 0.10% 0.10% 0.10% 0.10% 0.10%
Cost of debt (pre-tax) 4.17% 4.49% 4.39% 2.13% 2.45% 2.34%
Vanilla WACC (Appointee) 4.80% 5.56% 5.21% 2.74% 3.50% 3.15%
Source: Europe Economics
7.2 Retail margin and wholesale WACC
In this section, we set out the approach taken to determine the retail margin adjustment to calculate the
wholesale WACC. The main steps taken are as follows:
Net retail margin — in 2017 we provided evidence on the EBIT margins for a set of comparators and
regulatory precedents on retail margins. We concluded that such evidence points towards a fairly wide
Overall WACC
- 79 -
range64, that that the calculation of retail margins is subject to considerable methodological challenges,
and the basis for changing or challenging retail margins is fairly limited. Eventually we proposed using a
retail margin of 1 per cent. We remain of the view that this figure is appropriate and therefore we
propose a retaining a net retail margin assumption of 1 per cent.
Revenue requirements — by applying the net retail margin (1 per cent) to the wholesale charge
apportioned to household, Ofwat’s financial model produced a nominal figure for the average residential
retail margin revenue for 2020-25 of £100m. This cash figures is then adjusted to reflect the effective tax
rate, and result in a post-tax average annual revenue requirement 2020-25 of £92m.
RCV — the average annual RCV is £84,682m.
Margin adjustment — the retail margin adjustment is the post-tax annual requirement expressed as a
percentage of the RCV, i.e. 0.11 per cent. The margin adjustment is then subtracted from the vanilla
WACC to obtain the wholesale WACC.
Based on the information above, the wholesale WACC we recommend is a follows:
A nominal wholesale WACC of 5.10 per cent, with a range of 4.69-5.45 per cent.
A CPIH-deflated appointee WACC of 3.04 per cent, with a range of 2.63-3.39 per cent.
Table 7.2: 5 Retail margin and the wholesale WACC
Nominal CPI-deflated
Low High Point
estimate Low High
Point
estimate
Vanilla WACC 4.80% 5.56% 5.21% 2.74% 3.50% 3.15%
Retail margin adjustment 0.11% 0.11% 0.11% 0.11% 0.11% 0.11%
Wholesale WACC 4.69% 5.45% 5.10% 2.63% 3.39% 3.04%
Source: Europe Economics
64 These were 0.5 per cent to 3.97 per cent for household retail margin, and 1.36 per cent to 3.41 per cent) for non-
household retail margins.
Appendix
- 80 -
8 Appendix
8.1 Methodological issues when estimating raw equity betas
Traditionally raw equity betas have been estimated using the ordinary-least-squares OLS approach based on
daily return data. With regards to the choice of the time horizon, OLS estimates are often drawn from two
years of daily data because this strikes a good balance between the need for estimates to be based on a
sufficiently large sample, and the advantages of using up to date data which is more relevant for the purpose
of forming a forwards-looking view of beta.65 However other time horizons (e.g. from one year and up to
five years of daily data) have also been used.
However the UKRN Study takes a somewhat different approach with regards to beta estimationand
additional work conducted by Dr Donald Robertson66 and a report prepared by Indepen for Ofgem67 take
forward the recommendations made by the UKRN Study. The UKRN Study position on beta estimation can
be summarised as follows.
Betas should be estimated based on a long-term horizon (e.g longer than the 2 years horizon
typically used) because short-term beta estimates are not stable.
There are benefits in the use of low frequency data because this is less likely to display statistical issues
(eg heteroscedasticity) that are prevalent in high frequency (ie daily) data. As a result — albeit being
based on less observations — beta estimates produced with low frequency data can display less
uninformative volatility than those based on high frequency.
Because of heteroscedasticity, caution should be applied in the use of OLS estimates with high
frequency data. Other statistical techniques, such as the ARCH/GARCH framework, might be
preferable as they are better equipped to deal with heteroscedastic data. Furthermore, the Indepen
report suggests that, depending on the specific characteristics of the underlying data, different
techniques (eg different specifications of the ARCH/GARCH models) could be used estimate the betas
for different companies.
We consider these main methodological points in the remainder of this subsection.
8.1.1 Are betas intuitively too high?
We begin by challenging a flawed intuition. Estimation of (or determination, after re-gearing of) an equity beta
close to 1 does not imply that water companies, electricity distribution companies or other such utilities have
a risk profile similar to that of the average UK company. The beta of water companies and electricity
distribution companies is their asset beta, not their equity beta. There is no reason in theory or in empirical
practice why a company could not have an asset beta far below 1 but an equity beta close to 1 or far above
1. If regulated utilities had an unlevered beta of 0.3 and gearing levels of 90 per cent, their equity betas would
be 3. It would be applying incorrect intuition to then be claiming a regulator setting an equity beta of 3 was
assuming that water companies had three times as much risk as that of the average UK company. The riskiness
of a firm’s equity is connected to the riskiness of its assets, but it is an error to conflate the two, and doing
so will lead to highly flawed intuitions, such as the notion that there is something intuitively wrong about the
65 For example, at page 87 of Smithers & Co. (2003) “A Study into Certain Aspects of the Cost of Capital for Regulated
Utilities in the UK”, the authors recommend estimating betas using between one year and two years of daily data. 66 Dr Donald Robertson, (April 2018), “Estimating β”. 67 https://www.ukrn.org.uk/wp-
content/uploads/2019/01/final_beta_project_riio_2_report_december_17_2018_0.pdf
Appendix
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idea a utility could have an equity beta of 1. It would be a mistake to assume that utilities’ equity betas ought
to be 1 by default, and it would equally be a mistake to believe that they are unlikely to be 1.
8.1.2 Need to estimate beta based on a long-term horizon in order to improve stability
Betas could be calculated using the entire available set of historical data to construct a single beta estimate.
This would maximise the statistical confidence of estimates and limit the impact of possibilities such as that
forwards-looking estimates (eg those based on the most recent two years of data) are temporarily distorted
away from an underlying long-term beta value to which beta will revert over the period of a price control.
However, as Donald Robertson68, after setting out a series of empirical evidence that beta changes through
time69, “With such evidence of persistent time variation in the variances of these series it is extremely difficult to argue
that should be treated as a constant, except perhaps in the very short run.”
A firm’s beta reflects the ever-evolving relative riskiness of its future cash flows compared to other
investments. That reflects both changes impacting the companies own cash-flows but also events impacting
the entire economy. A firm’s asset beta need not change because of any change in the firm’s own business.
The beta could change because of changes in the finance sector or the housing sector or manufacturing or
Britain’s relative trade position in the world or all the plethora of other factors that evolve on a minute-by-
minute (or even more frequent) basis in any economy. We argue below that there are good reasons to
believe it is highly implausible that there is one beta for a water sector or other utility firm today that was
the same in, say the 1990s, but in any event, as was argued before the Competition Commission in the BT
Appeal of 201270, there is no reason a regulator must identify a way that a firm’s risks have changed in order
to justify a change in asset betas. BT argued that Ofcom’s asset beta analysis included an unjustified change
because “Ofcom had not provided evidence to show that BT’s business risks had in fact moved in the manner implied
by such asset betas”.71 The Competition Commission’s Assessment was that “The CAPM approach adopted by
Ofcom relies on financial market data to provide evidence of investors’ pricing of the systematic risks of a company.
As such it does not require wider evidence of a company’s business risks or explanations of how risks have changed.”72
It is sometimes suggested that observed fluctuations in betas for utilities (which can be of the order of a
doubling in only two to four years) are implausible, given that utility risks change only modestly, if at all. But
if an asset beta begins at a very low level, such as 0.2, it is by no means obvious that the correct way to think
about the issue is the asset beta doubling as opposed to the asset beta, say, recovering 0.2 of systematic risk
68 Robertson, D. “Estimating ”, April 19, 2018 69 The evidence that beta change over time is supported by both a simple inspection of the data, and more formal
statistical tests. A chart displaying 2-years rolling betas (based on daily data) for Severn Trent, National Grid, and United
Utilities clearly indicates that the betas are not constant over time. For example, over the period Jan-2000 to August
2017, the beta of National Grid fluctuates between 0.4 and 0.8, whilst the beta od Severn Trent display even wider
movements (eg between 0.05 and 0.8). Rolling betas based on 5 years of monthly data appear to move in a slightly
narrower range, but they still display a significant variations.
Since beta is formally defined as the ratio of the covariance between an asset returns and the market returns —
Cov(Ri,Rm) — over the variance of the market — Var(Rm)—, in order for a beta to be stable over time it must be the
case that:
Either Var(Rm) and Cov(Ri,Rm) are both constant in time (ie they are both homoscedastic); or
The time variation in Cov(Ri,Rm) mimics very closely that of Var(Rm).
The use of a Chi-squared test leads to a clear rejection of the hypothesis of homoscedasticity for, both, the market
returns, (ie Var(Rm) is time-varying), and the returns of all three assets (ie for each of the three assets, V(Ri) is also
time-varying). Therefore, in order to have constant betas it would be necessary for time variation in the covariances
to mimic that precisely that of Var(Rm), which is unlikely. 70 https://assets.publishing.service.gov.uk/media/55194c5fed915d1424000380/wba_determination.pdf 71 ibid. paragraph 3.63. 72 ibid. paragraph 3.103.
Appendix
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that was lost in the previous period — eg asset betas of some utilities could have become temporarily
depressed because of greatly increased perceived risk in other sectors of the economy (eg finance,
construction, sectors exposed to EU trade). Furthermore, in the case of some utilities — eg firms exposed
to the electricity sector — there are quite straightforward reasons to believe their risks may have increased
materially in recent years (specifically, large rises in wholesale price volatility, which estimates suggest could
in principle justify up to between a 50 and 80 per cent increase in beta by themselves).73
On the other hand, it may be worth observing that movements in a firm’s unlevered beta (the equity beta
unlevered as if the debt beta were zero74) may give an exaggerated picture of movements in that firm’s asset
73 The table below shows the ratio of volatility in 2017 to volatility in 2014 (the last full year supporting the data
underpinning the 2015 results). The volatility measure we are using is based on the standard deviation, and we express
it here in percentage terms, for ease of comparison between years.
Table: Change in volatility of electricity and gas prices
Average volatility for months in year
Electricity (baseload) Electricity (peakload)
2014 19% 73%
2017 29% 133%
Ratio of 2017 volatility to 2014 volatility 1.54 1.81
Source: Ofgem, Own calculations.
It can be proved that, subject to certain (fairly strong) assumptions, the ratio of the standard deviations of returns (above
the risk-free rate) should be equal to the ratio of the asset betas. At a given point in time, the relationship between the
asset beta in year 1 and average market returns can be written as:
1111 eRR m (1)
Where 1R is the excess return for year 1, mR is the excess return on the market, 1 is year 1’s beta coefficient and
1 is its alpha coefficient. 1e is the non-systematic component of the return in year 1.
Our modelling is intended to incorporate only systematic components of risk. Provided this is fully achieved, 01 e and
the above equation becomes:
mRR 111 (2)
Using the mathematical properties of variance, we can write the variance of 1R as follows:
)var()var()var(2
1111 mm RRR (3)
In the same way, we can derive an equivalent statement for year 2:
)var()var(2
22 mRR (4)
Dividing equation 4 by equation 3, we obtain the following relationship:
2
1
2
2
2
1
2
2
1
2
)var(
)var(
)var(
)var(
m
m
R
R
R
R (5)
The standard deviation of the excess return for each year is simply the square root of the relevant variance. Hence,
we can take the square root of equation (5) to give:
1
2
1
2
Q.E.D.
74 The term “unlevered beta” is often used as a synonym for asset beta in contexts in which it is assumed that the debt
beta is zero (in which case unlevered beta and asset beta are the same). Here we use the term “unlevered beta” as
Appendix
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beta if the debt beta moves in the opposite direction to the unlevered beta — which might occur if risks
driving the debt premiums of utilities up also tend to drive asset betas down.75
For example, suppose that a firm had a constant gearing of 50 per cent and its equity beta varied between
0.6 and 0.8 and back to 0.7 over a two-year period, in the way illustrated in the figure below. Then the
unlevered beta would rise from 0.3 to 0.4 and then back to 0.35. But if the debt beta started at 0.25, then
fell to 0.2 and rose back to 0.225, the asset beta would start at 0.425, rise to 0.5 and fall back to 0.4625, as
we see in the figure. If we normalise the unlevered and asset betas to a start-value of 100, we can see that
the movements in the asset beta are notably less pronounced than those in the unlevered beta. It is perhaps
worth remarking that only part of this effect arises from the variation in the debt beta. Simply having a larger
debt beta results in lower volatility in the asset beta, for any given shifts in the equity beta, other things being
equal, even if the debt beta does not change.
Figure 8.1: Movements in unlevered versus asset beta when debt beta moves contrariwise
This could be an argument for using a more dynamic and elaborate debt beta methodology than has been
used to date.
Ofwat is setting a cost of capital for a defined period of time which is forward looking, and therefore the beta
estimate should be relevant for that that period. This requires a fully forwards-looking approach to beta —
certainly to equity beta, and arguably to debt beta as well.76 It would be paradoxical to use fully up-to-date
spot estimates of, say, the risk-free rate but base betas on data that was 20 or more years old and reflecting
technologies, the general state of the economy from decades in the past, the regulatory framework from the
it was used in Europe Economics’ December 2017 cost of capital report to Ofwat, to refer to the equity beta
unlevered without any adjustment for debt beta (ie as if the debt beta were zero). 75 This was explored in the BT 2012 Appeal at ibid. paragraph 3.84 and commented upon in the Competition
Commission’s Assessment at 3.104. 76 Debt betas could be calculated dynamically in various ways, including in particular direct estimation correlating bond
yields with total equity returns (much as equity betas are calculated) or by decomposing constantly-evolving debt
spreads by using constantly-evolving risk-free rate and TMR estimates, along with some (probably less frequently
updated) estimate of the probability of default and the loss given default.
Appendix
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1990s77 and the balance of regulated versus unregulated asset of firms78 to assess the cost of capital over the
next five years.
It is not very plausible that a “long-run beta” really exists. Over the decades since water privatisation, the
roles of the finance sector and of assets such as housing have changed dramatically, affecting the riskiness of
water relative to the wider economy. The role of energy in the economy and the risks from geopolitics and
from factors such as climate change regulation or energy taxation have changed dramatically, affecting the
riskiness of water relative to other utilities. The water sector itself has changed, as new methods and
technologies have evolved, as firms have merged and restructured, companies have delisted and gone into
private ownership, and as regulation has evolved and competition and the roles of third party intermediaries
been facilitated. There is little to no reason to believe that these factors have, in sum, left the relative riskiness
of water and wastewater the same as they were two and more decades ago.
Furthermore, even if betas moved cyclically around some long-term mean, the correct approach would be
to use that evidence to assess how betas would evolve over the forthcoming price control period, rather
than to use a long-term beta. To some (limited) extent that is what is already done by taking account of 1
year daily betas as well as 2 year daily betas (since the 1 year betas provide a signal about how the 2 year
beta should be expected to move over the next year).
8.1.3 Need to estimate beta based on a long-term horizon in order to preserve
consistency within the overall CAPM framework
In the narrow sense, an investment horizon is the length of time that an investor expects to hold an asset.
Investment horizons can have a forced maximum when an asset matures at some point in the future or
depreciates over time. For example, if an investor purchases a bond that matures in five years’ time, it is not
possible for that investor to have a ten year horizon for that specific investment.
Regulatory WACC analysis involves some assumption about the relevant time period, or in some loose sense
an “investment horizon”. That can be seen, for example, when estimating the risk-free rate of return from
government bonds data, or when estimating the cost of debt from corporate bonds data. Because there is a
yield curve of different returns at different time periods, a choice must be made about what the relevant time
period is. Regulators will typically estimate a ten-year risk-free rate (though some, such as Ofcom, have placed
more weight upon five year bonds data because they had short price control periods of three years).
It is important, however, to grasp what is being said here. The term “ten-year risk-free rate” concerns the
implied time to maturity of an actual or notional asset, starting from today. It does not mean the use of ten-
year historical averages. Neither does the use of a ten year risk free rate imply that it is assumed that all
holders of the asset will hold it to maturity. One can buy a ten-year bond today and sell it tomorrow. Thus
“investment horizon” is not, in a strict sense, the correct term.
The question, then, is what is the relevant counterpart, in beta terms, to the risk-free bond that matures in
ten years? Do we need, for example, to use a “ten-year beta”, perhaps in the form of a daily or weekly beta
over ten years?
That notion seems to appear at various points in the UKRN Study, where in Appendix G the term “long
horizon” is used as if there were some tension between the use of up-to-the minute high frequency beta data
and the use of “long horizons” (which the authors interpret as assumed times to maturity being chosen to
roughly match the horizon to the average maturity of debt). In Appendix G they state: “But for regulators, who
77 Changes in this include not only significant methodological changes, but also more general points such as better
consultation and publication of RCV. 78 For example, regulated companies tended to diversify during the 1990s, but had typically disposed of non-regulated
businesses by the latter part of the 2000s.
Appendix
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deliberately pick long horizons, it appears at first sight to be distinctly counterintuitive to use such a short samples of
high frequency data to assess the systematic component of equity returns over long horizons. The conclusion of this
appendix is that on closer examination there appears to be a lot of support for this initial intuition.”
If regulators find that counterintuitive, they should not, as it would indicate an important confusion. It is in
no way in any more tension with ten-year horizons to use up-to-date high frequency data to estimate betas
than it is to use up-to-date high frequency data to estimate gilt yields or debt premia — both of which are
the standard methods used for estimating risk-free rates and the cost of debt.
The only way a tension could arise would be if there were a significant difference between the lifetime of an
equity asset (the period over which dividends could be expected) and the lifetime of a debt asset used for
debt premia or related purposes. That could happen, for example, if horizons were chosen on the basis of
typical debt lengths but assets depreciated much more rapidly than the periods of bonds (eg if bonds had a
maturity of 15 years but assets depreciated at 30 per cent per year). In practice, however, bond maturities
for utilities tend to be chosen to roughly correspond to asset lives (or a large portion thereof).
Beyond that, the use of a common risk-free rate between the cost of equity and cost of debt calculations will
tend to eliminate most, if not all, maturity differential issues, because the time dimension in the yield curve
will almost entirely be captured in the time dimension in the risk-free rate. Beta estimates can therefore
afford to be done on a fully forwards-looking basis, used up-to-date data in the same way up-to-date data are
used for risk-free rate and debt premium estimation. There is no reason why there should be any relationship
between the assumed horizon for risk-free rate estimation and the estimation window used for beta
estimation.
8.1.4 Returns versus excess returns
It has become standard in the past fifteen years to base beta estimates on models of returns as opposed to
excess returns. Such models will only produce a beta equivalent to the CAPM beta if either the risk-free rate
is invariant or if other fluctuations (such as movements in the ERP or correlations between movements in
the risk-free rate and shocks affecting returns in other ways) net out the impact of risk-free rate movements.
One concern is that if risk-free rate movements are large enough, relative to shocks, they could induce
systematic biases into beta estimates based on returns data, because when a risk-free rate changes that
induces a one-for-one change in both the market’s and any specific security’s percentage returns, so dragging
beta estimates towards 1.
One important reason why returns have been used in preference to excess returns is that there is no
straightforward benchmark for the risk-free rate over a short timescale. Measures such as LIBOR or OIS
tend to be dominated by policy rates and to be so low and exhibit such low variation over time, in the past
nine years, that their use is virtually indistinguishable from the simple use of returns.
Appendix
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8.1.5 Data frequency
The validity of the CAPM framework for estimating the cost of capital, requires that estimations are
conducted over time periods at which markets are “weakly efficient”.79 If markets exhibit mean reversion80
or other weak efficiency violations over some short timescale, the timescale needs to be extended to the
point at which they become weakly efficient and thus CAPM can be applied. It is likely that markets are not
weakly efficient over extremely short timescales (e.g. less than 1 second), since algorithmic high-frequency
arbitrage trading systems exist to exploit weak efficiency violations. Extensive studies suggest that, over
material timescales all major developed markets become weakly efficient.81 We consider it rather implausible
that systematic weak efficiency violations would endure at a timescale as long as a day without being
arbitraged away by algorithmic systems. However, if it could be proven that systematic weak efficiency
violations do occur over a longer timescale, it would be appropriate to extend beta windows.
Even if the form of weak efficiency violation were solely mean reversion, that would not necessarily imply
betas at timescales shorter than weak efficiency is achieved would be distorted upwards, but a more
fundamental point is that if weak efficiency is violated, there could be all sorts of other patterns in the data,
and they would affect the market as a whole as well as utilities stocks, with greatly variable impacts on betas.82
79 A market is defined as “weakly efficient” if past price and volume movements do not predict future movements, with
the consequence that stock price movements are completely independent of each other, and hence processes such
as price momentum (future price movements tending to be in the same direction as past price movements) or mean
reversion (future price movements tending to be in the opposite direction to past price movements) do not exist.
A consequence would be that so-called “technical analysis”, attempting to identify and then trade from patterns in
pricing data, cannot be effective. Since highly elaborate arbitrage pricing systems, operating at very frequency, devote
considerable resources to trading from technical patterns and arbitrage opportunities, it seems likely that market
inefficiencies exist at the timescales upon which they operate (often markedly less than a second). On the other
hand, precisely because such systems exist, it is also likely that they arbitrage away weak market inefficiencies if given
sufficient time to do so, so that markets eventually must become weakly efficient, at least to the scale at which
remaining anomalies are so low as to be impossible to make money by trading against. If weak market inefficiencies
persisted over all timescales, that would imply that markets fail to find and exploit enduring opportunities for infinite
near-riskless returns, which seems implausible. 80 In this context mean reversion refers to the idea that, whilst returns can take unusually high or unusually low values
in the short term, they eventually tend to revert to a the long-run average. 81 See: Malkiel, B. (2003) “The efficient market hypothesis and its critics”, Journal of Economic Perspectives, 17(1),
pp59-82. Available at: https://eml.berkeley.edu/~craine/EconH195/Fall_14/webpage/Malkiel_Efficient%20Mkts.pdf 82 We have explored whether UK utilities stocks show evidence of mean reversion, considering Severn Trent (SVT)
and United Utilities (UU) stocks. We find that on most tests we can reject the hypothesis that SVT and UU do not
follow random walks (i.e. on most tests their pricing evolution appears weakly efficient at day-long scales, which
would mean there was no mean-reversion basis for extending windows). However, the random walk tests are not
fully decisive in all specifications. Hence we went on to test for lagged impacts on the assumption there is not a
random walk (i.e. we assumed markets weren’t weakly efficient and went looking for the largest anomaly we could
find). Specifically, we searched the UU and SVT total returns series for significant autoregressive lags at different lag
lengths (in days).
We found potential lag lengths at various lengths. The models with the highest coefficients were at 9 days for UU
and 18 days for SVT. They were both reversing (i.e. partially mean-reverting) impacts. The effects were equivalent
to -0.035 per cent and -0.048 per cent of the return 9 and 18 working days earlier. So, if the price of UU went up
by 1 per cent on the Monday of one week, we should expect its price to fall by 0.035 per cent on the Thursday of
the following week.
We note that this suggests that, if an algorithm could predict the impact perfectly (which a risk-averse agent could
not, since the 0.035 coefficient is only an average, and trading on it would sometimes induce losses) and could trade
with transactions costs of less than 0.035 per cent, it could make indefinite sums of money.
Assuming that these markets do indeed exhibit mean reversion on the scale we identified, we explored what impact
that would have upon betas and whether the distortion was eliminated by using a weekly beta instead of a daily beta.
We simulated the effect in a stylised model with an anomaly-free beta of 0.5, a six-day mean-reversion anomaly of
0.035 per cent, daily shocks that, on standard days, were +/-2 per cent and one in every 20 days were +/-4 per cent,
and a trend annual rise of 7 per cent. We simulated over 4,000 days. We found that the anomaly (i.e. the partially
mean-reverting lag) induced an error in beta of of order 0.00001, i.e. of order one one thousandth of a percent. This
Appendix
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For a given length of the time window (e.g. two years, five years, 10 years, etc.), switching from daily to
weekly, monthly or quarterly data, involves a material loss in the number of datapoints used in statistical
models.83 There is a consequent loss of precision in models, with an almost inevitable broadening of
confidence intervals. That could easily mean, for example, that at the same time a monthly beta has a lower
central estimate than a daily beta, the upper bound of the monthly data confidence interval is higher than that
of the daily data estimate.
For example if we estimate United Utilities’ equity betas using 5 years of daily data and 5 years of monthly
data covering the period 01/Jan/2010—31/Dec/2014 we obtain the following results:
The central beta estimate using monthly data (0.323) is lower than the central estimate based on daily
data (0.501).
The upper bound of the beta estimate based on monthly data is higher (at the 90%, 95%, and 99%
confidence intervals) than the upper bound of the beta estimate obtained using daily data (see Table
below).
Table 8.1: Beta confidence intervals at various data frequencies
90% CI 95% CI 99% CI
Beta Central
estimate Low High Low High Low High
Monthly 0.323 0.059 0.587 0.007 0.639 -0.097 0.743
Daily 0.501 0.452 0.549 0.443 0.559 0.425 0.577
One standard way to construct a range for betas is to use the low and high points of the 95th percentile
confidence intervals. So in this case the daily range would be 0.443 to 0.559, whilst the monthly range would
be 0.007 to 0.639. In the past it has not been unusual for regulators to be conservative by choosing figures
in the upper part of a beta range.84 Therefore, a consequence of using monthly instead of daily data could
often be to produce higher determinations for beta, than would have been the case had they focused more
on daily data, even in cases where the central estimate is lower (which is not systematically so).
Another objection the UKRN Study and (to an extent) Indepen raise to the use of high frequency data
concerns various statistical properties of daily data. Specifically, daily financial time series display features such
as heteroscedasticity and serial correlation. Such features should be taken into account when estimating beta.
However the UKRN Study invites us to conclude that we should therefore consider using lower-frequency
data, to deal with such issues. This is wrong for a number of reasons.
First, heteroscedasticity and serial correlation are often present even in weekly or monthly data.85
Thus it is far from clear that the loss of information associated with a move from higher-frequency to
lower-frequency data comes with any substantial benefit.
is much less than the accuracy with which betas are determined anyway, and much less than plausible losses in
accuracy from lower data frequency owing to having fewer data points (on which, see further below). 83 For example, if we use a two-year rolling window of weekly data, we have only of order one fifth as many datapoints
as if we use a two-year rolling window of daily data. 84 How regulators choose a point estimate from within a range was explored by the consultancy “Economic Insights”
in a June 2014 report for the New Zealand Commerce Commission (“Regulatory Precedents for Setting the WACC
within a Range”). Of 53 decisions reviewed in that document, 35 involved choices of the point determination of the
WACC at above the mid-point of the quoted range. The authors remarked that, for those cases where the point
estimate used of the WACC is not explicitly above the mid-point of the range, “This often reflects adopting a
conservative view of the market risk premium and equity beta that are used in the Capital Asset Pricing Model (CAPM) for
determining the return on equity, where ‘conservative’ means erring on the high side.” 85 This is largely confirmed in the Indepen study.
Appendix
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Second, the presence of heteroscedasticity and serial correlation does not affect the biasedness of OLS
estimation, but only its efficiency. This means that OLS estimates based on heteroscedasticity and/or
serial correlation remain unbiased, but the degree of confidence we can place on such estimates (eg the
confidence interval around the estimates) are affected. There are however standard methods to
address these issues. For example, most statistical software provide the option of estimating OLS with
error correction methods that are designed with the precise purpose of adjusting standard errors in
the presence of serial correlation (eg the Newy-West error correction method) and heteroscedasticity
(eg White error correction method).
Third, the use of weekly or monthly data produced other issues. For examples estimates based on
weekly data can change significantly depending on the day of the week which chosen to record the
data.
Overall, we do not believe there is, as yet, robust evidence that the use of daily data will induce a systematic
upwards bias in betas even if weak efficiency is sometimes violated at day-long timescales. Accordingly we
believe it is potentially useful to consider betas calculated at longer timescales (e.g. five years of data) as well
as with lower frequency data (e.g. weekly or monthly), but recommend continuing to use daily data as the
base case, pending any proof of enduring material systematic weak efficiency violations over timescales longer
than one day.
8.1.6 Use of alternative estimation methods
There does appear to be variation in beta variance over time, ie betas can remain relatively stable for some
time (fluctuating within a narrow band) and display much wider variations in other periods. This might to
some extent reflect the fact that the CAPM model is conceptually incomplete. According to microeconomic
theory, agents should care about skewness, kurtosis and other moments of the returns distribution as well
as variance. Beta variance over time might be a symptom of the impacts these other factors would be having
upon returns if they were used in the model (eg in a third moment CAPM model) and that those other
factors evolve non-randomly. Therefore, to certain extent beta variation might be due to uninformative
volatility (ie measured betas changing more than actual betas do).
The traditional way to deal with this potential issue is by using two-year daily betas whilst also taking into
account beta estimates based on windows of different length (eg 5-years, and 1-year) and to exert some form
of judgment. A potential drawback with this approach is that it introduces judgement into the process of beta
estimation instead of a straightforward “let the data speak” approach. That could subject regulators to
pressure to use the discretion the process offers them to justify accepting systematically materially higher
beta numbers than the data imply. That risks meaning that the exercise of judgement introduces far larger
distortions than any distortions there are in the data that the judgement is attempting to correct for. If this
reasoning is correct, it could therefore imply there is some advantage in a more mechanical, less judgement-
based approach, even if in principle judgement-based adjustments could be adequate or superior.
One potential class of more mechanical ways to address the issue of time-varying variance has been the
proposals to move away from the traditional OLS estimation approach to make more use of the
ARCH/GARCH framework. This alternative approach could have two main potential benefits over OLS:
First, it allows an adjustment for variance variation through time that could, in principle, if suitable
methods were developed, not require the use of such long backwards-looking data windows;
Second, it reduced the role for regulatory judgments in interpreting beta data;
Third, it could reduce uninformative volatility in estimates.
Whist we agree that the use of a GARCH approach can be used as a useful cross-check to traditional OLS
estimates, we note that GARCH methods so far have not tended to produce greatly different betas from
Appendix
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non-GARCH methods.86 Furthermore, there is as yet not a consensus on which GARCH methods are to be
preferred. Consequently, at this stage we believe GARCH estimates are best used as a cross-check, to help
inform the use of judgement in interpreting the OLS-based estimates.
8.2 ARCH/GARCH estimation
The ARCH/GARCH approach we have used here is the same that has been proposed by Prof. Donald
Robertson87 and consists in using return data the from 1 January 2000 to estimate BEKK88 multivariate
GARCH mode in which the stock’s return and the market return are explained by two constant, i.e.:
(𝑟𝑖,𝑡
𝑟𝑀,𝑡) = (
𝑐1
𝑐2) + (
𝑢𝑖,𝑡
𝑢𝑀,𝑡)
and where the variance-covariance of the system’s residuals (i.e. 𝑢𝑖,𝑡 and 𝑢𝑚,𝑡) is time varying
𝐶𝑜𝑣 (𝑢𝑖,𝑡
𝑢𝑀,𝑡) = (
𝑉𝑎𝑟(𝑢𝑖,𝑡) 𝐶𝑜𝑣(𝑢𝑖,𝑡 , 𝑢𝑀,𝑡)
𝐶𝑜𝑣(𝑢𝑖,𝑡 , 𝑢𝑀,𝑡) 𝑉𝑎𝑟(𝑢𝑀,𝑡))
The time-varying variance-covariance matrix can be used to calculate an “instantaneous beta” for each data
point as follows:
𝛽𝑡 =𝐶𝑜𝑣(𝑢𝑖,𝑡 , 𝑢𝑀,𝑡)
𝑉𝑎𝑟(𝑢𝑀,𝑡)
A rolling average of the instantaneous betas can then be used to calculate time-varying betas defined on
different time horizons.
8.3 Derivation of the debt beta equation used for the decomposition
approach
We recall the definition of the expected return on debt.
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡
= 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡) ⋅ % 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 + (1 — 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡))
⋅ 𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡.
86 Armitage, S. (2018) “Heteroscedasticity and interval effects in estimating beta” explores the relationship between
OLS and GARCH estimates across a variety of securities. Its key findings are as follows.
The differences in beta from using the most ARCH-type models and OLS are typically modest. However,
there is an important minority for which impacts are larger. The difference in beta, when using daily data, is at
least 0.05 for 45 per cent of the sample, and at least 0.1 for 17 per cent.
The difference between OLS and ARCH betas, positive or negative, is largest for the highest-value, most
frequently traded shares.
A (well-known) problem with betas calculated from daily returns is downward bias in the estimates for less
liquid shares. Models in the ARCH category do not alleviate that downward bias. Indeed, mean and median
betas are slightly higher under OLS than with an ARCH model.
The difference between betas estimated from daily and monthly data is strongly correlated to daily volatility.
The most volatile shares see very large increases in beta as one moves from daily to monthly betas. In fact
there is a stronger link between differences in daily and 6-monthly betas and daily volatility than there is
between beta differences and frequency of trading. 87 See, e.g. D. Robertson (April 19, 2018), “Estimating β” 88 See Baba, Engle, Kraft and Kroner (1990) published as “Multivariate Simultaneous Generalised ARCH” by Engle and
Kroner, Econometric Theory, Vol. 11, Issue 1, Feb 1995, pp 122-150.
Appendix
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The definition of the debt premium is that
𝑑𝑒𝑏𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 − 𝑅𝐹𝑅,
where 𝑅𝐹𝑅 stands for risk-free rate, and which is equivalent to:
𝑝𝑟𝑜𝑚𝑖𝑠𝑒𝑑 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 = 𝑅𝐹𝑅 + 𝑑𝑒𝑏𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 .
From those two equations it follows that:
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡
= 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡) ⋅ % 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 + (1 — 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡)) ⋅ (𝑅𝐹𝑅
+ 𝑑𝑒𝑏𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚)
As noted above, from the CAPM we know that:
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑑𝑒𝑏𝑡 = 𝑅𝐹𝑅 + 𝛽𝐷 ⋅ 𝐸𝑅𝑃,
and therefore
𝛽𝐷 = (1—𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡))⋅ 𝑑𝑒𝑏𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 — 𝑝𝑟𝑜𝑏(𝑑𝑒𝑓𝑎𝑢𝑙𝑡)⋅ (𝑅𝐹𝑅 +% 𝑙𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡)
𝐸𝑅𝑃.7
8.4 Regulatory fair value gearing
8.4.1.1 Results to be explained 1. First, we have calculated yearly gearing from estimates of regulatory fair values of net debt for SVT
(Severn Trent Water) and UU (United Utilities) based on their regulatory fair values of debt (RFV). The
regulatory fair values of net debt are shown below for 2017, 2018, and 2019 (where possible).
Fair value net debt (RFV, £m) adjusted
for embedded cost of debt
year SVT UU
2019 6,113 7,370
2018 5,625 7,205
2017 5,523 7,325
Source: Companies’ annual reports and accounts.
2. Second, we have calculated a daily regulatory fair value gearing for SVT and UU using the same method
as in our 2017 report to Ofwat, where the enterprise value is calculated as the sum of market
capitalisation and fair value of debt less cash.89 Daily enterprise value gearings have been overlaid in the
graph below to highlight the similar results of the gearing methods.
89 Europe Economics (2017), ‘PR19 — Initial Assessment of the Cost of Capital’ [online].
Appendix
- 91 -
Figure 8.2: Regulatory fair value gearing
Notes: RFVg = fair value net debt / (fair value net debt + market cap); g = enterprise value gearing
8.4.2 Yearly regulatory fair value (RFV) gearing explanation
The calculation of yearly gearing is based on the fair value of debt and follows three stages:
Estimation of fair value of net debt;
Applying the embedded debt rule to yield the regulatory fair value of net debt;
Calculating gearing based on this regulatory fair value of net debt.
8.4.3 Fair value of net debt
Data on fair value of total debt, cash and cash equivalents, and the book value of net debt are taken from
annual reviews published by the companies.
We first estimate the fair value of net debt using the following equation:
𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡 = 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑡𝑡 − 𝑐𝑎𝑠ℎ 𝑎𝑛𝑑 𝑐𝑎𝑠ℎ 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡𝑠𝑡
Where 𝑡 denotes the value of the variable at the end of the year (as reported in the company reviews).
This does not account for the embedded debt rule that Ofwat has determined for the notional water
company.
8.4.4 Fair value net debt adjusted for embedded cost of debt
Ofwat has determined an embedded debt rule for the notional water company for the PR19. The proportion
of embedded debt held by the notional company is 80 per cent, as explained in the main text. We then
calculate the regulatory fair value of net debt adjusted for the embedded cost of debt using the following
equation:
30.00%
35.00%
40.00%
45.00%
50.00%
55.00%
60.00%
65.00%
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UU RFVg SVT RFVg UU ENTg SVT ENTg
Appendix
- 92 -
𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡
= 𝑁𝑒𝑤 𝑑𝑒𝑏𝑡 % ∗ (𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡 − 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡)
+ 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡
8.4.5 Regulatory fair value net debt gearing
With the values of regulatory fair debt calculated we then use the enterprise value (EV) to estimate the
gearing. For this we followed these steps:
Calculate yearly averages of EV (calendar years; i.e. the 2018 average is the average of daily EVs between
1/1/2018 and 31/12/2018).
Use the EV as denominator in the gearing equation:
𝑅𝐹𝑉 𝑔𝑒𝑎𝑟𝑖𝑛𝑔𝑡 =𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡
𝐸𝑉𝑡
Applying the formula, we find that the three-year (2017-2019) average gearing based on the embedded debt
rule is 56.53 per cent for UU and the two-year average (2017-2018) for SVT is 56.5 per cent.
SVT UU
2019 59.3% 56.6%
2018 56.8% 58.2%
2017 53.1% 54.8%
Average 56.4% 56.5%
We stress immediately that these are crude results using yearly averages of enterprise value (a variable which
changes daily) to calculate an average gearing for the year. We deal with this in a more robust way in the
next stage.
8.4.6 Daily regulatory fair value (RFV) gearing explanation
In general, regulatory fair value is defined as follows.
𝑅𝐹𝑉 𝑔𝑒𝑎𝑟𝑖𝑛𝑔 =𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡
𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡 + 𝑀𝑎𝑟𝑘𝑒𝑡𝐶𝑎𝑝
The yearly RFV gearings are calculated based on the fact that SVT and UU appear to report the fair values of
their debt only once per year. To gain a daily RFV gearing, we need to use a method that exploits a variable
that changes daily. We therefore use daily market capitalisation data in the denominator of the gearing
equation. The calculation of daily RFV gearings using the method employed in the 2017 Europe Economics
report follows these steps:
Imported Thomson Reuters data on Company Market Capitalisation for UU and SVT;
Calculate RFV gearing with regulatory fair value of net debt and market capitalisation.
Again, the data for fair values of debt were obtained from the annual reports published by United Utilities
and Severn Trent, which were then used to estimate a measure of regulatory fair value of net debt following
the method in the first section of this note.
8.4.7 Calculate daily regulatory fair value (RFV) gearing
These data are daily, whilst our fair values of net debt are yearly. We use the following equation to calculate
the daily RFV gearing.
Appendix
- 93 -
𝑅𝐹𝑉 𝑔𝑒𝑎𝑟𝑖𝑛𝑔𝑡 =𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡
𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡 + 𝑀𝑎𝑟𝑘𝑒𝑡𝐶𝑎𝑝𝑡
Where 𝑡 now denotes each day within the data window (3/1/2017 to 30/4/2019). Although 𝑅𝐹𝑉 𝑜𝑓 𝑛𝑒𝑡 𝑑𝑒𝑏𝑡𝑡
remains the same for each date of the year, the second component of the denominator changes daily,
therefore giving us a different RFV gearing for each day. Plotting these daily figures gives the graph below.
Note that we cannot calculate SVT’s RFV gearing for dates in 2019 because of the aforementioned inability
to locate its reported fair value of total debt for the year.
Figure 8.3: Regulatory fair value gearing
We can then plot the daily enterprise value gearing on the same graph to see whether the RFV gearing
approach yields dramatically different gearing estimates. As can be seen below, the two methods appear to
yield quantitatively very similar gearings for the two main companies.
30%
35%
40%
45%
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55%
60%
65%
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UU RFVg SVT RFVg
Appendix
- 94 -
Figure 8.4: Regulatory fair value gearing vs Enterprise value gearing
We can also compute yearly averages from our daily gearings. Taking a calendar-year average yields the
results below, which are graphed immediately after.
Table 8.2: Results
Regulatory fair value debt gearing Enterprise value gearings
UU RFVg SVT RFVg UU ENTg SVT ENTg
2019 56.7% 56.6% 57.0% 54.4%
2018 59.0% 55.6% 59.6% 54.5%
2017 54.1% 50.9% 53.5% 48.7%
30%
35%
40%
45%
50%
55%
60%
65%
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UU RFVg SVT RFVg UU ENTg SVT ENTg
Appendix
- 95 -
Figure 8.5: Results
54.1%59.0%
56.7%
50.9%
55.6%56.6%
53.5
59.6
57.0
48.7
54.5 54.4
30%
35%
40%
45%
50%
55%
60%
65%
2016 2017 2018 2019 2020
UU RFVg SVT RFVg UU ENTg SVT ENTg