1

The long term discount rate: Some comments from a practical point of view24. mai 2012

Prof. Thore JohnsenNorwegian School of Economics (NHH)

2

Structure

Are economic (growth) models useful in setting public discount rates?

A simple market calibration exercise Risk premium information from the stock market Summing up

3

Are economic (growth) models useful in setting public discount rates? Of course, but with a minimum of market calibration But, the models have not been very useful in explaining

(or predicting) the financial marketsDiscount rate = Risk free rate (real) + Risk Premium- Risk Free rate puzzle: too high- Equity premium puzzle: too low

Too much degree of freedom in more elaborate models, or too complex and unstable for practical use

4

Structure

Are economic (growth) models useful in setting public discount rates?

A simple market calibration exercise- Few long instruments with «risk free» real return

matching except for the UK 50-year indexed Gilt-market (excess demand)

- Will instead use the US 100-year corporate bond market

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100 Year Bonds - Yields 2001 - 2012

Walt Disney 2093 vs 2032

Coca Cola 2098 vs 2036

US Treasury 2030

US Treasury 2030

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100 Year Bonds – Yield spreads 2001 - 2012

WD 2032 vs Treasury 2030

2093 - 2032

CC 2036 vs Treasury 2030

2098 - 2036

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100 Year Bonds – Forward Yields (TLRL - TSRS) / (TL-TS)

WD93 = WD32 + Fwd purch. WD93 in 2032

CC98 = CC36 + Fwd purch. CC96 in 2036

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Uncertain future price and yield (in 2032-36) - Convexity adjusted forward yield

Dybvig, et. Al. (JB 1996; Weitzman JEEM 1998)

Price long bond = Price short bond + E[Future Price] Determine forward yield from expected future price

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100 Year Bonds – Stable 3.2 % Forward Yields

R93 [T32R32 + (T93-T32)3.2%]/T93

R98 [T36R36 + (T98-T36)3.2%]/T98

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Structure

Are economic (growth) models useful in setting public discount rates?

A simple market calibration exercise Risk premium information from the stock

market

1111

30. sep. 2008: Down 8.5 % SELL !! 1. oktober 2008: Up 5.5 % BUY !!Two days in the life of Oslo Stock Exhange…..

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The stock market is driven by expectations and risk

Stocks give a w return when investors demand more (and a higher return when they expect less)

Stock market and economic growth uncorrelated, across markets and over time (Dimson, Marsh & Staunton)- (but the stock market is a good predictor for future growth)

High correlation between long-run stock and bond returns, while short-run returns are negatively correlated

Discount rate = Risk free rate (real) + Risk Premium

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Pricing of OSE Large Caps Nov vs Aug 2008

Aug 08: RF 5.0 % MP 4.5 % Cost 12 %

OSE Large Caps 04.08.08 vs ROE-estimate for 2008

0

1

2

3

4

5

6

0,0 1,0 2,0 3,0 4,0 5,0

Static P/B (R08* / 11.9%)

Obs

erve

d P

/B

Seadrill

Statoil

Hydro

Corr = 0.81

Yara

Frontline(7,8 / 13,3)

Telenor

RCL

OrklaDnB Nor

Avg LC (2,0)

Aker Solutions

REC

StbThon

Krav 11,9% = 4,9% + 1,5·4,5%

OSE Large Caps 03.11.08 vs ROE-estimate for 2009

0,0

0,5

1,0

1,5

2,0

2,5

0,0 0,5 1,0 1,5 2,0 2,5

Static P/B (R09* / 14.5%)

Obs

erve

d P

/B

Seadrill

Statoil

Hydro

Corr = 0.40

Yara

Frontline(3,3 / 0,9)

Telenor

RCL

Orkla

DnB Nor

Avg LC (1,2)Aker Solutions

REC

Stb

Thon

Norske Skog

Krav 14,5% = 3,8% + 1,5·7%

Nov 08: RF 3.8 % MP 7 % Cost 14.5%

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Risikopremier konjunkturelt USA 1953 - 2009

7,0

-22,4-14,6

10,47,0

39,7

-30

-20

-10

0

10

20

30

40

TOPP BUNN TOPP

Ris

ikop

rem

ie re

l. Tb

ills (%

år)

Ekspansjon 5 Resesjon 1

Aksjer(snitt premie: 6,4 %)

Cyclical risk premiums US

Risikopremier konjunkturelt USA 1953 - 2009

7,0

-22,4-14,6

10,47,0

39,7

-2,2

2,45,3

0,3

4,82,2

-30

-20

-10

0

10

20

30

40

TOPP BUNN TOPP

Ris

ikop

rem

ie re

l. Tb

ills (%

år)

Ekspansjon 5 Resesjon 1

Aksjer(snitt premie: 6,4 %)

Statsobl. (snitt premie 1,1 %)

Equity, gov. bonds and GNP-growth Norway / US (deflated, log)

NORWAY:0.60Equity + 0.40Bonds = 3.2 % GNP-growth

US: 0.60Equity + 0.40Bonds = 4.5 % >> GNP-growth

8 %

6,5 %

1900 - 2010

6,5 %

7 %

> 1980

-GNP: 2.7 %-Real rate:1.8%

-GNP: 2.4 %-Real rate:3.8%

2.6 %

2.5 %

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15-yrs geometric real returns Norway / US 1900 – 20111900-1959:Equity: 3,2%Gov Bonds: 1,1%Real interest: 1,2%

1960-2011:Equity: 5,2%Gov. bonds: 2,9%Real interest: 2,5%

1900-1959:Equity: 6,9%Gov. bonds: 1,1%Real interest: 0,7%

1960-2011:Equity: 5,4%Gov. bonds: 3,3%Real inteest: 1,1%

NORWAY

US

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Summing up

Yes, the risk free (real) rate term structure has a dip at the (very) long end

But, the the term structure of risk premiums are problably upward bending (e.g. Pastor & Stambaug, JF 2012)

Use market calibration (political defense) More focus on benefits/cash flows than discount

rates in public projects