interest rate risk in the banking book and capital...
TRANSCRIPT
1
Interest Rate Risk in the Banking Book and Capital
Requirement - Issues on EVE and EaR
Roberto Nygaard*
The views expressed in this work are those of the author and do not necessarily reflect
those of the Banco Central do Brasil or its members.
Abstract
The interest rate in the banking book (IRRBB) is a risk factor presently under regulators
evaluation and will possibly affect capital requirements in the near future. In this
paper, we explore and compare the methodological issues of two approaches widely
used to calculate the capital derived from this risk — EVE and EaR. We conclude that
EaR is less suitable for the task of gauging the amount of capital required to cover risks
from the IRRBB. Our simulations expose the excessively unrealistic reinvestment and
funding hypotheses, especially when compared to those assumed for the EVE.
Moreover, calculations based entirely on earnings provide incorrect results due to the
accrual basis of earnings. As a consequence, EVE is suggested as more adequate
approach to evaluate capital requirements for the IRRBB in any case. Based on these
findings, we suggest a possible extra criteria to deal with non-maturity deposits.
Finally, we argue in favor of static simulations (instead of dynamic) for the purpose of
dimensioning a capital cushion.
* Financial System Monitoring Department, Banco Central do Brasil. E-mail: [email protected]
2
1 Introduction
In January 1996, the Basle Committee on Banking Supervision (BCBS) issued the
"Amendment to the Capital Accord to Incorporate Market Risks", extending capital
requirements to other types of risk, beyond credit risk. It sets up guidelines, principles,
definitions and methodologies imposing banks a specific capital charge to absorb
losses resulting from the different types of market risk. Among them, interest rate risk
receives special attention, as expected.
A particular definition was introduced related to the interest rate risk capital charge:
the segregation between trading and banking books. For the trading book, specific
methodologies were proposed. As for the banking book, only in July 2004 the
"Principles for the Management and Supervision of Interest Rate Risk" provided some
guidance on how to evaluate its interest rate risk. Moreover, the particular capital
charge was established based on a pillar 2 approach. In other words, the capital charge
aiming at absorbing losses from the interest rate in the banking book (IRRBB) was left
under national supervisory authorities’ discretion. In spite of these guidelines and
definitions about what supervisors should mind when evaluating the IRRBB, a closer
look reveals a quite abstract and general approach, not prescribing more specific
methodological details.
Differently from the trading book, where gains and losses result from market value
changes, as positions are intended to be traded in the short term, in the banking book
gains and losses arise when accrued based on their original contractual terms. In other
words, the gains will be the earnings1 gradually being realized as positions mature. But
earnings are dependent on the relationship between assets and liabilities which, in
turn, depend on the level or interest rates2 “(…) as the current or prospective risk to
both the earnings and capital of an institution arising from adverse movements in
interest rates, (…) affect the institution’s banking book. Changes in interest rates affect
an institution’s earnings by altering interest-sensitive income and expenses, and the
underlying value of an institution’s assets, liabilities, and off-balance sheet instruments
because the present value of future cash flows changes when interest rates change.”
Hence, the banking book assets and liabilities, and the associated gains or losses are
typically accrued and realized over time. This naturally leads to the idea of translating
this relationship into a present value of economic gains or losses dictated by earnings
evolution through time. Bottom line, banking book interest rate risk is overall a spread
or margins-like risk.
1 In the context of IRRBB, the concept earnings is said to focus on, or even means, the net interest
margin (NII). Minding that this margin follows an accrual basis, the NII can be seen as the accounting earnings derived from interest rate bearing assets and liabilities in the banking book. Throughout this paper, the term earnings can be interchanged with NII. 2 BCBS. “Range of Practices and Issues in Economic Capital Frameworks”: BIS, march 2009, Annex 3. If
not explicit, quotations refer to this document.
3
In order to address these issues, two approaches are broadly adopted: an earnings-
based approach, called EaR (Earnings at Risk) and an economic value based approach,
called EVE (Economic Value of Equity). EVE is defined as “the present value of assets
minus liabilities, measures the change in the market value of equity resulting from
interest rate shock scenarios, compared with the market value of equity under a base
scenario.” The usual interpretation associates EVE with longer term horizons, based on
discounted cash flows of currently contracted static assets and liability positions.
EaR on its turn is described as considering “(…) the loss of net interest income resulting
from interest rate movements, either gradual movements or one-off large interest rate
shock, over a given time horizon (typically one to two years).“ It is based on a
forecasted balance sheet, performed as precisely as possible, eventually including
dynamic simulations. Hence, given the complexity involved in forecasting the entire
balance sheet and the restrictive assumptions it asks, the time horizon of risk
exposures evaluation is limited to one or two years, as longer time period forecasts for
interest rates, business mix and volumes become unreliable. Other advantages and
disadvantages of each methodology could be listed, all arriving at a sort of cost benefit
relationship, that assumes simplicity and longer time horizons to economic value
models (EVE), and complexity and shorter periods to income models (EaR). And based
on the characteristics embracing EaR and EVE, they have been considered as
complementing each other, with a more precise view on the short term by the former
and a more broad view on the long run by the later.
However, this complementary view seems rather misleading. This is exactly what this
paper attempts to demonstrate: that EaR is not suitable for the task of determining a
present capital charge in the context of the IRRBB – consequently, EVE is the right
approach. Importantly, this finding does not rest on the precision or detail level
employed, or the time horizon assumed. By making explicit calculations under each
methodology and comparing results, we show that the difference in the monetary
amount required as a cushion for future (or scenario based) adverse situations by each
method derives from the inadequacy underlying the EaR as a methodology for capital
calculation requirement.
That is what we do in the first part of the paper: explore in detail the assumptions and
results of both EaR and EVE. More specifically, when we reconcile the results obtained
from each methodology, we show that differences are due to incorrect methodological
assumptions that underlies the usage of EaR for capital charge calculations. In
particular, we show that, besides the accrual basis of earnings, the reinvestment and
funding implicit assumptions play a fundamental role in driving the results.
Next, we propose an alternative way to model the implicit reinvestment and funding
assumptions using the EVE method explored in the first part. Finally, although we only
use static simulations throughout the paper, we briefly comment some issues arising
4
from the use of dynamic scenarios—that corroborates our preference for the static
models when gauging capital requirement in the context of the IRRBB.
2 EVE x EaR – The Adequacy of EVE
While evaluating the IRRBB and its corresponding capital requirement, two
methodologies are broadly adopted: Earnings at Risk (EaR) and Economic Value of
Equity (EVE). Formally, “Earnings at Risk” is a monetary (or earnings) amount that
results from a firm’s regular operation subject to losses under a given time horizon and
probability. “EVE”, on its turn, simply means the economic value of equity (or capital)
obtained as the present value of projected cash flows with no further implication. For
the purposes of this work, the terms “EaR” and “EVE” have been and will be used as
meaning “earnings based approach” and “economic value based approach”,
respectively, and not their strict or formal definitions. In other words, they are treated
as two different ways or path (earnings focused and cash flows focused, respectively)
to achieve the same goal: a capital cushion to absorb losses due to the IRRBB.
Capital requirement is usually calculated as the result of a stressed scenario - this
includes EaR and EVE. However, the discussion about the methodologies for
determining scenarios are out of the scope of this work. The focus here is on how EVE
and EaR translate these possible scenarios into capital results.
EaR and EVE are indeed two different procedures aiming at generating a present
capital cushion: EaR follows the earnings path, while EVE follows the cash flow path.
Before highlighting those differences, we start by describing an extreme situation
where both approaches produce the same result. Suppose that a firm, financial or not,
simply stop operating. When the last contracted cash flow happens (inflow or outflow)
and there are no contingencies or permanent assets left, all that remains is pure cash
and equity. At this point, accounting value (equity) and economic value (cash) will be
the same. Earnings will equal cash, as accrual and cash basis will finally match. In other
words, in this extreme and final situation, both the earnings and the economic
approaches will provide the same future value and hence the same present one.
However, in normal situations, differences show up between the capital requirement
calculated using EaR and EVE. In the following exercise we demonstrate that these
differences can be significant. And when differences are investigated and explained
from an economical perspective, it is argued that EaR is an inadequate approach when
the goal is to obtain an amount today to be used as a capital cushion, either on short
or long term simulations and under any degree of complexity involved in simulations
All the examples presented in this study are static, as no new position will be actively
or explicitly inserted during the evaluation. But further it is disclosed that reinvestment
hypothesis are always present and are determinant when comparing the adequacy of
EVE and EaR methodologies. A final note, supporting static against dynamic
simulations for capital requirement calculations is presented, relating the two type of
5
simulations to EVE and EaR results, including the before mentioned implicit
reinvestment and funding assumptions, and the fact that capital requirement is
frequently balanced
2.1 Exploring EVE and EaR
In this section, we stress the effect of the structure of assets and liabilities positions on
the results obtained for EVE and EaR. In other words, the intention is to verify the
effect on capital charges resulting from the mismatch of the cash flow basis (EVE)
approach and the accrual basis (EaR) approach. Differences are then interpreted from
an economical perspective and it is concluded that results obtained via earnings (EaR),
except in a very specific situation, are excessively unreal when compared to those from
EVE.
We present a simple balance sheet with one deposit (funding source) and one loan
(investment), both with the same notional value. Deposit and loan are described
below.
Loan
(1) Term Deposit
Notional $1,000.00 $1,000.00
Maturity (m) 12 6
Amortization month bullet
Term month bullet
IR(1)
15.0% 10.0%
Discount Rate 9.0% 9.0% (1) Constant amortization on the loan and compound interests in both cases.
The amortization and repayment schedules for the loan and the term deposit,
respectively, are shown in the table below. The table also presents the present value
of cash flows for each instrument (used in EVE) and the accruals (that will add up to
EaR):
m Loan NPV Term Deposit NPV EaR*
Outs Princ Paym
Int Int Paym
Cash Flow
1028,34 Outs Princ Paym
Int Int Paym
Cash Flow
1004.58
0 1000.00 1000.00
1 916.67 83.33 11.71 11.71 95.05 94.37 1000.00 7.97 0.00 3.74
2 833.33 83.33 10.74 10.74 94.07 92.73 1000.00 8.04 0.00 2.70
3 750.00 83.33 9.76 9.76 93.10 91.11 1000.00 8.10 0.00 1.66
4 666.67 83.33 8.79 8.79 92.12 89.51 1000.00 8.17 0.00 0.62
5 583.33 83.33 7.81 7.81 91.14 87.93 1000.00 8.23 0.00 -0.42
6 500.00 83.33 6.83 6.83 90.17 86.36 0.00 1000.00 8.30 48.81 1048.81 1004.58 -1.46
7 416.67 83.33 5.86 5.86 89.19 84.82 0.00 5.86
8 333.33 83.33 4.88 4.88 88.21 83.29 0.00 4.88
9 250.00 83.33 3.90 3.90 87.24 81.78 0.00 3.90
10 166.67 83.33 2.93 2.93 86.26 80.28 0.00 2.93
11 83.33 83.33 1.95 1.95 85.29 78.81 0.00 1.95
12 0.00 83.33 0.98 0.98 84.31 77.35 0.00 0.98
6
*Nominal values are displayed for each line of earnings.
EVE is obtained directly from the difference between the net present value (NPV) of
the cash flows for each financial instrument. On the other hand, instead of relying on
cash flows, EaR considers earnings accrual on the computation of the capital required.
However, the way EaR obtains a present value is not that straightforward, as the
nature of earnings is different from that of cash flows. We consider two methods of
treating the earnings in this exercise:
1) Discount earnings the same way we discount cash flows, that is, discount earnings at
each accrual date – called Discounted Earnings (EaR DE);
2) Obtain the future value of earnings at the final date of the simulation, as the sum of
all earnings, and then discount it to the present date – called Discounted Future Value
of Earnings (EaR DFVE).
In order to compare the capital charge from EVE and EaR, we first use EaR DE, that is,
each monthly earnings is discounted and its sum results in the EaR. The table below
display the results:
12 months
EaR DE 26.06
EVE 23.76
In the case considered, capital charges do not differ much between EVE and EaR.
However, varying maturities and terms in such a way that cash flow and earnings are
more imbalanced result in a very different picture. That is what we simulate in the next
exercise.
We set the loan maturity to 60 months, but keep the other original characteristics
(constant amortization, 15% interest rate). As for the deposit, we consider a range of
maturities, varying from 12 to 60 months in four steps of 12 months, while the other
characteristics remain the same (10% interest rate, bullet payment). Based on the
same 9% discount rate, 5 different values for EaR (using both DE and DFVE) and EVE
were obtained, one for each maturity of the deposit: 12, 24, 36, 48, 60. EVE and Ear
results are plotted below:
7
2.2 Implicit reinvestment assumptions
Following the hypothesis that all positions are static, only the currently contracted
positions will generate cash flows and earnings; no reinvestment or refunding
assumptions are considered - nor changing in positions during the lifetime of the
investment. Strictly speaking, it means that cash flows, after being received, do not
generate any income. Similarly, cash flow gaps are funded with zero cost. And this is
what EaR DFVE is displaying. EaR does not capture any reinvestment and/or funding
assumptions, unless made explicit. This is the main reason for the differences observed
between EaR DFVE and EVE.
EVE presents a different assumption. A well-known and elementary economic principle
is that cash flows, in order to be compared, must be set or “moved” to the same date,
which is typically today, based on a discount rate that plays the role of an opportunity
cost. That is the rule behind the net present value of future cash flows: all cash flows
are “brought” to present. Whenever a cash flow is present valued, an immunization
assumption is considered: in case we were to project future values of cash flows in
order to compare them in a future date instead of today, these cash flows should be
future valued under the same rate used to present value (discount) them. In doing
that, different future values will always generate the same present value, what allows
moving them in time. This is equivalent to assume that cash inflows are being
reinvested at the same rate used to fund cash outflows.
Table below illustrates this immunization effect (15% interest rate for the bond and 9%
discount rate):
t Notional Cash Flows (1) PV of Cash Flows (2) FV of Cash Flows (2)
0 1000.00 1028.40 1028.40
1 1000.00 11.71 11.63 12.14
2 1000.00 11.85 11.68 12.20
3 1000.00 11.99 11.74 12.25
4 1000.00 12.13 11.79 12.31
5 1000.00 12.27 11.84 12.36
-200
-100
0
100
200
300
12 24 36 48 60
$
Maturity
Differences EaR x EVE
EVE EaR DFVE EaR DE
8
6 1000.00 1012.42 969.72 1012.42
It shows in column (1) nominal cash flows calculated as compound interest, In column
(2) it displays the present value of each cash flow and the final present value as a sum
of each one in bold; (3) displays the future value to date 6 of each cash flow, and in
bold the sum of all future values but present valued to date 0. Present value is equal
under both procedures. And this is what EVE assumes: positive cash flows are invested
at the discount rate, and negative gaps are funded under this same rate.
EaR DE assumes the same zero cost for reinvestment and refunding, but it does
something else: it changes contractual conditions and this is due to the immunization
assumption that underlies the discounting procedure, and this is what explains the
differences between EaR DE and EaR DFVE. When discounted, earnings behave as if
they follow a different accrual rate, which is the discount rate. If this can be considered
a reinvestment hypothesis for cash, in the case of earnings this means that the original
accrual rate is being substituted for the discount rate if the original cash flow has not
yet been paid or received, minding that pure earnings never tells when cash flows
happen. Indeed, earnings show the path a given interest is following during its accrual
term. Obtain a present or future value for earnings dissociated from the originating
cash flow is equivalent to change the original interest rate for the discount rate, what
is equivalent to change contractual conditions. Minding that earnings does not tell
when a cash flow is paid or received, a pure look at earnings will very probably brake a
contractual item and produce wrong results even if reinvestment and funding
assumptions are made explicit.
As mentioned earlier, examples were intended to stress the differences observed in
both approaches. By assuming the same maturity either for the loan and the deposit,
and setting contractual conditions so that both will be performed on a single payment
at maturity (bullet bond like), all other conditions still, results are:
M Loan NPV (EVE)
Term Deposit NPV (EVE)
EaR
Outs Princ Paym
Int Int Paym
Cash Flow
1055.05 Outs Princ Paym
Int Int Paym
Cash Flow
1009.17 47.66
0 1000.00 1000,00
1 1000.00 0.00 11.71 0.00 0.00 1000.00 0.00 7.97 0.00 0.00 0.00 3.74
2 1000.00 0.00 11.85 0.00 0.00 1000.00 0.00 8.04 0.00 0.00 0.00 3.81
3 1000.00 0.00 11.99 0.00 0.00 1000.00 0.00 8.10 0.00 0.00 0.00 3.89
4 1000.00 0.00 12.13 0.00 0.00 1000.00 0.00 8.17 0.00 0.00 0.00 3.97
5 1000.00 0.00 12.27 0.00 0.00 1000.00 0.00 8.23 0.00 0.00 0.00 4.04
6 1000.00 0.00 12.42 0.00 0.00 1000.00 0.00 8.30 0.00 0.00 0.00 4.12
7 1000.00 0.00 12.56 0.00 0.00 1000.00 0.00 8.36 0.00 0.00 0.00 4.20
8 1000.00 0.00 12.71 0.00 0.00 1000.00 0.00 8.43 0.00 0.00 0.00 4.28
9 1000.00 0.00 12.86 0.00 0.00 1000.00 0.00 8.50 0.00 0.00 0.00 4.36
10 1000.00 0.00 13.01 0.00 0.00 1000.00 0.00 8.57 0.00 0.00 0.00 4.44
11 1000.00 000 13.16 0.00 0.00 1000.00 0.00 8.63 0.00 0.00 0.00 4.53
9
12 0.00 1000,00 13.32 150.00 1150.00 1055.05 0.00 1000.00 8.70 100.00 1100.00 1009.17 4.61
Bullet
EaR DE 47.66
EaR DFVE 45.87
EVE 45.87
Although the maturity of the bullet example is 12 months, results will equal under any
maturity if the structure of the loan and the deposit are perfectly matched, and if EaR
is obtained under EaR DFVE. What happens in this case is that all earnings and its
originating cash flows coincide with the accrual term. That is, at each month, interests
are paid and received and earnings are accrued. Whenever this condition is broken,
results will be different.
Earnings approach (EaR) is a frequently used methodology for budgeting and future
predictions of results (earnings) derived from balance sheet projections. But budgeting
goals are different from capital requirement ones and despite intuitively it can serve
both objectives, if the arguments here hold, that is not the case. Results prediction
indeed look for the future value of earnings, commonly seen in companies guidelines,
and that is what EaR gives. But it is not suitable for a capital charge calculation, as the
objective is a present value of economic losses.
In the real world, the EVE assumptions hold better. It is not reasonable to assume that
cash will stay put. It will be reinvested in something and the same for negative or cash
gaps: it can’t be funded assuming zero cost. If this is true, then an earnings approach
should take it into account to be more precise, not to mention the incorrectness of
basing calculation on pure earnings segregated from cash flow dates. But simulate this
under an earnings approach implies that the earnings resulting from this reinvestment
hypothesis must be explicitly displayed, and this a quite complex practical issue to
simulate.
The coherent and complete reinvestment hypothesis in the real world, not assuming
the issuance of new asset positions, is earn from positive net cash flow and pay the
funding cost for negative ones. And EVE indeed does that. As all received cash flows
are immunized, then this is true for positive and for negative ones. That is, negative
cash gaps are funded by the discount rate used, and positive cash gaps generate the
discount rate income.
EVE though has an advantage, not for its simplicity, but because it holds an inherent
and more reasonable implicit reinvestment assumption. It is worth noting that3 “The
3 COPELAND, T; WESTON, J, 1992. Financial Theory and Corporate Police, 3
rd ed: USA, Addison Wesley, p
24. Despite not explored here, this finding blurs the supposed contradiction of earnings stabilization and equity economic value stabilization. Indeed, earnings stabilization in this sense is much more a market
10
main differences between accounting definition and the economic definition of profit is
that the former does not focus on cash flows when they occur, whereas the latter does.
(…) Financial managers are frequently misled when they focus on the accounting
definition of profit, or earnings per share. The objective of the firm is not to maximize
earnings per share. The correct objective is to maximize shareholders’ wealth, which is
the price per share that in turn is equivalent to the discounted cash flows of the firm.”
2.3 Cost of Funding and Discount Rate
As said, the implicit reinvestment assumption in the EVE approach can be thought of as
if every paid or received cash flow was future valued up to the chosen time horizon by
a forward rate that is exactly the discount rate used to obtain the final EVE.
Graphically:
Where:
T = time horizon of EVE calculation
tf = original maturity of the cash flow
id = discount interest rate
ip = original or contractual interest rate of the position
Taking the same example used before, it is easy to manipulate the deposit and the
discount rates and calculate the EVE for any maturity of the deposit between 1 and 60
months, maintaining the original cash flows of the loan. In the same example used up
to here, loan and deposit rates are reset to be equal, in 10% (the original interest rate
in the examples above) and then in 15% (the same rate of the loan). Maturity of the
deposit is then made varying from one to 60 months. Intuitively, if loan and deposit
rates are equal, result should be zero. And if the deposit rate is lower than the loan
rate, results should be positive. Graph bellow shows EVE results for each maturity of
the 10% and 15% rate deposit (loan conditions stay still):
value portfolio short term strategy than a business strategy or goal. And this last is what capital requirement for IRRBB is about.
id T tf
id
ip
i
11
It is interesting to take a closer look to the EVE behavior described by the red line. The
15% funding rate used here is the same of the loan (or investment rate). Again, what
drives the final EVE are the reinvestment assumptions of the method. Once the loan is
monthly amortized, as time passes, a decreasing amount earns the original investment
rate. On the deposit side, once it is settled as a single payment, the longer the term,
the higher the participation of the original cost.
Despite closer to reality, the problem with the EVE calculated this way is that, the
bigger the amount of cash derived from positive or negative cash gaps, and the longer
the gaps, the more funding and/or investment original rates will approach the discount
rate. This can be thought of as the discount rate “diluting” the original contracted
rates, distorting the final economic (or present) value the more reinvestment and
funding rates differ from the discount rate used. Remembering that banks use to have
longer maturities for assets and shorter for liabilities, a trend will appear as funding
cost will be closer to the discount rate much before investment rates will do.
The question here is how close to reality such assumption is. Indeed what it is saying is
that even when there is positive cash, the bank prefers to earn less (or is not able to
earn more) than what it is paying for funding. Or, conversely, if we pay attention to the
higher EVE at lower deposit maturities, the assumption is that the cost of funding is
decreasing, as negative cash gaps will be funded at a lower (the discount) rate
(supposing that the cost of funding is higher than the discount rate).
It may be argued that funding and investment options are not entirely under the
discretion of a bank, what limits or reduces the ability for a rebalance. However, it may
be considered unreal to assume that the bank will simply stay put, which is indeed the
assumption behind this simulation.
-300
-200
-100
0
100
200
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
EVE
Loan rate 10% Loan rate 15%
12
It is possible though to simulate a situation where a bank can chose always the lower
funding cost for a given asset structure. Supposing that the discount rate is lower than
the asset earning rate, the best cost matching will happen if the bank only keeps funds
when there exists an asset backing it. The idea is that, whenever a cash is received, a
funding position is eliminated, as the spread produced by pure cash application will be
lower than that of the asset earning rate. This means that the cash gap is intended to
reach a minimum. It doesn’t mean that there is no liquidity gap (an unreal hypothesis)
but rather that the bank is able to eliminate funding when no investment is performed,
minding that funding tends to preset shorter maturities then assets. This assumption
means that, no matter the cash flow profile of the funding, it would only impact gains
or net margins when there is an asset to match it.
Indeed, other hypothesis or assumptions can be imagined to take advantage of the
implicit role played by the discount rate. The idea here is that it can be used as an
alternative or complimentary driver when dealing with non-maturity deposits (NMD),
usually focused on the behavior of the depositor, by modeling these funds based on
asset outstanding profile as well.
3 Dynamic x Static Simulations
Either based on earnings or economic value approaches, two types of simulations can
be used: static or dynamic. A static simulation is usually defined as a simulation where
all contracted cash flows are projected (earnings may be projected as well) and a net
present value of all is obtained. A dynamic simulation, on the other hand, will account
for explicit reinvestment choices, the issuance of new asset positions and all more
considered necessary to reproduce, precisely as possible, the evolution of the balance
sheet and the consequent earnings under a given time frame. Dynamically simulated, a
net present value would be obtained from assets and liabilities the same way carried
on static ones, but with obvious different results.
Put this way, one can conclude that dynamic simulations are much closer to reality
than a purely static one, despite more complex and burdensome. The price though for
this realism is that, if the simulation horizon gets too long, assumptions may not hold
making results not as accurate as expected, limiting its usage for short periods of no
more than 2 years usually.
The first thing about static simulations is that, even being static, some implicit
underlying assumptions regarding reinvestment and rolling of positions are always
there when received and paid cash flows are present valued. Dynamic simulations on
its turn seem to be always linked to earnings or EaR approach, but quite not to EVE.
Assuming continuity of business, the search for profitability must translate projects
and investments into earnings, as that is what stockholders and managers track in the
13
short run, but having the maximization of shareholders wealth in mind for the long
run.
However, capital cushion has a different perspective than a dynamic picture shows up.
It is aimed at protecting (a bank, in the case) from unexpected losses under a given risk
profile assumed. Despite the risk is potential, the ground (or positions) on where it will
be translated into a loss is not.
Another point to bear in mind is that capital requirements are frequently
(re)calculated. Its rationale is the same of as a dynamic hedge, as capital cushion is
frequently recalculated the same way a dynamic hedge is constantly rebalanced. This
means that as new positions or conditions take place, a new amount will be required
based on a gradual process.
If capital is allocated based on future (not contracted) positions, the loss will translate
the effect of this positions now, and this can be considered unreal. Even if it is highly
probable that these new positions will be issued, if a shock happens before the trade is
done, only contracted positions will generate the loss. The new ones will be traded
under the new scenario or level of interest rates, with price and profitability already
balanced. Besides, some room must be left for an active rebalancing role of the bank
as new interest rate conditions take place
If what is argued here holds, than static simulation grounds are more adequate when
dimensioning capital for the interest rate of the banking book, not to mention the
simplicity issue involved. Complexity then should focus on predicting cash flows as
precisely as possible and on what may happen to received and paid cash, dealing with
the static reinvestment assumptions mentioned earlier.
4 Conclusions and Suggestions
EVE and EaR, defined for the purposes of this paper as meaning cash flow based
approach and earnings based approach, respectively, are two methodologies widely
used and often seen as complementing each other, for calculating a capital
requirement for the IRRBB. However, results obtained by each one on a hypothetical
same situation, that is, asset and liability positions, can be significantly different. A
closer look on what makes them different shows that the accrual basis of earnings
strongly suggests that EVE is more adequate. The accrual basis of the EaR approach is
not suitable for the task of dimensioning a present capital monetary amount, as the
coherence between future and present values must be referenced on the cash flows
and not on the consequent earnings this cash flow generates. Besides, if EaR is used on
static simulations, the implicit reinvestment hypothesis assumes unreal zero costs for
funding and reinvestment. EVE, once based on cash flows, produces coherent results
between future or predicted values and its corresponding present value. Besides, it
14
assumes a more realistic reinvestment and funding hypothesis due to the
immunization effect of present valuing cash flows. EVE implicitly assumes that negative
cash gaps are funded at the discount rate cost, and positive cash gaps are reinvested
under this same discount rate cost.
However, the bigger the cash gaps – negative or positive – the more the original
funding and investment rates tend to be closer to the discount rate. A way to
attenuate this effect is to attach or model funding or liability cash flow profile to the
assets cash flow profile or outstanding. This can be used as an allocating driver when
dealing with NMD, where maturities are not determined. This tends to reduce the cash
gaps effect mentioned, besides mirroring a coherent economical behavior.
Independently of the methodology used, capital requirement calculations for the
IRRBB can be done based on static or on dynamic simulations. Static simulations do not
allow for the issuance of new positions, either for funding or investment. It was shown
though that implicit reinvestment and funding assumptions are always present even
on static simulations, and their effect on results must be considered. However, the
explicit issuance of positions, particularly assets or investment ones are not a coherent
scenario to base capital calculation requirements, as this capital is frequently balanced
based on actually contracted positions at calculation time, hence, behaving
dynamically.