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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: roberto.nygaard@bcb.gov.br

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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.

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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

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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

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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

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*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:

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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

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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

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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

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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

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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%

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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

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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

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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.