class notes
Economic capital ideas
Class Notes is an educational series, designed to pull together the threads of
recent developments and thinking about key issues in risk management and
derivatives dealing. In this instalment, Charles Smithson explains the concept
behind economic capital
Economic capital
is a measure of the amount of equity capital an enterprise
needs to support a risk. More specifically, it is the amount
of equity capital necessary to cover losses arising from that risk to some confidence level.1
For example, many of the large international banks define economic capital as the amount
of equity capital needed to cover losses 99.97% of the time.
In contrast with an accounting view, where capital could be viewed on the right-hand
side of the balance sheet, economic capital is a ‘left-hand-side-of-the-balance-sheet’
concept: the amount of capital needed is determined by the riskiness of the company’s
assets (including the firm’s business units and activities).
While equity capital is the source of the ‘needed’ capital as defined by economic capital,
the amount of equity capital required can be reduced by insurance and guarantees or by
transferring risk to a third party.
Rationale
Firms face a range of risks: market risk, credit risk, insurance risk (for example, mortality and
morbidity) and operational risk, as well as business risk, reputation risk, compliance risk and
liquidity risk. Each risk has its own risk measures. For example, market risk measures include
duration and convexity (for interest rates), the Greeks (delta, gamma, vega, theta, and so on)
and, more recently, value-at-risk (VAR), while credit risk measures include characteristics of
the obligor (probability of default), characteristics of the transaction (exposure in the event of
default and loss in the event of default) and characteristics of the portfolio, which do not
consider correlation (expected loss and concentrations).
For market, credit and operational risk at least, economic capital has become the
language of risk. While the risk-type-specific risk measures are still used, market risk,
credit risk and operational risk can all be expressed in terms of the amount of equity
capital needed to support that risk and, since the measures are in currency units, we have
an apples-to-apples measure.
In addition to providing a common language, economic capital permits the firm to
express its risk appetite. (Above we noted that many large banks use a 99.97%
confidence level for measuring economic capital. That confidence level was selected
1
obert Merton and Andre Perold described risk capital as providing a kind of asset insurance against the possibility of lower-than-expected
R
operating results.
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class notes
know about economic capital, not only for the enterprise as a
whole but also for component business units, the calculation
of economic capital is normally accomplished using a bottomup approach.
Recognising that the different risk types share common
determinants, some firms rely on a single model that produces
an economic capital value that reflects market risk and credit
risk (and, at least theoretically, operational risk).2 Clearly, the
benefit of such a model is that the correlations of market, credit
and operational risk are captured.
However, the more common approach is for the firm to use
individual models for each of the risk types. Economic capital for
market risk is obtained from some kind of VAR model. Economic
capital for credit risk is obtained from a credit capital model –
either internally developed or vendor-supplied. Economic capital
for operational risk could be obtained using a process approach
(which focuses on the chain of activities that comprise an
operation or transaction), a factor approach (which relates the level
of operational risk to factors that have been identified as
significant determinants) or an actuarial approach (which
identifies the loss distribution associated with operational risk).
The separate economic capital measures are then aggregated.
The obvious question is how to deal with the correlation between
risk types. Simply adding up the economic capital numbers for
the individual risk types is overly conservative, because it
assumes perfect positive correlation – in other words, no
diversification across risk types. However, estimating the degree
to which the different risk types are correlated is an extremely
difficult task. Approaches to this task are characterised as
bottom-up and top-down.
A bottom-up approach can be viewed as a five-step process:
Charles Smithson, Rutter Associates
because it corresponds 100% minus the historical likelihood of
an AA rated firm defaulting in a one-year period. This reflects
the risk appetite of senior management and the board in terms
of credit rating.)
Calculating economic capital at the enterprise level
Early work on economic capital envisioned being able to calculate
economic capital for a firm using a top-down approach. If it were
possible to obtain daily, weekly or monthly observations on
earnings, the resulting distribution would reflect not only the
effects of market, credit and operations risk, but also the
correlation of these risks. Specifying a confidence level determines
earnings-at-risk (EAR). To convert EAR to economic capital, the
enterprise identifies the amount of equity capital required today
to ensure that EAR in future periods is offset by risk-free earnings.
Economic capital =
Earnings at risk
r
Risk South Africa Autumn 2008
A top-down approach can be viewed as a three-step process:
(1) e stimate the distributions of the individual types of economic
capital;
(2) define the dependence structure; and
(3) generate joint distribution of risk types.3
Risk contributions
While the ability to measure economic capital at the enterprise
level and report that measure to stakeholders and regulators is
valuable, the value of the economic capital concept is potentially
much larger when it is applied to some core business decisions:
e 2006 IFRI-CRO Forum survey into the economic capital practices of 17 banking institutions and
Th
16 insurers in Europe, North America, Australia and Singapore indicated that insurance companies are
more likely than banks to incorporate the different risk types into a single economic capital model.
3
The 2005 survey conducted by PricewaterhouseCoopers and The Economist Intelligence Unit found that
33% of the 200 financial institutions surveyed do not incorporate the correlation between risk types. The
2006 IFRI-CRO Forum survey suggested that a similar, albeit smaller, percentage of respondents were
not incorporating correlation between risk types: six of the 33 participants reported that they use a simple
summation approach. Of the 27 that attempted to incorporate inter-risk correlation, 23 characterised
their approach to inter-risk diversification as top-down.
2
where r is the risk-free interest rate.
Because of difficulties in obtaining reliable high-frequency
earnings data and, more importantly, because firms want to
38
(1) e stimate the distributions of economic risk factor, which
might include the term structure of interest rates, credit
spreads, equity returns and other macroeconomic factors;
(2) relate the economic risk factors to individual risk types;
(3) generate marginal loss functions for risk-factor changes;
(4) define the dependence structure; and
(5) g enerate joint distribution of risk-factor changes and model
the impact of these risk factor changes on the loss function
for the enterprise.
Evaluating the performance of business unit managers.
A llocating capital to business units – that is, determining
which businesses to grow and which to shrink.
n Internal pricing.
n Entry/exit decision – that is, deciding which businesses to
acquire and which to divest.
n
n
An aggregate measure of economic capital for the enterprise is
not sufficient to address these issues. It is necessary to determine
the amount of economic capital that should be attributed to
individual business units or portfolios or transactions – called
risk contributions.
This is not a theoretical argument: firms are attributing
economic capital to individual business units/portfolios/
transactions. Rutter Associates’ 2004 Survey of Credit Portfolio
Management Practices demonstrated that fact in the case of
economic capital for credit risk. All of the 44 financial
institutions that participated in the survey indicated that they
attribute economic capital to individual business units or
individual transactions. The complication is that there is more
than one way to measure risk contributions.
Stand-alone risk contributions
The stand-alone risk contribution is the amount of equity capital
an individual business unit, portfolio or transaction would require
if it were an independent enterprise. (The model or models used
to measure economic capital for the enterprise would be run
again using the individual business unit/portfolio/transaction as
the enterprise.)
Stand-alone economic capital does not reflect the
diversification benefits that would be obtained if the business
unit/portfolio/transaction is part of a larger enterprise.4
Standard-deviation-based marginal risk contributions
The standard-deviation-based marginal risk contribution for the
ith business unit, portfolio or transaction is:
RC i = wi
∂σ E
∂wi
where σE is the standard deviation of returns for the enterprise,
and wi is the weight (position size) for the ith business unit or
portfolio or transaction
The measure is referred to as a standard-deviation-based
measure because it looks at the impact on the enterprise’s
standard deviation of changes in the size of individual business
units/portfolios/transactions. It is referred to as a marginal risk
contribution because of the use of the partial derivative: we are
looking at changes in the enterprise standard deviation with
respect to small changes in position size.
If the weights are scaled appropriately, the sum of the
standard-deviation-based risk contributions will add up to the
enterprise standard deviation.
1 Shortfall-based risk contribution
Probability
Simulated loss distribution
Loss corresponding to ‘threshold’
confidence level
Loss corresponding to confidence
level used to calculate economic capital
A diversified risk contribution measures the amount of total
enterprise economic capital that should be attributed to an
individual business unit/portfolio/transaction when it is viewed
as a part of the multi-business-unit/portfolio/transaction
enterprise. This approach attributes the diversification benefit to
the individual business units/portfolios/transactions that make
up the enterprise, in the form of economic capital contributions
that are lower than the stand-alone contributions. Consequently,
the sum of diversified risk contributions for all the business
units/portfolio/transactions will be equal to total economic
capital for the enterprise.
To provide some intuition for a shortfall-based diversified risk
contribution, consider attributing economic capital for credit
risk to the different business units/portfolios/transactions. Figure
1 illustrates the simulated loss distribution for the enterprise.
The loss corresponding to the confidence level defined by senior
management and the board (for example, the 99.97th percentile
in the case of the large, international banks) is identified by the
up arrow.
Select a threshold confidence level lower than the confidence
level used for measuring economic capital (for example, if the
confidence level for economic capital is 99.97%, the threshold
level might be 99.5%). In figure 1, the corresponding loss level is
indicated by the down arrow.
Identify the iterations of the simulation in which simulated
loss exceeded the threshold level. For business unit/portfolio/
transaction A, the conditional loss rate is:
Conditional
=
loss rate
Shortfall-based diversified risk contributions
Instead of considering how an individual business unit or portfolio
or transaction contributes to the enterprise standard deviation, a
shortfall-based measure focuses on the amount it contributes to
loss when the enterprise is under stress – that is, when the
observed (or simulated) magnitude of the loss for the enterprise is
in the upper tail of the loss distribution. (Consequently, these
measures are also referred to as tail-based measures.)5
Currency units
(for example, US dollar)
Mean
simulated loss
4
5
Conditional number of
defaults for ‘A’
Number of losses above
‘threshold’ level
onsequently, the sum of stand-alone capital for the enterprise’s individual business units or portfolios or
C
transactions will be greater than the total economic capital for the enterprise.
At least in the case of economic capital for credit risk, the survey evidence indicates that firms are moving
from standard-deviation-based to shortfall-based risk contributions. Between the 2002 and 2004
Rutter Associates’ surveys of credit portfolio management practices, the use of standard-deviation-based
risk contributions declined (from 50% to 38%), with the use of shortfall-based risk contributions
increasing (from 13% to 33%).
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CLASS NOTES
where the numerator is the number of defaults for A, conditional
on simulated loss for the enterprise exceeding the threshold level.
Then, the conditional attribution to business unit/portfolio/
transaction A – the shortfall-based risk contribution – is:
Conditional
Conditional loss
=
attribution to ‘A’
rate ‘A’ x LGD(A)
indicated that they were broadly comfortable with the accuracy
of outputs.
Looking only at economic capital for credit risk, the 2004
Rutter Associates Survey of Credit Portfolio Management
Practices found that 43 of the 44 financial institutions that
responded to the survey calculated economic capital.
Insurance companies
Shortfall-based marginal risk contributions
As long as the threshold is defined as a percentage (for
example, 99.97%), the marginal risk contributions sum to
total economic capital for the enterprise (Pearson (2002),
pages 161–162).
For the 16 insurance companies that participated in the 2006
IFRI-CRO Forum survey, economic capital frameworks had been
in place at insurance companies an average of four years. Like the
banks, 12 of the 16 insurance companies indicated that they were
broadly comfortable with the accuracy of outputs.
Writing in Best’s Review, a monthly magazine covering the
insurance industry, early in 2007, Robert Stein had a different
perspective. He noted that, even though nearly 90% of the
respondents to an Ernst & Young survey of North American
life insurers had indicated that economic capital is essential
to performance evaluation and making strategic decisions
about mergers and acquisitions, the majority of US insurers
have yet to integrate economic capital into their core decisionmaking process.
Which risk contribution measure is right?
Investors
As with so many things, the answer is: it depends. In this
instance, the right risk contribution measure depends on which of
the business decisions is being considered.
In 2004/05, the HSBC Financial Products Institute received
responses regarding risk measurement and management practices
from 20 mutual funds, 51 pension plan sponsors, 30 university
endowments, 20 foundations and nine hedge funds. These
responses indicated that economic capital had not made much of
an inroad with institutional investors: only three out of 49
institutional investors indicated they were employing an
economic capital measure for market risk and just five out of 115
indicated they were employing an economic capital measure for
credit risk. n
Instead of considering how a small change in the size of an
individual business unit, portfolio or transaction affects the
enterprise standard deviation, this measure considers how a small
change in the size of an individual business unit, portfolio or
transaction affects the expected shortfall (ES):
RC = wi
∂ ( ES )
∂wi
I t is generally agreed that stand-alone capital is appropriate for
measuring the performance of business unit managers.
n It is also generally agreed that marginal economic capital is the
appropriate measure for evaluating acquisitions or divestitures.
n However, there is less agreement about the appropriate
measure for allocating capital to business units and internal
pricing. While academics argue that marginal economic
capital should be used, practitioners appear to be using a
measure of diversified economic capital. Proponents of the
diversified economic capital approach point out that
marginal capital always under-allocates total enterprise
capital and that, even if the marginal capital numbers were
scaled up, the signals sent about profitability are potentially
misleading. Proponents of the marginal economic capital
approach argue that, because economic capital is not
additive across business units, any rule that fully allocates
enterprise economic capital across the business units will be
sub-optimal.
n
How widely used is economic capital?
In October/November 2005, PricewaterhouseCoopers and The
Economist Intelligence Unit conducted an online survey of
financial institutions in Asia, Europe and the Americas. Fortythree per cent of the 200 respondents reported they were using
economic capital: 27% were using economic capital across the
enterprise and 16% were currently using economic capital in
certain units.
Banks
For the 17 banks that participated in a 2006 survey by the
International Financial Risk Institute (IFRI) and the Chief Risk
Officer (CRO) Forum, economic capital frameworks had been in
place at banks an average of six years. And 12 of the 17 banks
40
Risk South Africa Autumn 2008
Charles Smithson is a partner at Rutter Associates. He would like to thank Neil
Pearson for his help on this article. Email: csmithson@rutterassociates.com
References
Christian C, 2006
Copula-based top-down approaches
in financial risk aggregation
Working Paper 32, the University of
Applied Sciences of bfi Vienna
IFRI Foundation and Chief Risk
Officer Forum (CRO Forum), 2006
Insights from the joint IFRI/CRO forum
survey on economic capital practice
and applications
Merton R and A Perold, 1993
Theory of risk capital in financial firms
Journal of Applied Corporate Finance
Pearson N, 2002
Risk budgeting: portfolio problem
solving using value at risk
Wiley
PricewaterhouseCoopers, 2005
Effective capital management:
economic capital as an industry
standard?
Rutter Associates, 2004
Rutter Associates survey of credit
portfolio management practices
Sponsored by International Association of Credit Portfolio Managers,
International Swaps and Derivatives
Association and Risk Management
Association
Rutter Associates
HSBC Financial Products Institute
2004–2005 survey of risk measurement
& management practices of
institutional investors
Stein R, 2007
Using economic capital as a tool
Best’s Review