Portfolio managers try to optimize the use of economic and not regulatory capital. What is the difference? First, we emphasize what they share; they both represent capital which the bank must hold to serve as a cushion against unexpected losses. Regulatory capital, however, is determined by the Basel accord according to a number of forfeits dependent upon outstanding balances and the category of counterparty. This definition produces an incorrect measure in the context of marked to market accounting; hence the need for economic risk.
These shortcomings can be categorized as the adoption of a measure for credit risk which does not distinguish between corporates. Further governments are assigned a very low credit risk somewhat arbitrarily.
Finally the forfeits are identical for short- and long-term commitments, when obviously the latter carry higher risk. Most alarmingly the regu- lators measure portfolio risk as the simple addition of the individual risks which ignores diversification effects. This has the unfortunate effect of a diversified portfolio and a concentrated portfolio potentially having the same risk.
These concerns are being addressed within the new framework of Basel. We cover this in Section 2.16.
Due to these inefficiencies in measuring credit exposure any target performance based upon regulatory capital may not depend upon the true credit risk. Economic capital is intended to correct these distortions.
Ultimately any difference will be reflected in customer pricing; get this wrong and the bank could end up subsidizing the competition.
Figure 2.9 shows how the use of regulatory capital will miss-price the loan.
The amount of economic capital is derived using the VAR method- ology. There are a number of distinct steps involved in the derivation.
These include:
• The shape of the loss distribution.
• A tolerance level.
• A horizon period.
It will be helpful to inspect the loss distribution of a loan portfolio depicted in Figure 2.10. The reader should note the distinct shape in comparison to a normal distribution. This is often interpreted as the distinction between credit and market risk. This can be misleading as market risk itself is really only approximated by the normal distribu- tion. (The reason the normal distribution is so important in finance is
that it is both a good approximation to reality and analytically tractable.)
We have highlighted in the chart the jargon beloved of the practi- tioner. Reading from left to right any loss on the portfolio between zero and the ‘expected’ loss is taken care-of through a combination of reserves, hedging and policies. As we pass the average loss, we move into ‘unexpected territory’, the implications for management are that losses in this region must be provisioned through capital.
We then encounter the next vertical line which depicts the limit of unexpected losses which is exactly the capital at risk (CAR). As we move further to the right the losses are no longer cushioned. Any loss that actually occurred would be referred to as ‘exceptional losses’.
They are not provisioned against because they are very rare and to do so would ultimately be uncompetitive because too much capital would have to be set aside.
From this picture it is implicit that we have separated out two vital ingredients necessary to establish risk management. The actual real world described by the distribution together with the human decision on the location of the vertical lines. The human involved employs sea- soned judgement, gained through many years experience managing loan portfolios, no doubt.
If you are a neophyte there are a number of methodologies employed to establish the location of this line. One is a gimmick and depends on how risk averse the managers are. It is a gimmick because their hands are usually tied.
They are tied because of the restriction on the amount of available capital. We offer a little illustration. Suppose we use the gimmick and come up after much deliberation in committee meetings with a toler- ance of two-and-a-half per cent on a loan portfolio with expected losses of 1.4 per cent per annum and a volatility of 6 per cent
0 5 10 15 20
Unexpected loss (%)
Target price (%)
1 2 3 4 5 6
Regulatory capital Customer rate
Figure 2.9 Target prices of credit risk.
per annum then the maximum risk is given by:
However, the available capital is only 12 per cent of the nominal so:
This implies a tolerance level of about 3.8 per cent.
The main business driver of risk aversion is the target rating, mainly because of funding considerations, whereby the bank finances its business at libor plus a spread related to their credit rating.
Implicit in a rating is a default rate. Thus the tolerance level should be identical to the figure associated with the target rating. For example, if we assume that the target rating has a probability of default rate of 0.25 per cent, then under the assumptions of a normal distribution the multiple associated with this probability is close to three.
This multiple generates a requirement for capital of 18.26 per cent using the above figures for earning and volatilities. This is the eco- nomic capital required to achieve the desired rating. This is a some- what extreme example, highlighting an unrealistic quantity of capital.
The usual goal of management would be to ensure the portfolio has a loss volatility, at any time, consistent with the rating demand.
2.12 CAR
We gave some simple examples illustrating the build-up of CAR (Figure 2.10) from the confidence level. Moreover these were based on the unreal- istic assumption of a normal distribution. With low confidence levels, indeed many banks will set out to achieve a 0.5 per cent tolerance level.
The so-called ‘tail risk’ becomes of paramount concern. Unfortunately the shape of the so-called ‘fat tail’ in a loan portfolio makes the meas- ure especially sensitive to the assumptions of the loss distribution. We describe modifications to the distribution in Section 2.3 on funda- mental credit.
Choice of horizon
In general the probability of default grows with the increase of the horizon date. The so-called cumulative default rate can be obtained
1.4 t 6 12
fi
t 1.77.1.4 1.96 6 13.16. 3
3The assumed way of getting from the tolerance level to the monetary amount was none other than the normal distribution. (Consequently using 2.5% gives an inverse normal of 1.96%.)
from each of the yearly, variable default rates. Consequently the CAR for credit risk increases with increasing horizon length.
What horizon length should we deploy?
Within the loan market there are two possibilities of either using the residual maturity on existing facilities or the period of time required for raising capital, that is the existing capital only has to absorb losses until sufficient extra-funds are available. The assumptions here are worth questioning since in the event of loan provisioning it might not be possible to tap funds according to typical operations.
Build of hurdle rate given a capital at risk (i.e. risk-adjusted return)
We now move on to discuss risk-adjusted performance. Performance within the banking portfolio cannot adequately be captured using trad- itional accounting measures. This is simply because within the financial world there is no performance without a compensating risk exposure.
Consequently only some risk-reward combination is meaningful.
The benefit of risk-adjusted performance is that it allows compari- son of profitability across different loans.
The two main measurements of risk-adjusted profitability are the risk-adjusted return on capital (RAROC) and the shareholders value added (SVA).
0
Expected Probability loss
Portfolio loss distribution
Unexpected loss limit
Losses (%)
0 2 4 6 8 10 12 14
0.25 0.2 0.15 0.1 0.05
Figure 2.10 The definition of CAR.
Risk-adjusted ratios include return on risk-adjusted capital (RORAC) and RAROC which adjusts revenues for expected losses.
To obtain RAROC the expected loss should be deducted from earn- ings and the result divided by the capital necessary to absorb unex- pected losses.
The definitions:
The shareholders measure is
with examples in Table 2.6.
In Table 2.7 we set out the usual calculation for using the CAR to obtain the pricing of a loan. This is common within commercial banks
SVA earnings hurdle rate CAR, RAROC earnings expected loss (EL)
CR (or UL) .
Table 2.6 Example of the RAROC and SVA calculation.
Item Value
Loan portfolio valuation $100 000 000
Expected default rate 1%
Volatility of default 5%
Hurdle rate 25%
CAR (1.65*Vol. *exposure) $8 250 000
Earnings $3 000 000
Expected loss $2 000 000
RAROC 24.2%
SVA $937 500
Table 2.7 Customer rate given an RAROC.
Item Value
Loan portfolio valuation $100 000 000
CAR $6 000 000
Expected loss $2 000 000
RORAC 22%
Operating costs 2%
Cost of debt 10%
Risk premium, CARRORAC/loan
portfolio valuation 1.32%
Price (expected lossoperating costs
cost of debtrisk premium) 15.32%
who wish to know how to maintain a rating; consequently the CAR is the value that drives the analysis.