Business — Banking — Management — Marketing & Sales

The implication of what precedes is that we need both risk contributions, but for different purposes. Absolute risk contributions are ex post measures. They measure risk contributions for a given set of facilities. Therefore, absolute risk contributions serve to allocate capital for an existing portfolio. Marginal risk contributions are ex ante measures and serve for risk-based pricing.

Ex Ante versus Ex Post Views of Risk and Return

Ex ante marginal risk contributions are adequate for risk-based pricing of new facilities. However, once included in a portfolio, the return of new facilities on their allocated capital becomes lower than the target return obtained on the marginal risk contribution at the pricing time. This is not relevant since all other facility returns over their absolute risk contributions improve because of the dilution of these existing absolute risk contributions within an increasingly diversified portfolio. Therefore:

• Absolute risk contributions serve to allocate capital to existing facilities and to set up limits. This allows us to allocate capital in such a way that all capital allocations sum to the portfolio capital. In addition, limits for an existing portfolio can be set in terms of capital, and compared to the capital usage of each subportfolio.

• Marginal contributions serve for pricing. Marginal risk contributions ensure that the portfolio return remains at least at the target level.

See Figure 52.1.

Capital Allocation

As long as the capital is a multiple of the portfolio loss volatility, allocating the loss volatility provides an allocation proportional to capital. Let capital be m x ct_p . Then, if the ARC^p are the basis for capital allocation, the sum of all ARC^p will be the aggregated loss volatility, and m x ARC^p will be the capital allocation to facility i. Since all ARC^p are additive, they aggregate for any subgroup of facilities, by customer, business units or any other criteria. Since all ARC^p are post-diversification effects, they embed more information than the allocation according to the facility standalone risks, which do not include the correlation structure of facilities.

However, it is always possible to allocate capital at the pro rata of exposures, or of standalone risks measured by the standalone loss volatilities. This is a management choice of an appropriate allocation key depending on the trade-off between ease of interpretation and the need to capture differentiated correlation effects.

Risk-adjusted Performance versus Risk-based Pricing

This discussion of risk contributions relates to the distinction between the ex ante measure of risk required to meet a target return on capital, and the ex post risk-based performance using given revenues. Once a facility enters the portfolio, its ex post return, on its allocated capital, drops, compared to the ex ante pricing based on marginal contributions. This phenomenon results from an absolute risk contribution of the new facility higher than the ex ante marginal risk contribution. Nevertheless, the ex post risk-based performances using absolute risk contributions remain necessary for comparing ex post the risk-return profiles of facilities, clients, products and business units.

Without risk-based pricing, we do not know the required revenues. Without ex post risk-adjusted performances based on absolute risk contributions, we cannot compare the risk-return profiles of facilities or subportfolios. Hence, both are necessary because they serve different purposes.

These issues require further developments regarding: the target rate of return on capital for ex ante pricing; the ex post monitoring of risk-adjusted performance; mispricing, defined as the discrepancy between the theoretical target price and the effective price given competition. Chapters 53 and 54 discuss further the ex ante view of the determination of target revenues with risk-based pricing using marginal risk contributions to capital and the ex post view of risk-adjusted performances once revenues are given.

Risk-adjusted Performance

In the financial universe, there is no expected performance without a price to pay in terms of risk. Since only risk-return combinations are meaningful, comparing performances across transactions or business units is inconsistent, and pricing risk to customers without risk adjustment is not feasible. The entire risk-return monitoring and pricing systems depend on such risk adjustments.

Ex post, Risk-Adjusted Performance Measurement (RAPM) serves for comparisons. Ex ante, Risk-Based Pricing (RBP) serves for determining a pricing in line with risk and with the overall profitability goal of the bank. In the first case, income is given, whereas the purpose of RBP is to define what is its minimum level. The risk adjustments are the risk contributions.

Because risk contributions do not depend on the source of risk, market or credit risk, risk-adjusted performance calculations do not either. The same calculations apply to both market and credit risk contributions and performances.

The standard measures of risk-adjusted performance are the Risk-adjusted Return on Capital (RaRoC) and Shareholders Value Added (SVA) (see Bennett, 1991). The first RaRoC ratio is a profitability percentage comparable to minimum risk-adjusted benchmarks, or hurdle rates. The SVA is a value, which combines both percentage profitability and size of transactions, to find whether a transaction or a subportfolio creates or destroys value for shareholders. Both serve in conjunction. The ratio ignores the size effect, so that we do not know whether a transaction with a RaRoC close to the hurdle rate generates much income or not without looking at its size. A high SVA figure does not indicate whether it results from a low percentage RaRoC combined with a large size and vice versa.

Risk adjustments use both expected loss and economic capital allocation. A RaRoC measure nets the expected loss from income and divides the netted income by economic capital. SVA measures net the expected loss plus the cost of economic capital, valued as a hurdle rate times the amount of capital, from income. The reference for the hurdle rate is the cost of capital of the bank.

The hurdle rate, or cost of equity for the bank, is the unit price of risk of each specific bank. This price of risk raises practical and conceptual issues. Market spreads for banks and loans are not in line with the capital charge allocated by banks to transactions and their required return, except by chance. Market spreads are a common reference for all players, while the risk contributions and the cost of equity vary across banks. The risk contributions change because the portfolio structures of banks differ. The cost of equity also changes because the market compensates equity based on the general risk of the banks equity stocks, the //, as the well-known Capital Asset Pricing Model (CAPM) demonstrates.

This chapter defines the risk-based performance measures and discusses their required inputs. The next chapter provides numerical examples illustrating these definitions. The first section discusses the two basic risk-adjusted performance measures, RaRoC and SVA, their inputs and relative merits. The second section discusses the revenue and cost inputs for determining income. The third section addresses the definition of the hurdle rate, or the price of risk, referring to the market cost of equity. The last section discusses the consistency issue between the banks price of risk versus the markets price of risk, as observed in credit spreads, and its implications.