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Section 14. Risk-adjusted Performance

Traditional measures of performances are book returns on equity and capital (ROE or ROC), or ratios of profit to equity and to the capital base. The book return on asset (ROA) is the ratio of the all-in income from lending to the size of the loan. For the trading book, the profitability is its P & L, measured as the variation of value over a period.

But such ratios are not risk-adjusted and cannot serve for comparing performances across facilities or sub-portfolios with different risks or for making explicit the relationship between risk management guidelines and the bank's profitability. The metric for risk-adjusting performances are the capital allocations, or risk contributions.

The standard measures of risk-adjusted performance are "RaRoC," or "risk-adjusted return on capital" and "SVA," or "shareholders value added"1. In simple terms, RaRoC measures a profit divided by risk, using capital as a metric of risk, while SVA measures whether facilities add value by charging to client more that the cost of risk of a position.

This section includes two chapters.

• Chapter 55 explains the rationale for defining risk-adjusted measures of performance. It makes a distinction between risk-adjusted performance of existing portfolio lines and risk-based pricing for new transactions, which relate, respectively, to risk contributions and marginal risk contributions.

• Chapter 56 focuses on implementations: economic income statements, monitoring risk-based performance and consistency of risk-based pricing with the overall return required for the bank's portfolio.

RaRoC and Shareholders' Value Added

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 cost of capital "fallacy" refers to using a single value for the cost of capital, embedding the average risk of the bank's equity to activities of which risks differ. The cost of capital should be differentiated according to risks. In risk-adjusted performance, we keep the cost of capital constant, but we account for risk by allocating capital to transactions or sub-portfolios. If the risk increases, the capital allocation increases and the cost of the capital charge increases, even though the cost of capital to the bank remains the same.

Section 55.1 defines the cost of capital, which combines the required return of equity, the capital allocated to each transaction of the sub-portfolio and the risk-adjusted performance measures, the risk-adjusted return on capital (RaRoC) and shareholders' value added (SVA). Section 55.2 discusses risk-based pricing for new transactions and shows that pricing is consistent with marginal risk contributions. Section 55.3 details the calculation of the RaRoC ratio. Section 55.4 makes explicit the risk premium due to capital charge, or the value of capital-based risk. Section 55.5 introduces SV Ameasures of performance and shows the consistency with RaRoC measures. Section 55.6 focuses on discrepancies between the market price of credit risk and the capital-based price of the same risk. Such discrepancies lead to arbitrages by banks that are further illustrated in Chapter 59 on credit portfolio management.

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