One such measure is referred to as risk- adjusted return on capital, or RaRoC where capital is defined as economic capital. 50
Fundamentals of Financial Risk Management Risk-adjusted Performance This can be defined simply as: where NI is net income, R represents revenues, D is debt costs, O is operating expense and EL is expected loss, EC is economic capital and HR is the bank’s hurdle rate. 51 RaRoC NI EC HR NI R D O EL
Fundamentals of Financial Risk Management Risk-adjusted Performance A value for RaRoC that meets or exceeds the target return HR is a viable project. An alternative way of expressing risk- adjusted performance is with the shareholder value-added (SVA) metric. It basically modifies RaRoC by adjusting for the cost of capital using the HR as the unit measure of capital cost. It may be formally defined as: 52 SVA NI HR * EC 0
Fundamentals of Financial Risk Management Risk-adjusted Performance SifiBank Holding Co. has conducted its assessment of economic capital across each business unit according to the earlier discussion in this chapter aggregating across credit, market and operational risk with the estimates shown in Table 6-3. SifiBank Holding Co. has a target rate of return of 15%. 53
Fundamentals of Financial Risk Management Risk-adjusted Performance As useful as this may be it still ignores potential risk diversification effects that may exist between business units. Drawing from portfolio theory, the VaR for SifiBank Holding Company can be defined as the following: where represents the ith business units weight (percent of portfolio assets) and is the correlation coefficient between business unit i and j. The correlation coefficient can also be used to define the covariance between any two business units as follows: To be more accurate, the correlations might actually exist among different risk types across units and the risk analyst would thus need to compute compute a matrix of correlations for each combination of risk (i.e., credit, market, operational) and business unit. While this adds to the complexity of the problem, the above example preserves the conceptual portfolio VaR problem. 54 VaR P w i 2 VaR i i 1 3 2 w i w j VaR i VaR j ij j 1 3 i 1 3 ij ij i j
Fundamentals of Financial Risk Management Risk-adjusted Performance Applying this formula to SifiBank Holding Company’s business units based on the correlation structure among the divisions results in a portfolio 99% VaR of $238 billion. This obtained by taking the unit VaR for each division (defined as the standard deviation of each division times 2.33), aggregating across the weighted sums for each division at the bottom of the table, taking the square root of that result and multiplying it by the portfolio value of $1 trillion. 55
Fundamentals of Financial Risk Management Risk-adjusted Performance 56
Fundamentals of Financial Risk Management Risk-adjusted Performance The fact that the correlations between business units are not perfect (i.e., ) suggests that there is a risk diversification benefit resulting in lower VaR than in that case.
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