Learning objectives: Define, compare, and contrast risk capital, economic capital and regulatory capital, and explain the motivations for using economic capital. Describe the RAROC (risk-adjusted return on capital) methodology and its benefits. Compute and interpret the RAROC for a project, loan, or loan portfolio, and use RAROC to compare business unit performance.
Questions:
606.1. Peter Smith works at Bland Bancorp, a large international bank and financial services firm. The bank has recently made several significant investments but their success and profitability are highly uncertain; further, the bank has also made several acquisitions. At a board committee meeting, Peter is asked to explain the difference between risk capital, economic capital and regulatory capital. Which of the following is the TRUE statement that is part of his response?
a. "Economic capital is less than risk capital because risk capital is the capital required to guarantee shareholders with 100.0% confidence that it holds enough risk capital to ride out any eventuality"
b. "Regulatory capital is almost certainly higher than economic capital in our securitization business, therefore we do not need to know its economic capital; in other words, whenever regulatory capital exceeds economic capital, there is no reason or need to know economic capital"
c. "We need enough risk capital to absorb unexpected losses and remain solvent over a time horizon with a selected confidence level, but with respect to risk capital, (unlike regulatory capital) the horizon and confidence belong to us as policy parameters."
d. "For capital budgeting purposes, we should use ex ante RAROC with economic capital in the numerator; for performance evaluation we should use ex post RAROC with regulatory capital in the numerator"
606.2. With respect to risk-adjusted performance metrics, let "ratio consistent" refer to a ratio that adjusts both the numerator and denominator for risk. Among the risk-adjusted performance measures discussed in Crouhy, each of the following is true statement about the defined metric EXCEPT which statement is not true?
a. RAROC (risk-adjusted return on economic capital) risk-adjusts the numerator's return by subtracting expected loss from expected revenue and risk-adjusts the denominator by substituting economic capital for accounting capital. RAROC is therefore ratio-consistent.
b. RORAC (return on risk-adjusted capital; aka, ROCaR or ROC) only adjusts the the denominator, in practical applications using VaR in the denominator. Because its numerator is "net income," RARAC is ratio-inconsistent.
c. RAROA (risk-adjusted return on risk-adjusted assets) has a denominator in common with RORAA (return on risk-adjusted assets) but RAROA employs "risk-adjusted expected net income" in the numerator while RORAA employs "net income" in the numerator. Therefore, RAROA is ratio-consistent but RORAA is ratio-inconsistent.
d. NPV (net present value) the discounted value of expected cash flows but its glaring weakness is that it is not compatible with the capital asset pricing model (CAPM) and, related, NPV has no convenient method for incorporating risk
606.3. Assume a $1.0 billion corporate loan portfolio offers a return of 5.0% per annum. The bank (the lender) has a direct operating cost of $6.0 million per annum and an effective tax rate of 25.0%. The portfolio is funded by $1.0 billion in retail deposits with a transfer-priced interest rate charge of 1.40%. Risk analysis of the unexpected losses associated with the portfolio tell us we need to set aside economic capital of $80.0 million against the portfolio; i.e., 8.0% of the loan amount. The bank's economic capital must be invested in risk-free securities and the risk-free rate on government securities is only 1.0%. The expected loss on the portfolio is assumed to be 1.0% per annum; i.e., $10 million. Which is NEAREST to the risk-adjusted return on economic capital (RAROC)?
a. 8.75%
b. 13.00%
c. 19.50%
d. 25.25%
Answers here:
Questions:
606.1. Peter Smith works at Bland Bancorp, a large international bank and financial services firm. The bank has recently made several significant investments but their success and profitability are highly uncertain; further, the bank has also made several acquisitions. At a board committee meeting, Peter is asked to explain the difference between risk capital, economic capital and regulatory capital. Which of the following is the TRUE statement that is part of his response?
a. "Economic capital is less than risk capital because risk capital is the capital required to guarantee shareholders with 100.0% confidence that it holds enough risk capital to ride out any eventuality"
b. "Regulatory capital is almost certainly higher than economic capital in our securitization business, therefore we do not need to know its economic capital; in other words, whenever regulatory capital exceeds economic capital, there is no reason or need to know economic capital"
c. "We need enough risk capital to absorb unexpected losses and remain solvent over a time horizon with a selected confidence level, but with respect to risk capital, (unlike regulatory capital) the horizon and confidence belong to us as policy parameters."
d. "For capital budgeting purposes, we should use ex ante RAROC with economic capital in the numerator; for performance evaluation we should use ex post RAROC with regulatory capital in the numerator"
606.2. With respect to risk-adjusted performance metrics, let "ratio consistent" refer to a ratio that adjusts both the numerator and denominator for risk. Among the risk-adjusted performance measures discussed in Crouhy, each of the following is true statement about the defined metric EXCEPT which statement is not true?
a. RAROC (risk-adjusted return on economic capital) risk-adjusts the numerator's return by subtracting expected loss from expected revenue and risk-adjusts the denominator by substituting economic capital for accounting capital. RAROC is therefore ratio-consistent.
b. RORAC (return on risk-adjusted capital; aka, ROCaR or ROC) only adjusts the the denominator, in practical applications using VaR in the denominator. Because its numerator is "net income," RARAC is ratio-inconsistent.
c. RAROA (risk-adjusted return on risk-adjusted assets) has a denominator in common with RORAA (return on risk-adjusted assets) but RAROA employs "risk-adjusted expected net income" in the numerator while RORAA employs "net income" in the numerator. Therefore, RAROA is ratio-consistent but RORAA is ratio-inconsistent.
d. NPV (net present value) the discounted value of expected cash flows but its glaring weakness is that it is not compatible with the capital asset pricing model (CAPM) and, related, NPV has no convenient method for incorporating risk
606.3. Assume a $1.0 billion corporate loan portfolio offers a return of 5.0% per annum. The bank (the lender) has a direct operating cost of $6.0 million per annum and an effective tax rate of 25.0%. The portfolio is funded by $1.0 billion in retail deposits with a transfer-priced interest rate charge of 1.40%. Risk analysis of the unexpected losses associated with the portfolio tell us we need to set aside economic capital of $80.0 million against the portfolio; i.e., 8.0% of the loan amount. The bank's economic capital must be invested in risk-free securities and the risk-free rate on government securities is only 1.0%. The expected loss on the portfolio is assumed to be 1.0% per annum; i.e., $10 million. Which is NEAREST to the risk-adjusted return on economic capital (RAROC)?
a. 8.75%
b. 13.00%
c. 19.50%
d. 25.25%
Answers here:
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