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# P2.T7.706. Economic capital

#### Nicole Seaman

##### Director of FRM Operations
Staff member
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Questions:

706.1. Patty is a Risk Analyst who has been asked by her firm's Chief Risk Officer (CRO) to review the firm's risk modeling practices. She is currently evaluating a popular risk model used by the firrm to asses the risk of its equity portfolios, in particular the firm depends on a parametric linear value at risk (VaR) approach. Her boss, the CRO, has asked her specifically to ensure that model risk is mitigated and consistent with best practices. If Patty's mission is to mitigate model risk, which of the following practices is advisable?

a. Avoid embedding simplifying assumptions into models that specify price behavior
b. Only use volatility and correlation parameters if they are directly and currently observed
c. Avoid mark-to-model approaches because they are discouraged by accounting and regulatory bodies
d. Ensure that an independent vetting team is provided with a mathematical statement of the model and its components

706.2. Assume that you want to identify the risk-adjusted return on capital (RAROC) of a new, contemplated $3.0 billion corporate loan portfolio that offers a headline return of 10.0%. The bank has an operating direct cost of$15.0 million per annum and an effective tax rate of 30.0%. The loan portfolio is funded by $3.0 billion of retail deposits with a "transfer priced" interest charge of 5.0%. Risk analysis of the unexpected losses (UL) associated with the portfolio indicates that for this portfolio that bank should allocate economic capital (EC) of$360.0 million, which is 12.0% of the loan amount. This economic capital must be invested in risk-free securities and the current risk-free interest rate is 3.0%. The expected loss on this portfolio is assumed to be 3.0% per annum, i.e., \$90 million. Finally, the bank's equity beta, β(E), is 1.30, and the market's excess return is 8.0% such that the equity risk premium is 5.0%.

What is this loan's RAROC and, from the perspective of an adjusted RAROC, is the new portfolio advisable?

a. RAROC equals 13.140%, and the portfolio is advisable because its ARAROC is greater than the risk-free rate
b. RAROC equals 10.850%, and the portfolio is advisable because its ARAROC is greater than the risk-free rate
c. RAROC equals 7.220%, and the portfolio is advisable because its ARAROC is greater than the risk-free rate
d. RAROC equals 5.980%, and the portfolio is not advisable because its ARAROC is less than the risk-free rate

706.3. Crouhy, Galai, and Mark say that "we should be careful not to confuse the concept of risk capital (aka, economic capital), which is intended to capture the economic realities of the risks a firm runs, and regulatory capital. First, regulatory capital only applies to a few regulated industries, such as banking and insurance companies, where regulators are trying to protect the interests of small depositors or policy holders. Second, while regulatory capital performs something of the same function as risk capital in the regulators’ eyes, it is calculated according to a set of industrywide rules and formulas and sets only a minimum required level of capital adequacy. It rarely succeeds in capturing the true level of risk in a firm—the gap between a firm’s regulatory capital and its risk capital can be quite wide. Furthermore, even if regulatory and risk capital are similar numbers at the level of the firm, they may not be similar for each constituent business line (i.e., regulatory capital may suggest that an activity is much riskier than management believes to be the case, or vice versa)."

In addition to the distinction between economic capital and regulatory capital articulated above, EACH of the following statements is true EXCEPT which is inaccurate?

a. Economic capital normally does NOT absorb expected losses (EL)
b. Economic capital equals risk capital plus (+) goodwill plus (+) burned-out capital
c. Adjusted RAROC is an increasing function of economic capital as a percentage of a loan portfolio
d. Economic capital is normally unexpected loss (UL) at some selected confidence level and time horizon

Answers here:

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