2013 FRM Calendar

P2.T6.305. Credit Value at Risk (CVaR)

14 Mar 2013   by Suzanne Evans

Exam Relevance: Optional

AIM: Define Credit VaR (Value-at-Risk)

Questions:

305.1. A firm has current asset value of \$1.0 billion with asset volatility of 25.0%. Its sole debt issue is a zero-coupon bond with face value of \$800 million due in one year. The risk free rate is only 3.0% but the firm's expected return (ROA) is 12.0%. (Note: these assumptions given, so far, complete the set of necessary inputs into the Merton. Technically, the problem given below can be solved at this point. For a difficult challenge, far more difficult than you would encounter on the exam, you can attempt the problem with only the assumptions given so far). Here are the additional implications of the Merton model:

- Merton probability of default = 10.6%
- The actuarial expected loss (EL; i.e., the future value of the "actuarial default put") = \$8.40 million
- The expected loss given default (LGD) = \$8.40 million EL / 10.6% PD = \$79.25 million
- The 0.001 quantile of the future bond value = \$503.00 million

Which is nearest to the implied Credit VaR (CVaR) at the 99.9% confidence level?

1. \$288.60 million
2. \$394.11 million
3. \$437.04 million
4. \$501.25 million

305.2. Which of the following best summarizes the 99.9% Credit VaR (CVaR)?

1. 99.9% CVaR = (Current bond value - PV of expected loss) - Current 0.001 Quantile of Bond Value
2. 99.9% CVaR = (Bond's par value - Future expected loss) - Future 0.001 Quantile of Bond Value
3. 99.9% CVaR = (Bond's par value - Future 0.001 Quantile of Bond Value)
4. 99.9% CVaR = (Bond's expected terminal value - Future expected loss) - Future 0.001 Quantile of Bond Value

305.3. According to Malz, each of the following is true about Credit VaR EXCEPT:

1. CVaR (alpha) = Unexpected loss (alpha), where alpha is a significance or confidence level
2. For a fixed quantile of future bond value (e.g., \$503 million) and increase in expected loss implies a decrease in CVaR; i.e., CVaR excludes EL
3. Like market risk VaR (MVaR), CVaR compares a future value with a current value
4. An increase in the firm's expected return (mu) will, ceteris paribus, increase the CVaR