Selected 8008 PRM Certification Questions Answers

The 10-day VaR is = $25m x SQRT(10) = $79.06m. Choice 'b' is the correct answer.

Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates. Therefore Choice 'a' is the correct answer.

GARCH is a mean reverting model of volatility, with a steady state mean that the model reverts to in the absence of market shocks. EWMA is not mean reverting and volatility under EWMA stays constant in the absence of shocks. Therefore statement I is correct.

Both EWMA and GARCH models are designed to address volatility clustering, which explains much of the non-normality of returns. When returns are standardized to the volatility calculations under either of these methods, the returns appear far closer to the normal distribution than non-standardized returns. (If it were not to, then there would have been no point in using these techniques.) Statement II is correct.

Steady state variance under GARCH is defined as ω / (1 - α - β), where α and β are the two parameters (called the reaction and persistence coefficient respectively). Clearly, it is affected by more than just the persistence coefficient, therefore statement III is not correct.

Sub-additivity is a very desired property in risk measures. It implies the sum of the parts is greater than the whole. In the case of risk measures, the whole is smaller than the sum of the parts due to diversification. Statement IV is true.

Therefore the correct answer is Choice 'c'

Under the contingent claims approach, a firm will default on its debt when the value of its assets fall to less than the face value of the debt. Debt holders can protect themselves against such an event by buying a put on the assets of the firm, where the strike price is equal to the value of the debt. In other words, Risky Debt + Put on the firm's assets = Risk free debt. This is because if the value of the assets is greater than the value of the debt, they will be paid in full. If the value of the assets is lower than the value of the debt, they will exercise the put and be paid in full.

Therefore the value of the put on the firm's assets with a strike equal to the value of the debt represents the cost of eliminating credit risk. Choice 'b' is the correct answer.

Note that it is improbable that a put on the firm's assets is available in real life to debt holders. However, the same effect can be synthetically achieved by using the shares of the firm as a proxy for its assets, and shorting an appropriate number of shares. Such a synthetic put will require frequent readjustments.