PRMIA 8008 Exam With Confidence Using Practice Dumps

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'

The exact formula for VaR is = -(Zα σ + μ), where Z α is the z-multiple for the desired confidence level, and μ is the mean return. Now Zα is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%, and μ is often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero.

Therefore in practice the formula for VaR just becomes -Zασ, and since Z is always negative, we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR.

For this question, there are two ways to get the answer. If we use the formula, we know that -Zασ= 250,000 (as μ=0), and therefore -Zασ - μ = 250,000 - 10,000 = $240,000.

The other, easier way to think about this is that if the mean changes, then the distribution's shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves up by $10,000. Therefore the VaR cutoff, which was previously at -250,000 on the graph also moves up by 10k to -240,000, and therefore $240,000 is the correct answer.

The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.

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.