PRMIA 8008 - PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition

A situation where a firm has more liabilities than assets does not necessarily imply default, so long as the firm is able to pay its obligations when they come due. Therefore, short term debts have a greater bearing on a firm's default than longer term debt. However, this is not to say that merely having enough to pay off the short term debts (ie debts due within one year) is enough to avoid default. Over time, the long term debt will also be turning to short term debt, and it may not be possible for the firm to roll over its liabilities without lenders considering the long term debt. The KMV approach considers the entire short term debt and half of the long term debt as the critical value of assets below which default will be triggered. Therefore Choice 'c' is the correct answer.

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.

Choice 'c' relates to operational risk and process capabilities, generally not a concern when evaluating market risk of a portfolio. Choice 'a', Choice 'b' and Choice 'd' represent real concerns for the risk manager when building stress tests for the value of a portfolio.

Choice 'a' is relevant because certain shocks may be inconsistent with each other, and therefore implausible. For example, an increase in futures prices may be inconsistent with without spot prices and/or interest rates increasing according to the no-arbitrage condition. Choice 'b' is relevant when modeling a covariance matrix in a stressed situation with higher correlations, as a hypothetical covariance matrix which is not positive semi-definite may give absurd results (negative variance). Choice 'd' is relevant as liquidity risks may affect the price that can be realized for positions held.

First of all, if prices are lognormally distributed, that implies the returns (which are equal to the log of prices) are normally distributed. To say that prices are lognormally distributed is just another way of saying that returns are normally distributed.

Since the correlation between the two securities is zero, this means their variances can be added. But standard deviations, or volatilities cannot be added (they will be the square root of sum of variances). VaR is nothing but a multiple of standard deviation, and therefore it is not additive if correlations are anything other than 1 (ie perfect positive, which would imply we are dealing with the same asset). Therefore VaR(A+B)=SQRT(VaR(A)^2 + VaR(B)^2). This implies the combined VaR of a portfolio with these two securities will be less than the sum of VaRs of the two individual securities.

Thus Choice 'c' is the correct answer and the other choices are wrong.

Incremental VaR is the change in portfolio VaR resulting from a change in a single position. This is accurately described by VaR_(p+a) - VaR_p. The other answers are incorrect, and describe other concepts.

It is important to know and understand the ideas behind MVaR (marginal VaR), CVaR (component VaR) and iVaR (incremental VaR), and the differences between them.

Pre-settlement risk is the risk that one of the counterparties defaults prior to the date for the maturity of the transaction in question. This may be an unrelated default, in fact there may have been no default on that particular contract, but the party may have defaulted on its other obligations, or filed for bankruptcy. To deal with such cases and to protect the interests of both the parties, it is common to provide for immediate termination of positions and settlement based on the current replacement value of the contracts. Therefore statements I and II are correct.

Statement III is correct as well - the exposure from an OTC derivative contract derives from its current replacement value, and not the notional. If the current replacement value is negative, then the credit exposure is considered equal to zero.

Statement IV is correct as it is quite common to restate all exposures - those from credit lines, OTC derivatives etc - in loan equivalent terms prior to estimating credit risk.

Statement I is true as expected losses are the 'cost of doing business' and charged against the P&L of the unit holding the exposure. When evaluating the business unit, expected losses are taken into account. Unexpected losses however require risk capital reserves to be maintained against them.

Statement II is not true. Credit portfolio loss distributions are not symmetrical, in fact they are highly skewed and have heavy tails.

Statement III is true. The notional, or the face value of a defaulted debt is the basis for a claim in bankruptcy court, and not the market value.

Statement IV is false. In the case of over the counter instruments, the replacement value of the contract represents the amount of the claim, and not the notional amount (which can be very high!).

PCA is a statistical tool that decomposes a positive semi-definite matrix into its principal components. The first few principal components explain nearly all the variation and other components can then be ignored as they are too small in the larger picture. PCA in risk management is applied to a positive semi-definite correlation or covariance matrix to reveal the principal components that cause the variation. By allowing a focus on a few components, PCA reduces dimensionality.

While performing the math of PCA is unlikely to be asked in the PRMIA exam, you should remember that principal components have the additional property of being uncorrelated to each other which makes it useful as it is possible to vary one of the components without having to worry about the effect of that on the other components.

Volatility clustering leads to levels of current volatility that can be significantly different from long run averages. When volatility is running high, institutions need to shed risk, and when it is running low, they can afford to increase returns by taking on more risk for a given amount of capital. An institution's response to changes in volatility can be either to adjust risk, or capital, or both. Accounting for volatility clustering helps institutions manage their risk and capital and therefore statements I and II are correct.

Regulatory requirements do not require volatility clustering to be taken into account (at least not yet). Therefore statement III is not correct, and neither is IV which is completely unrelated to volatility clustering.