Free PRMIA 8008 Practice Exam with Questions & Answers | Set: 9

The persistence parameter, β, is the coefficient of the most recent day's returns in GARCH calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under GARCH will never change in response to returns.

Some parts of this question draw upon contingent claims framework to the value of a firm. According to this framework, the relationship between the debt and equity holders of a firm can be viewed as follows: The equity holders have a call option on the assets of the firm with a strike price equal to the value of the debt, and the debt holders have sold them this call. This is so because should the value of the assets of the firm fall below the value of the debt, the equity holders can walk away by handing over the assets to the debt holders in full extinguishment of their claims. If the value of the firm's assets is greater than the value of debt, the equity holders will exercise their call option. At the same time, it is also possible to view the debtholders as holding an asset and having sold a put on the assets of the firm with a strike price equal to the value of the debt. If the value of the assets of the firm were to fall below the value of the debt, they will end up buying the assets at a price equal to the value of the debt.

An increase in the volatility of returns on the assets of a firm increases the volatility of the asset value. This means the likelihood that the asset value will go below the value of the debt of the firm will increase. Callable debt can be considered to be a summation of two separate securities: a regular debt, for which the firm pays interest and receives a principal loan; and a call option that the debt holders have sold to the firm allowing the firm to buy back the debt. In return, the firm pays an implied 'premium' to the debt holders who have agreed to buy the callable debt. Therefore the total payments by the company to callable debt holders is equal to the interest payments plus the premium payment for the option. An increase in asset volatility will increase the value of this option as it is likely that the assets will increase in value, and strengthen the company's credit, and lower its spread at which time it would like to repay the debt and refinance/roll over at the new lower rate. Therefore an increase in volatility will increase the 'premium' demanded by the callable debt holders, thereby increasing the total yield and lowering the value of the callable debt. Therefore Choice 'b' (An increase in the value of the callable debt of the firm) is incorrect.

An increase in asset volatility will decrease the value of the firm as it is now riskier than before (higher standard deviation, same expected returns). Therefore Choice 'a' (An increase in the value of the equity of the firm) is false too.

The value of the implicit put in the debt of the firm will increase and not decrease as the volatility of the underlying assets increases. Therefore Choice 'c' (A decrease in the value of the implicit put in in the debt of the firm) is incorrect too.

Choice 'd' (A decrease in the value of the non-callable debt issued by the firm) is correct because higher asset volatility will increase the riskiness of the company's debt, making the required yield higher and decreasing its value.

Stress testing provides an independent and complementary perspective to other risk management tools such as value-at-risk and economic capital. Both are tools that serve similar purposes but are not interchangeable. Stress testing, no matter how exhaustively done, can not replace other tools such as those based on analytical or historical models. It can provide a useful sense check to validate models and assumptions, but is not a replacement for traditional techniques. Therefore statement I is false.

Stress testing can certainly help identify risks with new products for which historical data may be limited, and analytical models may be based upon many unproven assumptions. It can help challenge the risk characteristics of new products where stress situations have not been observed in the past. Therefore statement II is correct.

ICAAP stands for the 'internal capital adequacy assessment process' performed by a bank (remember the acronym and its expansion). Stress testing is an integral part of a firm's ICAAP, and not distinct. It is one of the elements of the internal process. Therefore statement III is false.

Statement IV is correct as stress testing is indeed a powerful tool that can communicate risks throughout the organization as the stress scenarios are easier to comprehend than arcane statistical models. They are also easier to explain to regulators, and are a powerful communication tool.

Thus Choice 'c' is the correct answer.

Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for the portfolio. This property makes component VaR extremely useful for risk disaggregation and allocation.

Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the portfolio VaR, in fact their sum would be greater.

Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR for a portfolio from a new position added to the portfolio - and if that position is $1, it would be identical to the marginal VaR.

Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all the positions are 100% correlated, which effectively would mean they are all identical securities which means the portfolio has only one asset).

Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR for the portfolio.

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.

EVT, when used in the context of operational risk measurement, focuses on tail events and attempts to build a distribution of losses beyond what is covered by VaR. Statements I, II and II are correct. Statement IV describes conditional VaR (CVAR) and not EVT.

Choice 'c' is the correct answer.

A LIBOR based loan requires cash to move from the lender to the borrower in the amount of the notional. The Overnight Index Swap requires only the exchange of interest payments, and therefore represents less risk.

Therefore the LIBOR based loan is a riskier exposure.

The LIBOR is generally higher than the OIS. In fact, the difference between the two, the LIBOR-OIS spread, is a standard measure of the risk premium in the market that goes up when the risk of default by counterparty banks is considered high. This is because when the market perceives the risk of default to be high, the participants need a risk premium to take on the default risk which is considerably lesser with the OIS.

The capital adequacy ratio, also called the minimum capital requirement for credit risk per Basel II is 8% of risk weighted assets. The other choices are incorrect.

This question relates to fitting a distribution to the true severity of the operational risk loss we are trying to model. The quality of the fit, or the precision of the fit, has two elements to the difference between the severity as represented by our model and the true severity. To understand this, consider the three data points below:

a. The true severity,

b. The best approximation of the true severity in the model space, and

c. The fit based on the dataset.

- True severity is what we are trying to model.

- The model space refers to the collection of analytical distributions (log-normal, burr etc) that we are considering to arrive at the estimate of the severity.

- The 'best approximation of the true severity in the model space' is reached by estimating the parameters of the distribution that optimizes the risk functional.

- The 'fit' is the actual parameter estimates we settle for with the distribution we have determined best fits the true estimate of our severity. When estimating parameters, we have various methods available for estimation - the least squares method, the maximum likelihood method, for example, and we can get different estimates depending upon the method we choose to use.

Our severity model will be different from the true severity, and the total difference can be split into two types of errors:

1. Fitting error, represented by 'c - b' above: The difference between the fit based on the dataset and the best approximation of the true severity is called 'fitting error', ie, a measure of the extent to which we could have estimated the parameters better.

2. Approximation error, represented by 'b - a' above: Approximation error is the difference between the true severity, and the best approximation of the true severity that can be achieved within the model space is called 'approximation error'.

One can reduce the approximation error by expanding the model space by adding more distributions. This will reduce the approximation error, but generally has the effect of increasing the fitting error because the complexity of the model space increases, and there are more ways to fit to the true severity.

In an interest rate swap, the parties agree to exchanging interest rate payments, with one party being a fixed interest rate payer and the other paying floating rates. The party receiving fixed rates and paying floating can be considered to be long a fixed rate bond and short a floating rate note. Therefore an IRS can be modeled as a combination of a fixed coupon bond and a floating rate note. Choice 'b' is the correct answer.