Pass the PRMIA PRM Certification 8005 Questions and answers with ExamsMirror

Economic capital is often calculated with a view to maintaining the credit ratings for a firm. It is the capital available to absorb unexpected losses, and credit ratings are also based upon a certain probability of default. Economic capital is often calculated at a level equal to the confidence required for the desired credit rating. For example, if the probability of default for a AA rating is 0.02%, and the firm desires to hold an AA rating, then economic capital maintained at a confidence level of 99.98% would allow for such a rating. In this case, economic capital set at a 99.8% level can be thought of as the level of losses that would not be exceeded with a 99.8% probability, and would help get the firm its desired credit rating.

Choice 'c' is the correct answer. Economic capital does not target minimizing the cost of capital, nor is it a provision for losses arising from market risk. The concept of economic capital is unrelated to where an institution or firm is based, therefore Choice 'a' is incorrect as well.

The three pillars under Basel II are minimum capital requirements, supervisory review process and market discipline. Therefore statement I is false. The other two statements are accurate. Therefore Choice 'd' is the correct answer.

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.

Choice 'c' correctly describes Altman's z-score. All other choices are incorrect.

The distance to default is the number of standard deviations that expected asset values are away from the default point. The expression in Choice 'd' represents distance to default. Choice 'd' is the correct answer. The other choices are incorrect.

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate andthis discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increase in dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)