8008 Exam Dumps - PRMIA PRM Certification Questions and Answers

All of the listed reports (or information) would be useful to a risk manager analyzing liquidity risk. Therefore Choice 'c' is the correct answer. Additionally, reports on assets brought on margin (that may result in collateral or margin calls), trading exposures to different counterparties, reports on financial health, share price and credit ratings of key counterparties will also be useful.

The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.

The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

Basel II proposes three approaches to compute operational risk capital - the basic indicator approach (BIA), the standardized approach (SIA) and the advanced measurement approach (AMA). There is no operational risk approach called the factor based approach.

The Options Theoretic approach to calculating economic capital is a top-down approach that considers the value of capital as being equivalent to a call option with a strike price equal to the notional value of the debt - ie, the shareholders have a call option on the assets of the firm which they can acquire by paying the debt holders a value equal to their notional claim (ie the face value of the debt). Therefore Choice 'a' is the correct answer and the other choices are incorrect.

A computation of Altman's Z-score considers the following ratios:

- Working capital to total assets

- Retained earnings to total assets

- EBIT to total assets

- Market cap to debt

- Sales to total assets

Nearly all the numbers above are accounting measures derived straight from the balance sheet or the income statement. Market capitalization is a market driven number. Therefore Choice 'c' is the correct answer as the Altman credit risk score considers both accounting and market based measures.

Altman's score, though computationally straightforward and intuitively easy to understand, was introduced in the late sixties and has been very accurate in predicting corporate bankruptcies, which is why it continues to be used extensively.

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.

Normal mixtures have higher peaks, and therefore higher kurtosis than a normal distribution with an equivalent mean and variance. Therefore statement I is correct.

The term 'normal mixture' literally means that - the distribution is derived by summing two or more normal distributions. Statement II is correct. One interesting thing to note about normal mixtures is that their mean and variances are just the weighted averages of the means and variances of their underlying component normal distributions. But their kurtosis is higher than that of either of the components. They are more peaked, and have fatter tails, a property that makes them useful in finance.

Unfortunately there is no analytical formula for calculating VaR based on normal mixtures. However, we can back solve for VaR (using Excel's Solver, for example), given we know the density functions for the underlying normal distributions. Statement III is not correct.

A recap would be in order here: calculating operational risk capital is a multi-step process.

First, we fit curves to estimate the parameters to our chosen distribution types for frequency (eg, Poisson), and severity (eg, lognormal). Note that these curves are fitted at the UoM level - which is the lowest level of granularity at which modeling is carried out. Since there are many UoMs, there are are many frequency and severity distributions. However what we are interested in is the loss distribution for the entire bank from which the 99.9th percentile loss can be calculated. From the multiple frequency and severity distributions we have calculated, this becomes a two step process:

- Step 1: Calculate the aggregate loss distribution for each UoM. Each loss distribution is based upon and underlying frequency and severity distribution.

- Step 2: Combine the multiple loss distributions after considering the dependence between the different UoMs. The 'dependence' recognizes that the various UoMs are not completely independent, ie the loss distributions are not additive, and that there is a sort of diversification benefit in the sense that not all types of losses can occur at once and the joint probabilities of the different losses make the sum less than the sum of the parts.

Step 1 requires simulating a number, say n, of the number of losses that occur in a given year from a frequency distribution. Then n losses are picked from the severity distribution, and the total loss for the year is a summation of these losses. This becomes one data point. This process of simulating the number of losses and then identifying that number of losses is carried out a large number of times to get the aggregate loss distribution for a UoM.

Step 2 requires taking the different loss distributions from Step 1 and combining them considering the dependence between the events. The correlations between the losses are described by a 'copula', and combined together mathematically to get a single loss distribution for the entire bank. This allows the 99.9th percentile loss to be calculated.

A high score under the probit and logit models indicates a higher default risk, while under Altman's methodology it indicates a lower default risk. Therefore Choice 'd' is the correct answer.

Using the beta for VaR calculations is a significant simplification based on the CAPM and the assumption that any specific risks are diversified away. The one thing a risk model based on the CAPM does not consider is the specific risk of individual stocks, because, as mentioned, these are considered to be offsetting each other so that the portfolio only carries market risk reflected in the beta.

Therefore Choice 'c' is not true and therefore the correct answer.