Free PRMIA 8008 Practice Exam with Questions & Answers | Set: 11

In statistics, which is relevant to risk management, a distinction is often drawn between 'frequentists' and 'Bayesians'. Frequentists rely upon data to draw conclusions as to probabilities. Bayesians consider conditional probabilities, ie, take into account what things are already known, and inject sometimes subjective a-priori probabilities into the calculations. Statement I describes Bayesians, and not frequentists. In reality however, the difference is merely academic. Risk managers use whichever technique best applies to the given situation without making it about ideology.

The difference between 'Knightian uncertainty' and 'Risk' is similarly academic. Knightian uncertainty refers to risk that cannot be measured or calculated. 'Risk' on the other hand refers to things for which past data exists and calculations of exposure can be made. To give an example in the context of the financial world, the risk from a pandemic creating systemic failures from a failure of payment and settlement systems and the like is 'Knightian uncertainty', but the market risk from equity price movements can be modeled (albeit with limitations) and is calculable. Statement II is therefore correct.

Once a risk is identified, it can be mitigated, accepted, avoided or eliminated, or transferred by way of insurance. Therefore statement III is correct.

Confidence accounting is a conceptual idea that suggests that accounting statements make reference to ranges as opposed to point estimates in financial statements. For example, instead of saying that the pension obligation is $xx million, the company should say the pension obligation is in a range of $xx m - $yy m with a certain confidence level. Statement IV is therefore inaccurate.

Frequency modeling is performed using discrete distributions that have a positive integer as a resultant - this allows for the number of events per period of time to be modeled. Of the distributions listed above, Poisson, negative binomial and binomial can be used for modeling frequency distributions. The Poisson and negative binomial distributions are encountered the most in practice.

The gamma distribution is a continuous distribution and cannot be used for frequency modeling.

While conceptually VaR is a fairly straightforward concept, a number of decisions need to be made to select between the different choices available for the exact mechanism to be used for the calculations.

The Basel framework requires banks to estimate VaR at the 99% confidence level over a 10 day horizon. Yet this is a decision that needs to be explicitly made and documented. Therefore 'I' is a correct choice.

At various stages of the calculations, portfolio values need to be determined. The valuation can be done using a 'full valuation', where each position is explicitly valued; or the portfolio(s) can be reduced to a handful of risk factors, and risk sensitivities such as delta, gamma, convexity etc be used to value the portfolio. The decision between the two approaches is generally based on computational efficiency, complexity of the portfolio, and the degree of exactness desired. 'II' therefore is one of the decisions that needs to be made.

The decision as to disclosing the VaR in financial filings comes after the VaR has been calculated, and is unrelated to the VaR calculation system a bank needs to set up. 'III' is therefore not a correct answer.

Though the Basel framework requires a 10-day VaR to be calculated, it also allows the calculation of the 1-day VaR and and scaling it to 10 days using the square root of time rule. The bank needs to decide whether it wishes to scale the VaR based on a 1-day VaR number, or compute VaR for a 10 day period to begin with. 'IV' therefore is a decision to be made for setting up the VaR system.

Since the business units are perfectly correlated, we can get the combined EC as equal to the sum of the individual EC estimates. Therefore Choice 'a' is the correct answer.

Statement I is not correct as VaR does not set an upper limit on losses. In this case, the bank expects the losses to exceed $253m 5% of the times, and the VaR number does not indicate any theoretical maximum amount of losses.Statement II is incorrect as there is a 95% (and not 5%) probability that the bank's losses will not exceed $253mStatement III is correct and describes VaR.Statement IV is incorrect, as regulatory capital is a more complex computation for which VaR is only one of the various input.Therefore Choice 'b' is the correct answer.

Steady state variance under the GARCH model is given by the formula ω/(1 - α – β). In this case, steady state variance therefore works out to 0.00025/(1 - 0.1 - 0.8) = 0.0025. Since this is the variance, volatility is the square root of 0.0025, which works out to 0.05.

Thus, 5% (=0.05) is the correct answer, and the others are incorrect.

Also recall the following in respect of GARCH:

Concentration risk in a credit portfolio arises due to a high degree of correlation between the default probabilities of the issuers of securities in the portfolio. For example, the fortunes of the issuers in the same industry may be highly correlated, and an investor exposed to multiple such borrowers may face 'concentration risk'.

A low degree of correlation, or independence of individual defaults in the portfolio actually reduces or even eliminates concentration risk.

The fact that issuers are from the same country may not necessarily give rise to concentration risk - for example, a bank with all US based borrowers in different industries or with different retail exposure types may not face practically any concentration risk. What really matters is the default correlations between the borrowers, for example a lender exposed to cement producers across the globe may face a high degree of concentration risk.

When calculating volatility weighted VaR, returns are adjusted by a factor equal to the current volatility divided by the historical volatility, ie the volatility that existed during the time period the returns were earned. If the current volatility is greater than the historical volatility (also called contemporary volatility), then it has the effect of increasing the magnitude of any past returns (whether positive or negative). This in turn increases the VaR.

Consider an example: if the current volatility is 2%, and a return of -5% was earned at a time when the volatility was 0.8%, then the volatility weighted return would be 12.5% (=-5% x 2%/0.8%). Clearly, this has the effect of increasing the VaR.

Choice 'd' is therefore the correct answer.