Pass the PRMIA PRM 8008 Questions and answers with ValidTests

The $10m cash flow due in 6 months is equivalent to a bond with a present value of 10m/(1.05)^0.5 =$9,759,000. Essentially, the question requires us to calculate the VaR of a bond.

The VaR of a fixed income instrument is given by Duration x Interest Rate x Volatility of the interest rate x z-factor corresponding to the confidence level.

In this case, since the question requires us to calculate the value "closest to" the correct answer, we can use an estimate for the modified duration of the bond as equal to 0.5 years/(1+r) = 0.5/1.05 = 0.47 years. The VaR would be given by 0.5 * 5% * 15% * 2.326 * sqrt(1/250) * 9,759,000 = $5,384 which is closest to $5,500. Therefore Choice 'a' is the correct answer. Note that we have to multiply by sqrt(1/250) as the given volatility is annual and the question is asking for daily VaR. All other answers are incorrect.

For the PRM exam, it is important to remember the z-multiples for both 99% and 95% confidence levels (these are 2.33 and 1.64 respectively).

The value at risk for an equity portfolio is its standard deviation multiplied by the appropriate z factor for the given confidence level. If we knew the standard deviation, VaR would be easy to calculate. The standard deviation can be derived using a correlation matrix for all the stocks in the portfolio, which is not a trivial task. So we simplify the calculation using the CAPM and essentially say that the standard deviation of the portfolio is equal to the beta of the portfolio multiplied by the standard deviation of the market.

Therefore VaR in this case is equal to Beta x Mkt Std Dev x Value x z-factor, and therefore Choice 'a' is the correct answer.

Statement I is correct. Data is often divided into two sets - a 'training set' that is used to create and fine-tune the model while the 'control set' is used to prove that the model works on sample data. Back testing is then perfomed using actual data that becomes available over time, or may already be available as historical data.

Statement II is incorrect. A risk manager often spends a great deal of time in managing data, and ensuring that the data being used is accurate enough for the purpose it is being used for. A risk manager can expect to spend a good part of his or her team's time in cleansing data. While he or she can try to get the IT processes and systems to produce correct data in the first place so it requires minimal subsequent cleansing or validation, this task is likely to remain a key part of a risk manager's role for quite some time in the future given the challenges nearly all organizations face in managing risk data.

Statement III is correct. There was not enough granular data available on the underlying components of some of the derivative debt securities whose markets dried up during the crisis that began in 2007. This was because investors became increasingly unsure of what the value of these securities, such as CDOs was, leading to market seizure and firesale prices.

Statement IV is not correct. There is no easy solution to the lack of enough historical data, which is used to create as well as test models, and construct stress scenarios. Analytical approaches are not a good enough substitute for real market data. During the recent crisis, many instruments had rather short histories and there was not enough data available, and risk managers and portfolio managers relied upon analytical approaches to value and price them. Many of the assumptions that underpinned these approaches were untested in the real world and turned out to be incorrect.

Therefore Choice 'c' is the correct answer and the rest are incorrect.

The commercial paper has greater credit risk as the entire notional is outstanding. On the forward contract, only the replacement value of the contract, which normally would be a mere fraction of the notional, would be at risk.

Therefore Choice 'd' is the correct answer.

Operational risk as defined in Basel II specifically excludes strategic and reputational risk. Therefore Choice 'd' is the correct answer.

Note that Basel II defines operational risk as follows:

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes, people and systems or from external events. This definition includes legal risk, but excludes strategic and reputational risk.

The VaR for a spot FX position is merely a function of the standard deviation of the exchange rate. If V be the value of the position (in this case, EUR 15m x 1.5 = USD 22.5m), z the appropriate z value associated with the level of confidence desired, and σ be the standard deviation of the portfolio, the VaR is given by ZσV.

In this case, the 10-day standard deviation is given by SQRT(10/250)*16%. Therefore the VaR is =1.645*15*1.5*(16%*SQRT(10/250)) = USD 1.1844m. Choice 'c' is the correct answer.

Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn).

For this question, we can calculate the marginal probability of default for year 2 by solving the equation [1 - (1 - 20%)(1 - P2) = 45%] for P2. Solving, we get the marginal probability of default during year 2 as 31.25%. Since this is the annual marginal probability of default, we will need to convert it to a monthly number, which we can do by solving the following equation where M1 is the monthly marginal probability of default.

1 - 31.25% = (1 - M1)^12, implying M1 = 3.07%

The VaR in this case will be the top quintile of observations. In this case, since there are exactly 100 observations, this would mean the worst return would become the VaR. Therefore Choice 'b' is the correct answer. Choice 'a' and Choice 'c' make no sense. This highlights that at higher confidence levels, fewer and fewer observations impact the VaR if we are using historical simulation based VaR.

The square root of time rule can be used to convert, say a 1-day VaR to a 10-day VaR, by multiplying the known number by the square root of time to get the VaR over a different time horizon. However, there are key assumptions that underlie the application of this rule, and statements I to IV correctly state those assumptions.

Statements V and VI are not correct, because the application of the square root of time rule requires the absence of serial correlations, and also the absence of volatility clustering (ie independence). Therefore Choice 'c' is the correct answer.

The square root of time rule is also applied to convert volatility or standard deviation for one period to the volatility for a different time period. Remember that VaR is just a multiple of volatility, and therefore the assumptions that apply to the square root of time rule for VaR also apply to the same rule when used in the context of volatilities or standard deviation.

When a default occurs, the proportion of the exposure represented by the recovery rate is recovered. For example, if the recovery rate is 40% for a loan, the actual loss in the event of a default would be $60 for a $100 loan. In other words, the loss given default = 1 - recovery rate. Hence Choice 'd' is the correct answer. All other choices are incorrect.