PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 351:

  What is the risk horizon period used for credit risk as generally used for economic capital calculations and as required by regulation?

  A. 1-day
  B. 1 year
  C. 10 years
  D. 10 days
  B. 1 year

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  Explanation

  The credit risk horizon for credit VaR is generally one year. Therefore Choice 'b' is the correct answer.

• Question 352:

  Which of the following cannot be used to address the issue of heavy tails when modeling market returns

  A. EVT
  B. EWMA
  C. Normal mixtures
  D. Student's t-distribution
  B. EWMA

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  Explanation

  Normal mixtures, EVT and the t-distribution are all possible solutions addressing the issue of heavy tails in financial returns.

  EWMA and GARCH address volatility clustering, which is the other problem when doing risk calculations. Therefore Choice 'b' is the correct answer as EWMA is not used to address heavy tails but volatility clustering.

• Question 353:

  A portfolio has two loans, A and B, each worth $1m. The probability of default of loan A is 10% and that of loan B is 15%. The probability of both loans defaulting together is 1%. Calculate the expected loss on the portfolio.

  A. 500000
  B. 250000
  C. 1000000
  D. 240000
  B. 250000

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  Explanation

  The easiest way to answer this question is to ignore the joint probability of default as that is irrelevant to expected losses. The joint probability of default impacts the volatility of the losses, but not the expected amount. One way to think about it

  is to think of asset portfolios, where diversification reduces risk (ie standard deviation) but the expected returns are nothing but the average of the expected returns in the portfolio. Just as the expected returns of the portfolio are not affected

  by the volatility or correlations (these affect standard deviation), in the same way the joint probability of default does not affect the expected losses. Therefore the expected losses for this portfolio are simply $1m x 10% + $1m x 15% =

  $250,000.

  This can also be seen from the lens of a joint probability distribution as follows:

  

  There are four possibilities for this portfolio:

  -

  Only loan A defaults: loss of $1m: 9% probability

  -

  Only loan B defaults: loss of $1m: 14% probability

  -Both loan A and B default: loss of $2m: 1% probability

  -Neither A nor B default: loss of $0m: 76% probability

  Therefore the expected losses on the portfolio are ($1m x 9%) + ($1m x 14%) + ($2m x 1%) + ($0m x 76%) = $250,000.

  (Notes: How is the above table calculated? The totals (10%, 90%, 15% and 85%) are filled in first. The top left cell (both A and B default) is given as 1%. We can now calculate the rest of the cells as the totals are known.)

• Question 354:

  There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds over a one year horizon are 0.03 and 0.08 respectively. If the default correlation is zero, what is the one year expected loss on this portfolio?

  A. $11m
  B. $5.26m
  C. $5.5m
  D. $1.38m
  C. $5.5m

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  Explanation

  The probabilities of default of the two bonds are independent (as indicated by a zero default correlation). The various possible states of the portfolio are as follows: First bond defaults, and the second does not: Probability * Loss = 0.03*0.92 * $50m = $1.38m Second bond defaults, and the first does not: Probability * Loss = 0.97*0.08 * $50m = $3.88m Both bonds default: Probability * Loss = 0.03*0.08 * $100m = $0.24m Thus total expected loss on this portfolio = $5.5m. Since recovery rates are not provided, those should be assumed to be zero. There is an easier way to solve this as well: default correlation does not affect expected losses, but their volatility. You can calculate the expected losses of the two bonds and add them up, ie, $50m*0.03 + $50m *0.08 = $5.5m

• Question 355:

  Which of the following are likely to be useful to a risk manager analyzing liquidity risk for an international bank?

  I - Information on liquidity mismatches II - Funding concentration III - Lending concentration IV - A report on illiquid assets

  A. I and II
  B. III and IV
  C. I, II, III and IV
  D. I, II and IV
  C. I, II, III and IV

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  Explanation

  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.

• Question 356:

  What is the 1-day VaR at the 99% confidence interval for a cash flow of $10m due in 6 months time? The risk free interest rate is 5% per annum and its annual volatility is 15%. Assume a 250 day year.

  A. 5500
  B. 1744500
  C. 109031
  D. 85123
  A. 5500

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  Explanation

  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.

• Question 357:

  An equity manager holds a portfolio valued at $10m which has a beta of 1.1. He believes the market may see a dip in the coming weeks and wishes to eliminate his market exposure temporarily. Market index futures are available and the current futures notional on these is $50,000 per contract. Which of the following represents the best strategy for the manager to hedge his risk according to his views?

  A. Sell 200 futures contracts
  B. Buy 220 futures contracts
  C. Sell 220 futures contracts
  D. Liquidate his portfolio as soon as possible
  C. Sell 220 futures contracts

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  Explanation

  The number of futures contracts to sell are equal to $10m x 1.1/$50,000 = 220. Liquidating his portfolio would reduce the beta to zero, but would also get rid of the bets he wants to play on. Therefore Choice 'c' is the correct answer. (Note that futures and spot prices generally move together allowing futures positions to be used for hedging the risk against movement in spot prices. However there is a basis risk between spot and futures, therefore the a perfect hedge is never possible with futures. If interest rates move a great deal, spot and futures prices may diverge. Of course, this risk is generally quite low but may become amplified with large leveraged portfolios. Just something to be aware of.)

• Question 358:

  For a corporate bond, which of the following statements is true:

  I - The credit spread is equal to the default rate times the recovery rate II - The spread widens when the ratings of the corporate experience an upgrade III - Both recovery rates and probabilities of default are related to the business cycle and move in opposite directions to each other IV - Corporate bond spreads are affected by both the risk of default and the liquidity of the particular issue

  A. I, II and IV
  B. III and IV
  C. III only
  D. IV only
  B. III and IV

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  Explanation

  The credit spread is equal to the default rate times the loss given default, or stated another way, default rate times (1 - recovery rate). It is not equal to the default rate times the recovery rate. Therefore statement I is not correct. When ratings

  are upgraded by rating agencies, the spread contracts and not widen.

  Therefore statement II is not correct.

  Both recovery rates and probabilities of default are related to the business cycle, and they move in opposite directions. Economic recessions witness an increase in the default rate and a decrease in the recovery rate, and economic

  expansions result in a decrease in the default rate and an increase in the recovery rates when default does happen. Therefore statement III is correct. Bond spreads incorporate both the risk of default, but also considerations of liquidity in the

  case of corporate bonds. Hence statement IV is correct.

• Question 359:

  Credit exposure for derivatives is measured using A. Current replacement value

  B. Notional value of the derivative

  C. Forward looking exposure profile of the derivative

  D. Standard normal distribution

  Correct Answer. C
  C

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  Explanation

  Current replacement values are a very poor measure of the credit exposure from a derivative contract, because the future value of these instruments is unpredictable, ie is stochastic, and the range of values it can take increases the further ahead in the future we look. Therefore it is common for credit exposures for derivatives to be measured using forward looking exposure profiles, which are distributions of the expected value of the derivative at the time horizon for which credit risk is being measured. To be conservative, a high enough quintile of this distribution is taken as the 'loan equivalent value' of the derivative as the exposure. Choice 'c' is the correct answer.

  The notional value of derivative contracts generally tends to be quite high and unrelated to their economic value or the counterparty exposure. Therefore notional value is irrelevant.

• Question 360:

  Which of the formulae below describes incremental VaR where a new position 'm' is added to the portfolio? (where p is the portfolio, and V_i is the value of the i-th asset in the portfolio. All other notation and symbols have their usual meaning.)

  

  A. Option A
  B. Option B
  C. Option C
  D. Option D
  A. Option A

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  Explanation

  Incremental VaR is the change in portfolio VaR resulting from a change in a single position. This is accurately described by VaR_(p+a) - VaR_p. The other answers are incorrect, and describe other concepts. It is important to know and understand the ideas behind MVaR (marginal VaR), CVaR (component VaR) and iVaR (incremental VaR), and the differences between them.