PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 181:

  All else remaining the same, an increase in the joint probability of default between two obligors causes the default correlation between the two to:

  A. Increase
  B. Decrease
  C. Stay the same
  D. Cannot be determined from the given information
  A. Increase

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  Explanation

  The default correlation between two obligors goes up if the joint probability of default between them increases. This is intuitive. Also consider the formula for the default correlation between two obligors Default correlation = [P(1,2) - P1 * P2] / P1*(1-P1)*P2*(1-P2); where P(1,2) is the joint probability of default between the two and P1 and P2 are their individual probabilities of default. Obviously, an increase in P(1,2) will cause the default correlation to increase.

• Question 182:

  Which of the following are true:

  I - Monte Carlo estimates of VaR can be expected to be identical or very close to those obtained using analytical methods if both are based on the same parameters.

  II - Non-normality of returns does not pose a problem if we use Monte Carlo simulations based upon parameters and a distribution assumed to be normal.

  III - Historical VaR estimates do not require any distribution assumptions.

  IV - Historical simulations by definition limit VaR estimation only to the range of possibilities that have already occurred.

  A. III and IV
  B. I, III and IV
  C. I, II and III
  D. All of the above
  B. I, III and IV

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  Explanation

  Statement I is true. If a Monte Carlo simulation is based upon the same parameters as used for analytical VaR, and enough number of simulations are carried out, we would get the same results as with analytical VaR. Statement II is false.

  We cannot use Monte Carlo simulations using parameters based upon a normal assumption when the underlying distribution is not normal. For example, if a return stream is based upon say a uniform distribution, we cannot use a simulation

  based upon drawings from a normal distribution even though we use the same mean and standard deviation.

  Statement III is true. This is the advantage of historical simulations - no assumptions are necessary. (Historical simulations however often suffer from the great disadvantage of the paucity of data that would cover all possibilities.) Statement IV

  is true. The results of historical simulations are limited to the data they are based upon.

• Question 183:

  When pricing credit risk for an exposure, which of the following is a better measure than the others:

  A. Expected Exposure (EE)
  B. Notional amount
  C. Potential Future Exposure (PFE)
  D. Mark-to-market
  A. Expected Exposure (EE)

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  Explanation

  Exposure for derivative instruments can vary significantly over the lifetime of the instrument, depending upon how the market moves. The potential future exposure represents the extremes, not the most likely outcome. The expected exposure is the most suitable measure for pricing the credit risk. Over time, as multiple transactions are entered into, the expectation (or the mean) will be realized - though individual transactions may have more or less by way of exposure. The notional amount may not be relevant, though for loans it may be the most important contributor to the expected exposure. Mark-to-market will represent the exposure at a given point in time, but cannot be predicted nor be used to price the credit risk.

• Question 184:

  The minimum 'multiplication factor' to be applied to VaR calculations for calculating the capital requirements for the trading book per Basel II is equal to:

  A. 3
  B. 4
  C. 1
  D. 2
  A. 3

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  Explanation

  The minimum multiplication factor specified under Basel II is 3. Therefore the correct answer is Choice 'a'. The exact requirements are laid down below. Each bank must meet, on a daily basis, a capital requirement expressed as the higher of

  (i) its previous day's value-at-risk number measured according to the parameters specified in this section and (ii) an average of the daily value-at-risk measures on each of the preceding sixty business days, multiplied by a multiplication factor. The multiplication factor will be set by individual supervisory authorities on the basis of their assessment of the quality of the bank's risk management system, subject to an absolute minimum of 3. Banks will be required to add to this factor a "plus" directly related to the ex- post performance of the model, thereby introducing a built in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 1 based on the outcome of so-called "backtesting."

• Question 185:

  Which of the following statements are true:

  I - Credit VaR often assumes a one year time horizon, as opposed to a shorter time horizon for market risk as credit activities generally span a longer time period.

  II - Credit losses in the banking book should be assessed on the basis of mark-to-market mode as opposed to the default-only mode.

  III - The confidence level used in the calculation of credit capital is high when the objective is to maintain a high credit rating for the institution.

  IV - Credit capital calculations for securities with liquid markets and held for proprietary positions should be based on marking positions to market.

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

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  Explanation

  Statement I is correct as credit VaR calculations often use a one year time horizon. This is primarily because the cycle in respect of credit related activities, such as loan loss reviews, accounting cycles for borrowers etc last a year. Statement II is false. There are two ways in which loss assessments in respect of credit risk can be made: default mode, where losses are considered only in respect of default, and no losses are recognized in respect of the deterioration of the creditworthiness of the borrower (which is often expressed through a credit rating transition matrix); and the mark-to-market mode, where losses due to both defaults and credit quality are considered. The default mode is used for the loan book where the institution has lent moneys and generally intends to hold the loan on its books till maturity. The mark to market mode is used for traded securities which are not held to maturity, or are held only for trading. Statement III is correct. The confidence interval, or the quintile of losses used for maintaining credit ratings tends to be very high as the possibility of the institution's default needs to be remote. Statement IV is correct too, for the reasons explained earlier.

• Question 186:

  The VaR of a portfolio at the 99% confidence level is $250,000 when mean return is assumed to be zero. If the assumption of zero returns is changed to an assumption of returns of $10,000, what is the revised VaR?

  A. 260000
  B. 240000
  C. 273260
  D. 226740
  B. 240000

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  Explanation

  The exact formula for VaR is = -(Z + ), where Z is the z-multiple for the desired confidence level, and is the mean return. Now Z is always a negative number, or at least will certainly be provided the desired confidence level is greater than 50%

  , and is often assumed to be zero because generally for the short time periods for which market risk VaR is calculated, its value is very close to zero. Therefore in practice the formula for VaR just becomes -Z, and since Z is always negative,

  we normally just multiply the Z factor without the negative sign with the standard deviation to get the VaR. For this question, there are two ways to get the answer. If we use the formula, we know that -Z= 250,000 (as =0), and therefore -Z - =

  250,000 - 10,000 = $240,000. The other, easier way to think about this is that if the mean changes, then the distribution's shape stays exactly the same, and the entire distribution shifts to the right by $10,000 as the mean moves up by

  $10,000. Therefore the VaR cutoff, which was previously at - 250,000 on the graph also moves up by 10k to - 240,000, and therefore $240,000 is the correct answer.

  The other choices are intended to confuse by multiplying the z-factor for the 99% confidence level with 10,000 etc.

• Question 187:

  An assumption of normality when returns data have fat tails leads to:

  I - underestimation of VaR at high confidence levels II - overestimation of VaR at low confidence levels III - overestimation of VaR at high confidence levels IV - underestimation of VaR at low confidence levels

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

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  Explanation

  When returns are non-normal and have fat tails, an assumption of normality in returns leads to underestimation of VaR at high confidence levels. At the same time, at lower confidence levels the normal distribution may give higher VaR

  estimates. Therefore Choice 'a' is correct. The other choices are incorrect.

  Also refer to the tutorial about VaR and heavy tails.

• Question 188:

  For a corporate issuer, which of the following can be used to calculate market implied default probabilities?

  I - CDS spreads II - Bond prices III - Credit rating issued by SandP IV - Altman's scoring mod

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

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  Explanation

  Generally, the probability of default is an input into determining the price of a security. However, if we know the market price of a security, we can back out the probability of default that the market is factoring into pricing that security. Market implied default probabilities are the probabilities of default priced into security prices, and can be determined from both bond prices and CDS spreads. Credit ratings issued by a credit agency do not give us 'market implied default probabilities', and neither does an internal scoring model like Altman's as these do not consider actual market prices in any way. Therefore Choice 'b' is the correct answer and the others are not.

• Question 189:

  Which of the following describes rating transition matrices published by credit rating firms:

  A. Expected ex-ante frequencies of migration from one credit rating to another over a one year period
  B. Probabilities of default for each credit rating class
  C. Probabilities of ratings transition from one rating to another for a given set of issuers
  D. Realized frequencies of migration from one credit rating to another over a one year period
  D. Realized frequencies of migration from one credit rating to another over a one year period

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  Explanation

  Transition matrices are used for building distributions of the value of credit portfolios, and are the realized frequencies of migration from one credit rating to another over a period, generally one year. Therefore Choice 'd' is the correct answer. Since they represent an actually observed set of values, they are not probabilities nor are they forward looking ex-ante estimates, though they are often used as proxies for probabilities. Choice 'a' and Choice 'c' are not correct. They include more than information on just defaults, therefore Choice 'b' is not correct.

• Question 190:

  An operational loss severity distribution is estimated using 4 data points from a scenario. The management institutes additional controls to reduce the severity of the loss if the risk is realized, and as a result the estimated losses from a 1-in10-year losses are halved. The 1- in-100 loss estimate however remains the same. What would be the impact on the 99.9th percentile capital required for this risk as a result of the improvement in controls?

  A. The capital required will decrease
  B. The capital required will stay the same
  C. The capital required will increase
  D. Can't say based on the information provided
  C. The capital required will increase

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  Explanation

  This situation represents one of the paradoxes in estimating severity that one needs to be aware of - the improvement in controls reduces the weight of the body/middle of the distribution and moves it towards the tails (as the total probability under the curve must stay at 100%) and the distribution becomes more heavy tailed. As a result, the 99.9th percentile loss actually increases. instead of decreasing, creating a counterintuitive result. Therefore the correct answer is that the capital required will increase. If scenario analysis produces such a result, the analyst must question if the 1 in 100 year loss severity is still accurate. If the new control has reduced the severity in the body of the distribution, the question as to why the more extreme losses have not changed should be raised.