PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 281:

  Which of the following are true:

  I - The total of the component VaRs for all components of a portfolio equals the portfolio VaR.

  II - The total of the incremental VaRs for each position in a portfolio equals the portfolio VaR.

  III - Marginal VaR and incremental VaR are identical for a $1 change in the portfolio.

  IV - The VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than (or in extreme cases equal to) the sum of the individual VaRs.

  V - The component VaR for individual components of a portfolio is sub-additive, ie the portfolio VaR is less than the sum of the individual component VaRs.

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

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  Explanation

  Statement I is true - component VaR for individual assets in the portfolio add up to the total VaR for the portfolio. This property makes component VaR extremely useful for risk disaggregation and allocation. Stateent II is incorrect, the incremental VaRs for the positions in a portfolio do not add up to the portfolio VaR, in fact their sum would be greater. Statement III is correct. Marginal VaR for an asset or position in the portfolio is by definition the change in the VaR as a result of a $1 change in that position. Incremental VaR is the change in the VaR for a portfolio from a new position added to the portfolio - and if that position is $1, it would be identical to the marginal VaR. Statement IV is correct, VaR is sub-additive due to the diversification effect. Adding up the VaRs for all the positions in a portfolio will add up to more than the VaR for the portfolio as a whole (unless all the positions are 100% correlated, which effectively would mean they are all identical securities which means the portfolio has only one asset). Statement V is in incorrect. As explained for Statement I above, component VaR adds up to the VaR for the portfolio.

• Question 282:

  Loss provisioning is intended to cover:

  A. Unexpected losses
  B. Losses in excess of unexpected losses
  C. Both expected and unexpected losses
  D. Expected losses
  D. Expected losses

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  Explanation

  Loss provisioning is intended to cover expected losses. Economic capital is expected to cover unexpected losses. No capital or provisions are set aside for losses in excess of unexpected losses, which will ultimately be borne by equity. Choice 'd' is the correct answer.

• Question 283:

  A Bank Holding Company (BHC) is invested in an investment bank and a retail bank. The BHC defaults for certain if either the investment bank or the retail bank defaults. However, the BHC can also default on its own without either the investment bank or the retail bank defaulting. The investment bank and the retail bank's defaults are independent of each other, with a probability of default of 0.05 each. The BHC's probability of default is 0.11. What is the probability of default of both the BHC and the investment bank? What is the probability of the BHC's default provided both the investment bank and the retail bank survive?

  A. 0.0475 and 0.10
  B. 0.11 and 0
  C. 0.08 and 0.0475
  D. 0.05 and 0.0125
  D. 0.05 and 0.0125

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  Explanation

  Since the BHC always fails when the investment bank fails, the joint probability of default of the two is merely the probability of the investment bank failing, ie 0.05. The probability of just the BHC failing, given that both the investment bank and

  the retail bank have survived will be equal to 0.11 - (0.05+0.05-0.05*0.05) = 0.0125. (The easiest way to understand this would be to consider a venn diagram, where the area under the largest circle is 0.11, and there are two intersecting

  circles inside this larger circle, each with an area of 0.05 and their intersection accounting for 0.05*0.05. We need to calculate the area outside of the two smaller circles, but within the larger circle representing the BHC).

  Refer diagram below, please excuse the awful colors.

  

• Question 284:

  There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds are 0.03 and 0.08 respectively, over a one year horizon. If the probability of the two bonds defaulting simultaneously is 1.4%, what is the default correlation between the two?

  A. 0%
  B. 100%
  C. 40%
  D. 25%
  D. 25%

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  Explanation

  Probability of the joint default of both A and B =

  

  We know all the numbers except default correlation, and we can solve for it. Default Correlation*SQRT(0.03*(1 - 0.03)*0.08*(1 - 0.08)) + 0.03*0.08 = 0.014. Solving, we get default correlation = 25%

• Question 285:

  An investor holds a bond portfolio with three bonds with a modified duration of 5, 10 and 12 years respectively. The bonds are currently valued at $100, $120 and $150. If the daily volatility of interest rates is 2%, what is the 1-day VaR of the portfolio at a 95% confidence level?

  A. 115.51
  B. 163.11
  C. 370
  D. 165
  A. 115.51

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  Explanation

  The total value of the portfolio is $370 (=$100 + $120 + $150). The modified duration of the portfolio is the weighted average of the MDs of the different bonds, ie =(5 * 100/370) + (10 * 120/370) + (12 * 150/370) = 9.46. This means that for every 1% change in interest rates, the value of the portfolio changes by 9.46%. Since the daily volatility of interest rates is 2%, the 95% confidence level move will be 1.65 * 2% = 3.30%. Thus, the VaR of the portfolio at the 95% confidence level will be 3.3 * 9.46% * $370 = $115.51. All other answers are incorrect.

• Question 286:

  Which of the following statements is correct?

  A. Funding liquidity risks present themselves in the form of an adverse market impact on prices from a trade
  B. Dynamic simulations of liquidity needs require an assumption of counterparty risk remaining constant
  C. Market liquidity risk is idiosyncratic while funding liquidity risk is not
  D. Market liquidity risks present themselves in the form of higher bid offer spreads
  D. Market liquidity risks present themselves in the form of higher bid offer spreads

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  Explanation

  Simulations of liquidity needs can be of various types: historical simulations, where the current positions are subjected to the kind of liquidity shocks experienced in the past; static simulations, where a static view of current positions, counterparty credit position, and the business is considered; and dynamic simulations where all factors are dynamically changed including counterparty credit standing, changes to the current portfolio and behavioural aspects of the business. Choice 'b' is incorrect as dynamic simulations require no such assumptions. Liquidity risk is often thought of in terms of market liquidity risk and funding liquidity risk. Market liquidity risk relates to the the liquidity for a particular type of asset drying up. For example, during the 2007-2009 crisis a large number of corporate bonds and structured products became extremely illiquid. Market liquidity risk manifests itself in the form of higher bid offer spreads, higher pricde impact, and a reduction in the normal market size (ie, the 'normal' size of a trade for which a dealer quote is valid for). Therefore Choice 'd' is correct. Similarly, Choice 'a' is incorrect as adverse price impact results from market liquidity risk and not funding liquidity risk. Market liquidity risk applies to the entire market and all its participants. It is not idiosyncratic. Therefore Choice 'c' is incorrect too. Funding liquidity risk on the other hand applies to an individual institution that is under liquidity stress in the sense of not being able to meet its obligations such as margin or collateral calls because of a lack of liquid assets. Thus it is funding liquidity that is idiosyncratic. Market liquidity risk often leads to funding liquidity risks materializing as firms are unable to get to the funds they were relying upon due to assets becoming illiquid.

• Question 287:

  Which of the following statements is true in relation to a normal mixture distribution:

  I - The mixture will always have a kurtosis greater than a normal distribution with the same mean and variance II - A normal mixture density function is derived by summing two or more normal distributions III - VaR estimates for normal mixtures can be calculated using a closed form analytic formula

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

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  Explanation

  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.

• Question 288:

  Which of the following is the best description of the spread premium puzzle:

  A. The spread premium puzzle refers to observed default rates being much less than implied default rates, leading to lower credit bonds being relatively cheap when compared to their actual default probabilities
  B. The spread premium puzzle refers to dollar denominated non-US sovereign bonds being priced a at significant discount to other similar USD denominated assets
  C. The spread premium puzzle refers to AAA corporate bonds being priced at almost the same prices as equivalent treasury bonds without offering the same liquidity or guarantee as treasury bonds
  D. The spread premium puzzle refers to the moral hazard implicit in the monoline insurance market
  A. The spread premium puzzle refers to observed default rates being much less than implied default rates, leading to lower credit bonds being relatively cheap when compared to their actual default probabilities

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  Explanation

  Choice 'a' is the correct answer. The other choices represent non-sensical statements.

• Question 289:

  Conditional VaR refers to:

  A. expected average losses conditional on the VaR estimates not being exceeded
  B. value at risk when certain conditions are satisfied
  C. expected average losses above a given VaR estimate
  D. the value at risk estimate for non-normal distributions
  C. expected average losses above a given VaR estimate

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  Explanation

  Conditional VaR is the expected average losses above a given percentile, or a given VaR estimate at the given level of confidence. For example, if we know what the 99% VaR is, we still do not know what we can expect our losses to be if this VaR loss estimate were to be exceeded. Conditional VaR provides the answer to this question by providing an estimate of the average or expected losses beyond 99% mark. Therefore Choice 'c' is the correct answer and the other choices are mostly non-sensical.

• Question 290:

  Which of the following statements are true:

  I - The sum of unexpected losses for individual loans in a portfolio is equal to the total unexpected loss for the portfolio.

  II - The sum of unexpected losses for individual loans in a portfolio is less than the total unexpected loss for the portfolio.

  III - The sum of unexpected losses for individual loans in a portfolio is greater than the total unexpected loss for the portfolio.

  IV - The unexpected loss for the portfolio is driven by the unexpected losses of the individual loans in the portfolio and the default correlation between these loans.

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

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  Explanation

  Unexpected losses (UEL) for individual loans in a portfolio will always sum to greater than the total unexpected loss for the portfolio (unless all the loans are correlated in such a way that they default together). This is akin to the 'diversification effect' in market risk, in other words, not all the obligors would default together. So the UEL for the portfolio will always be less than the sum of the UELs for individual loans. Therefore statement III is true.This 'diversification effect' will be affected by the default correlations between the obligors, in cases where the probability of various obligors defaulting together is low, the UEL for the portfolio would be much less than the UEL for the individual loans. Hence statement IV is true.I and II are false for the reasons explained above.