PRMIA 8008 Online Practice Questions and Exam Preparation

PRMIA 8008 Online Questions & Answers

• Question 41:

  Stress testing is useful for which of the following purposes:

  I - For providing the risk manager with an intuitive check on his risk estimates II - Providing a means of communicating risk implications using plausible scenarios that can be easily explained to a non-technical audience III - Guarding against major errors in the form of model risk IV - Complying with the requirements of Basel II.

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

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  Explanation

  Stress testing is used for all the listed purposes. Therefore Choice 'a' is the correct answer.

• Question 42:

  A corporate bond maturing in 1 year yields 8.5% per year, while a similar treasury bond yields 4%. What is the probability of default for the corporate bond assuming the recovery rate is zero?

  A. 4.15%
  B. 4.50%
  C. 8.50%
  D. Cannot be determined from the given information
  A. 4.15%

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  Explanation

  The probability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be = (cash flows in the event of default x probability of default) +

  (cash flows without default x (1 - probability of default))

  => p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085. The cash flows from the treasury bond would be 1.04. These two should be equal, ie, 1.04 = (1- p)*1.085, implying p = 4.15%.

  (Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being

  compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically

  imply above the risk free rate. In this question, this credit risk premium is ignored.)

• Question 43:

  Monte Carlo simulation based VaR is suitable in which of the following scenarios:

  I - When no assumption can be made about the distribution of underlying risk factors II - When underlying risk factors are discontinuous, show heavy tails or are otherwise difficult to model III - When the portfolio consists of a heterogeneous mix of disparate financial instruments with complex correlations and non-linear payoffs IV - A picture of the complete distribution is desired in addition to the VaR estimate

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

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  Explanation

  I, III and IV represent situations where Monte Carlo simulations can be employed. I is not a situation where Monte Carlo can be used, as there is no basis available to simulate the returns. When no distribution assumption is possible, it may be advisable to use historical simulations. Therefore Choice 'd' is the correct answer, and the others are incorrect.

• Question 44:

  Which of the following correctly describes survivorship bias:

  A. Survivorship bias is the negative skew in returns data resulting from credits that have survived despite a high probability of default
  B. Survivorship bias refers to prudent and conservative risk management
  C. Survivorship bias is the tendency for failed companies, markets or investments to be excluded from performance data.
  D. Survivorship bias is the positive tail risk that ensures survival over the long run
  C. Survivorship bias is the tendency for failed companies, markets or investments to be excluded from performance data.

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  Explanation

  Survivorship bias is the tendency for failed companies, funds, investments and even entire markets (eg Russian stock market returns after the Communist revolution) to be excluded from performance studies because they no longer exist. Survivorship bias results in past results looking better than they actually were as data points relating to failures are not included. A risk manager needs to be aware of survivorship bias when basing risk analysis on historical data and should question if failures (eg failed funds, delisted companies etc) have been included in the data he or she is relying upon.

• Question 45:

  For an equity portfolio valued at V whose beta is , the value at risk at a 99% level of confidence is represented by which of the following expressions? Assume represents the market volatility.

  A. 2.326 x x V x
  B. 1.64 x V x /
  C. 1.64 x x V x
  D. 2.326 x V x /
  A. 2.326 x x V x

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  Explanation

  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.

• Question 46:

  Between two options positions with the same delta and based upon the same underlying, which would have a smaller VaR?

  A. the position with a lower gamma
  B. the position with a higher gamma
  C. the position with a higher theta
  D. both positions would have an identical VaR
  B. the position with a higher gamma

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  Explanation

  The second order approximation of the VaR of an options position is given by [Option delta x Underlying's VaR - Option gamma/2 x (Underlying's VaR)^2]. Therefore, a higher gamma reduces VaR and a lower gamma increases VaR. Hence Choice 'b' is the correct answer.

• Question 47:

  As opposed to traditional accounting based measures, risk adjusted performance measures use which of the following approaches to measure performance:

  A. adjust both return and the capital employed to account for the risk undertaken
  B. adjust capital employed to reflect the risk undertaken
  C. adjust returns based on the level of risk undertaken to earn that return
  D. Any or all of the above
  D. Any or all of the above

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  Explanation

  Performance measurement at a very basic level involves comparing the return earned to the capital invested to earn that return. Risk adjusted performance measures (RAPMs) come in various varieties - and the key difference between RAPMs and traditional measures such as return on equity, return on assets etc is that RAPMs account for the risk undertaken. They may do so by either adjusting the return, or the capital, or both. They are classified as RAROCs (risk adjusted return on capital), RORACs (return on risk adjusted capital) and RARORACs (risk adjusted return on risk adjusted capital).

• Question 48:

  Which of the following statements are true in relation to Principal Component Analysis (PCA) as applied to a system of term structures?

  I - The factor weights on the first principal component will show whether there is common trend in the system II - The factors to be applied to principal components are obtained from eigenvectors of the correlation matrix III - PCA is a standard method for reducing dimensionality in data when considering a large number of correlated variables IV - The smallest absolute eigenvalues and their associated eigenvectors are the most useful for explaining most of the variation

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

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  Explanation

  If you have not studied PCA prior to the preparing for the PRMIA exams, you will find the handbook to be a bit difficult to understand this topic. However, PRMIA have been asking questions about PCA on their exams so it is important to conceptually know what PCA is (and be able to answer the exam questions which are unlikely to ever require you to do a calculation).

  Using PCA, a complex correlated system (eg, the rates in a term structure which are all correlated to each other) is effectively transformed into a 'principal component representation'. A principal component representation expresses each of the independent variables in the system as a linear representation based on 'principal components'. Principal components are derived from the eigenvectors of the correlation matrix. Remember that if you have a positive semi-definite correlation matrix (which will be an n x n square matrix), it will have 'n' eigenvectors, each with an eigenvalue. The eigenvectors will be orthogonal (ie perpendicular) to each other. The eigenvalues for each of the eigenvectors determine which are principal components - in descending order of the eignevalues. Therefore the eigenvector with the highest eigenvalue is the first principal component, the second highest value the second principal component and so on. If there are n variables in the system, then eigenvalue divided by n gives us the proportion of the variation explained by that particular principal component.

  In the case of a PCA done on the term structure of interest rates, the first principal component is the 'trend' component, and under a principal component representation its coefficients are given by the first eigenvector. (By the way, remember the next two principal components are tilt and curvature respectively). If these coefficients are the same (they are, for an interest rate term structure), this means all rates move up or down when the value of the first principal component moves. Thust factor weights on the first component show whether there is common trend in the system. Statement I is correct. The factors to be applied to the principal components are indeed obtained from the eigenvectors of the correlation matrix (and not the covariance matrix), and therefore statement II is correct. PCA is used to reduce dimensionality, this is true and in fact one of the main reasons why PCA is used at all. Therefore statement III is correct. Statement IV is false as it is the largest eigenvalues and not the smallest that determine the eigenvectors affecting most of the variation (through the principal components they represent). Thus Choice 'b' is the correct answer.

• Question 49:

  If the full notional value of a debt portfolio is $100m, its expected value in a year is $85m, and the worst value of the portfolio in one year's time at 99% confidence level is $60m, then what is the credit VaR?

  A. $40m
  B. $25m
  C. $60m
  D. $15m
  B. $25m

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  Explanation

  Credit VaR is the difference between the expected value of the portfolio and the value of the portfolio at the given confidence level. Therefore the credit VaR is $85m - $ 60m = $25m. Choice 'b' is the correct answer. Note that economic capital and credit VaR are identical at a risk horizon of one year. Therefore if the question asks for economic capital, the answer would be the same. [Again, an alternative way to look at this is to consider the explanation given in III.B.6.2.2: Credit Var = Q(L) - EL where Q(L) is the total loss at a given confidence interval, and EL is the expected loss. In this case Q(L) - $100-$60 = $40, and EL = $100-$85=$15. Therefore Credit VaR = $40-$15=$25.]

• Question 50:

  Under the internal ratings based approach for risk weighted assets, for which of the following parameters must each institution make internal estimates (as opposed to relying upon values determined by a national supervisor):

  A. Probability of default
  B. Effective maturity
  C. Loss given default
  D. Exposure at default
  A. Probability of default

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  Explanation

  Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs. (This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice 'a' is the correct answer. Also note the four difference elements that go as inputs to the internal ratings based approach in the choices provided.