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  1. Home
  2. PRMIA Certification
  3. 8010 Exam
  4. PRMIA.8010.v2022-03-04.q88 Dumps
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Question 31

The sensitivity (delta) of a portfolio to a single point move in the value of the S&P500 is $100. If the current level of the S&P500 is 2000, and has a one day volatility of 1%, what is the value-at-risk for this portfolio at the 99% confidence and a horizon of 10 days? What is this method of calculating VaR called?

Correct Answer: A
Explanation
If the current level of the S&P 500 is 2000, and a single day volatility is 1%, and the delta (ie change in portfolio value from a one point change) is $100, then the 1 day volatility for the portfolio in dollars is 2000 *
1% * $100 = $2,000.
At the 99% confidence level, the value of the inverse cumulative density function for the normal distribution is
2.33 (=NORMSINV(99%), in Excel). Therefore the 1 day VaR will be 2.33 * $2000 =$4,660. Extending it to
10 days using the square root of time rule, we get the 10 day VaR as equal to SQRT(10)*4660 = $14,736.
Since this method of calculating VaR relies upon a delta approximation of a risk factor (in this case the S&P500), it is the parametric approach to calculating VaR (the other methods being historical simulation, and Monte Carlo simulation).
The
2015 Handbook provides an excellent example of parametric (and other) VaR calculations in Chapter 3 of Volume III of Book 3. The spreadsheet used for the illustration can be downloaded from
http://www.prmia.org/prm-exam/handbook-resources.
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Question 32

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

B)

C)

D)

Correct Answer: A
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.
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Question 33

The probability of default of a security over a 1 year period is 3%. What is the probability that it would not have defaulted at theend of four years from now?

Correct Answer: B
Explanation
The probability that the security would not default in the next 4 years is equal to the probability of survival raised to the power four. In other words, =(1 -3%)^4 = 88.53%. Choice 'b' is the correct answer.
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Question 34

For a 10 year interest rate swap, what would be the worst time for a counterparty to default (in terms of the maximum likely credit exposure)

Correct Answer: D
Explanation
Right after inception' is incorrect as the interest rate swap (IRS) would be valued at close to zero right after inception and the credit risk would be minimum. Choice 'a' (ie 10 years, at maturity) is incorrect as at maturity there would be no more cash flows to exchange, and the replacement value of the contract would again be close to zero.
Therefore the worst time for the counterparty to default is somewhere between inception and maturity - in fact the range of possible outcomes for the contract increases with the passage of time, and we should find the worst time to default to be a later date. However, towards maturity, the value of the contract starts to go towards zero again, and the maximum value is reached around 7 years. 2 years is too early for the maximum to be reached for the10 year IRS, and therefore choice a is the correct answer.
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Question 35

Which of the following statements is true
I. If no loss data is available, good quality scenarios can be used to model operational risk II. Scenario data can be mixed with observed loss data for modeling severity and frequency estimates III. Severity estimates should not be created by fitting models to scenario generated loss data points alone IV. Scenario assessments should only be used as modifiers to ILD or ELD severity models.

Correct Answer: B
Explanation
There are multiple ways to incorporate scenario analysis for modeling operational risk capital - and the exact approach used depends upon thequantity of loss data available, and the quality of scenario assessments.
Generally:
- If there is no past loss data available, scenarios are the only practical means to model operational risk loss distributions. Both frequency and severity estimates can be modeled based on scenario data.
- If there is plenty of past data available, scenarios can be used as a modifier for estimates that are based solely on data (for example, consider the MAX of the loss estimates at the desired quantile as provided bythe data, and as indicated by scenarios)
- If high quality scenario data is available, and there is sufficient past data, one could mix scenario assessments with the loss data and fit the combined data set to create the loss distribution. Alternatively, both could be fitted with severity estimates and then the two severities could be parametrically combined.
In short, there is considerable flexibility in how scenarios can be used.
Statement I is therefore correct, and so is statement II as both indicate valid uses of scenarios.
Statement III is not correct because it may be okay to create severity estimates based on scenario data alone.
Statement IV is not correct because while using scenarios as modifiers to other means of estimation is acceptable, that isnot the only use of scenarios.
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