Suzanne Evans
Well-Known Member
AIMs: Define the Value-at-Risk (VaR) ... and explain the limitations of VaR. Define the properties of a coherent risk measure and explain the meaning of each property: Explain why VaR is not a coherent risk measure.
Questions:
29.1. A portfolio contains three independent bonds each with identical (i.i.d.) $100 par value, 3.0% probability of default (EDF) and loss given default (LGD) of 100%. What is, respectively, the 95.0% confident and 99.0% confident portfolio value at risk (VaR)?
a. zero and zero at both 95% and 99%
b. $100 and $100 at both 95% and 99%
c. $200 @ 95% and $300 @ 99%
d. $285 @ 95% and $300 @ 99%
29.2. Your colleague reports a 95.0% one-day value-at-risk (VaR) of $1.4 million for a equities portfolio. If we assume 250 trading days in a year, each of the following is a valid conclusion EXCEPT which of the following is FALSE (cannot be concluded from the statement)?
a. If the VaR is accurate, we do expect the daily loss to exceed $1.4 million at least twelve (12) days during the year
b. If the return distribution is normal, then we can assume the VaR is sub-additive
c. This is a parametric VaR and therefore cannot characterize a heavy-tailed distribution
d. If the returns are i.i.d. normal, we can scale to a 10-day VaR with $1.4*SQRT(10) = $4.3 million 95% 10-day VaR
29.3. Your colleague Stan collected the 99.0% daily value at risk (VaRs) for each of three business units within his division: $10.0, $14.0 and $19.0 million. He aggregated them to arrive at a divisional VaR of $43.0 million. However, he subsequently observes that the distributions are non-normal (and non-elliptical) such that VaR in this context is not sub-additive.
a. No impact: lack of sub-additivity has no impact on the summation of VaR
b. Owing to diversification benefits, the true divisional VaR is less than $43.0 million
c. The true divisional VaR may be greater than $43.0 million
d. VaR's lack of sub-additivity is a minor, theoretical matter of little practical significance; if the VaR lacked positive homogeneity, that would be of greater practical significance
Answers:
Questions:
29.1. A portfolio contains three independent bonds each with identical (i.i.d.) $100 par value, 3.0% probability of default (EDF) and loss given default (LGD) of 100%. What is, respectively, the 95.0% confident and 99.0% confident portfolio value at risk (VaR)?
a. zero and zero at both 95% and 99%
b. $100 and $100 at both 95% and 99%
c. $200 @ 95% and $300 @ 99%
d. $285 @ 95% and $300 @ 99%
29.2. Your colleague reports a 95.0% one-day value-at-risk (VaR) of $1.4 million for a equities portfolio. If we assume 250 trading days in a year, each of the following is a valid conclusion EXCEPT which of the following is FALSE (cannot be concluded from the statement)?
a. If the VaR is accurate, we do expect the daily loss to exceed $1.4 million at least twelve (12) days during the year
b. If the return distribution is normal, then we can assume the VaR is sub-additive
c. This is a parametric VaR and therefore cannot characterize a heavy-tailed distribution
d. If the returns are i.i.d. normal, we can scale to a 10-day VaR with $1.4*SQRT(10) = $4.3 million 95% 10-day VaR
29.3. Your colleague Stan collected the 99.0% daily value at risk (VaRs) for each of three business units within his division: $10.0, $14.0 and $19.0 million. He aggregated them to arrive at a divisional VaR of $43.0 million. However, he subsequently observes that the distributions are non-normal (and non-elliptical) such that VaR in this context is not sub-additive.
a. No impact: lack of sub-additivity has no impact on the summation of VaR
b. Owing to diversification benefits, the true divisional VaR is less than $43.0 million
c. The true divisional VaR may be greater than $43.0 million
d. VaR's lack of sub-additivity is a minor, theoretical matter of little practical significance; if the VaR lacked positive homogeneity, that would be of greater practical significance
Answers:
