Learning Objectives: Define the VaR measure of risk, describe assumptions about return distributions and holding period, and explain the limitations of VaR.
Questions:
808.1. An asset's returns are normally distributed with an expected annual return of 15.0% and volatility of 10.0% per annum; i.e., µ = 0.150 and σ = 0.10. If there are 250 trading days per year, which is nearest to the time horizon at which the 95.0% absolute VaR is approximately zero?
a. 10 days
b. 150 days
c. 300 days
d. Given its nonzero volatility, the absolute VaR cannot be zero
808.2. Patricia the Risk Analyst has estimated the relative value at risk (VaR) for an asset by assuming its arithmetic returns are normally distributed; recall that relative VaR is the worst expected loss relative to the expected future value, or put another way, relative VaR is identical to an absolute VaR that assumes zero drift. Her estimate for the 10-day 95.0% confident relative VaR is $5.20. In this case, each of the following is true EXCEPT which is false?
a. The corresponding 3-day 99.0% VaR is approximately $4.03
b. The corresponding 20-day 95.0% VaR is approximately $7.35
c. The corresponding 20-day 99.0% VaR is approximately $22.99
d. The corresponding 10-day 95.0% lognormal VaR is less than $5.20, where lognormal VaR = P*(1 - exp[µ*Δt - σ*α*sqrt(Δt)])
808.3. Ralph wants to estimate the value at risk (VaR) for his firm's portfolio of equity securities. The total portfolio contains about 90 long positions, and the 90*89/2 = 4,005 pairwise correlation assumptions vary from -0.25 to +0.83. The total portfolio consists of six sub-portfolios, each holding 15 positions. Ralph is evaluating different approaches to estimating the portfolio's VaR. He will analyze VaR for each sub-portfolio, to ensure VaR remains within limits, and he will also aggregate these sub-portfolio estimates in order to determine VaR for the total portfolio. Among his requirements is that his risk measures are coherent. In this situation, which of the following statements is TRUE?
a. If Ralph requires a coherent VaR, then he must use the Monte Carlo simulation (MCS) approach
b. If Ralph employs a parametric (aka, analytical) approach to estimating VaR, then his VaRs will be subadditive
c. If Ralph assumes a long holding period, for example, a year or longer, then by convention should assume the drift is zero
d. If Ralph employs a delta-normal approach (i.e., the risk factors are multivariate normal) to estimating VaR, then his VaRs will be subadditive
Answers here:
Questions:
808.1. An asset's returns are normally distributed with an expected annual return of 15.0% and volatility of 10.0% per annum; i.e., µ = 0.150 and σ = 0.10. If there are 250 trading days per year, which is nearest to the time horizon at which the 95.0% absolute VaR is approximately zero?
a. 10 days
b. 150 days
c. 300 days
d. Given its nonzero volatility, the absolute VaR cannot be zero
808.2. Patricia the Risk Analyst has estimated the relative value at risk (VaR) for an asset by assuming its arithmetic returns are normally distributed; recall that relative VaR is the worst expected loss relative to the expected future value, or put another way, relative VaR is identical to an absolute VaR that assumes zero drift. Her estimate for the 10-day 95.0% confident relative VaR is $5.20. In this case, each of the following is true EXCEPT which is false?
a. The corresponding 3-day 99.0% VaR is approximately $4.03
b. The corresponding 20-day 95.0% VaR is approximately $7.35
c. The corresponding 20-day 99.0% VaR is approximately $22.99
d. The corresponding 10-day 95.0% lognormal VaR is less than $5.20, where lognormal VaR = P*(1 - exp[µ*Δt - σ*α*sqrt(Δt)])
808.3. Ralph wants to estimate the value at risk (VaR) for his firm's portfolio of equity securities. The total portfolio contains about 90 long positions, and the 90*89/2 = 4,005 pairwise correlation assumptions vary from -0.25 to +0.83. The total portfolio consists of six sub-portfolios, each holding 15 positions. Ralph is evaluating different approaches to estimating the portfolio's VaR. He will analyze VaR for each sub-portfolio, to ensure VaR remains within limits, and he will also aggregate these sub-portfolio estimates in order to determine VaR for the total portfolio. Among his requirements is that his risk measures are coherent. In this situation, which of the following statements is TRUE?
a. If Ralph requires a coherent VaR, then he must use the Monte Carlo simulation (MCS) approach
b. If Ralph employs a parametric (aka, analytical) approach to estimating VaR, then his VaRs will be subadditive
c. If Ralph assumes a long holding period, for example, a year or longer, then by convention should assume the drift is zero
d. If Ralph employs a delta-normal approach (i.e., the risk factors are multivariate normal) to estimating VaR, then his VaRs will be subadditive
Answers here:
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