P2.T5.400. Boudoukh's hybrid approach to value at risk (VaR)
AIMs: Describe the existing approaches to VaR measurement and their advantages and disadvantages. Explain the characteristics that are desirable for VaR estimates. Describe the process of implementing the hybrid approach.
Questions:
400.1. Donald Smith, FRM, has collected an historical series of daily portfolio returns. His historical window consists of (K) observations. In order to estimate value at risk (VaR), he wants to choose between exponential smoothing (EXP; e.g., RiskMetrics) and basic historical simulation (HS). His colleague Betty (citing the reading "The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk" by Boudoukh et al) argues against both of these approaches. Each of her arguments is valid EXCEPT which criticism is not accurate?
a. EXP is highly parametric in that it assumes multivariate normality, but financial data series do not seem to fit this assumption. They tend to exhibit fat-tails, skewness, and unstable correlations.
b. EXP discards (i..e., does not use) most of the data in the historical window of (K) observations; this approach only effectively uses the two or three most recent returns
c. HS percentiles are notoriously difficult to estimate and this is especially true for extreme tails of the distribution.
d. HS uses flat (equal) weights over the most recent (K) observations and, implicitly, HS assumes the return series is i.i.d.
400.2. For a given series of historical returns, denoted R(t), assume we develop a 95.0% value at risk (VaR) such that, if our VaR model is correct, the Prob[R(t+1) < -VaR(t)] = 5.0%; that is, we expect the next daily return to exceed (be worse than) the VaR with probability of 5.0%. Further, we can think of an indicator variable I(t), which is one (1) if the VaR is exceeded, and zero (0) otherwise; i.e., I(t) is a Bernoulli variable. Which of the following statements is most correct about the return series, R(t), and the indicator, I(t)?
a. Both R(t) and I(t) series are likely to exhibit serial (auto-) correlation
b. Both R(t) and I(t) must be serially independent
c. While R(t) may exhibit serial correlation, I(t) must be independent (i.i.d.)
d. While I(t) may exhibit serial correlation, R(t) must be independent (i.i.d.)
400.3. Mary Parker, FRM, is today (T0) employing a hybrid approach (hybrid of EXP and HS) to estimate VaR for her equity portfolio. Her hybrid approach parameters are K = 100 and lambda (a.k.a., smoothing constant, decay factor) = 0.94, which reflects a data window of 100 returns. It happens that only last week the trading market was atypically disrupted: her portfolio experienced adverse shocks for three days in a row, with daily returns worse than -5.0% on each of the 3rd, 4th and 5th prior days. Further, each of the worst ten returns have occurred within the last thirty days. As of today (T0), her hybrid approach produces a 95.0% VaR of 2.97%. Per convention, the expected loss is expressed as a positive: Prob[R(t+1) < -VaR(t)] = 5.0%. Assume that over the next 10 days, due to calm markets, the portfolio's daily returns are near zero.
a. Neither HS nor hybrid VaR will change
b. HS will be unchanged but hybrid VaR will be GREATER than 2.97% (i.e., quantile of the loss distribution will "get worse")
c. HS will be unchanged but hybrid VaR will be LESS than 2.97% (i.e., quantile of the loss distribution will "get better")
d. Both HS and hybrid VaR will increase
Answers here:
AIMs: Describe the existing approaches to VaR measurement and their advantages and disadvantages. Explain the characteristics that are desirable for VaR estimates. Describe the process of implementing the hybrid approach.
Questions:
400.1. Donald Smith, FRM, has collected an historical series of daily portfolio returns. His historical window consists of (K) observations. In order to estimate value at risk (VaR), he wants to choose between exponential smoothing (EXP; e.g., RiskMetrics) and basic historical simulation (HS). His colleague Betty (citing the reading "The Best of Both Worlds: A Hybrid Approach to Calculating Value at Risk" by Boudoukh et al) argues against both of these approaches. Each of her arguments is valid EXCEPT which criticism is not accurate?
a. EXP is highly parametric in that it assumes multivariate normality, but financial data series do not seem to fit this assumption. They tend to exhibit fat-tails, skewness, and unstable correlations.
b. EXP discards (i..e., does not use) most of the data in the historical window of (K) observations; this approach only effectively uses the two or three most recent returns
c. HS percentiles are notoriously difficult to estimate and this is especially true for extreme tails of the distribution.
d. HS uses flat (equal) weights over the most recent (K) observations and, implicitly, HS assumes the return series is i.i.d.
400.2. For a given series of historical returns, denoted R(t), assume we develop a 95.0% value at risk (VaR) such that, if our VaR model is correct, the Prob[R(t+1) < -VaR(t)] = 5.0%; that is, we expect the next daily return to exceed (be worse than) the VaR with probability of 5.0%. Further, we can think of an indicator variable I(t), which is one (1) if the VaR is exceeded, and zero (0) otherwise; i.e., I(t) is a Bernoulli variable. Which of the following statements is most correct about the return series, R(t), and the indicator, I(t)?
a. Both R(t) and I(t) series are likely to exhibit serial (auto-) correlation
b. Both R(t) and I(t) must be serially independent
c. While R(t) may exhibit serial correlation, I(t) must be independent (i.i.d.)
d. While I(t) may exhibit serial correlation, R(t) must be independent (i.i.d.)
400.3. Mary Parker, FRM, is today (T0) employing a hybrid approach (hybrid of EXP and HS) to estimate VaR for her equity portfolio. Her hybrid approach parameters are K = 100 and lambda (a.k.a., smoothing constant, decay factor) = 0.94, which reflects a data window of 100 returns. It happens that only last week the trading market was atypically disrupted: her portfolio experienced adverse shocks for three days in a row, with daily returns worse than -5.0% on each of the 3rd, 4th and 5th prior days. Further, each of the worst ten returns have occurred within the last thirty days. As of today (T0), her hybrid approach produces a 95.0% VaR of 2.97%. Per convention, the expected loss is expressed as a positive: Prob[R(t+1) < -VaR(t)] = 5.0%. Assume that over the next 10 days, due to calm markets, the portfolio's daily returns are near zero.
a. Neither HS nor hybrid VaR will change
b. HS will be unchanged but hybrid VaR will be GREATER than 2.97% (i.e., quantile of the loss distribution will "get worse")
c. HS will be unchanged but hybrid VaR will be LESS than 2.97% (i.e., quantile of the loss distribution will "get better")
d. Both HS and hybrid VaR will increase
Answers here:
