Hi,
This is a question from a Garp practice exam.
Why in this question can we not use the sum of absolute VAR for Alpha and absolute VAR for Omega to calculate the maksimum possible VAR for portfolio. The maximum possible daily VAR is then based on a correlation(p) = 1 between Alpha and Omega.
Absolute VAR Alpha (10.263) + Absolute VAR Omega (12.814) = Maximum VAR for the portfolio (23.077) (where p =1 between the 2 portfolios)
Relative VAR Alpha (10.363) + Relative VAR Omega (12.953) = Maximum VAR for portfolio (23.316) -which is same as GARP answer
The GARP answer follow a different approach, but the question is based on a Relative VAR for Omega and Alpha although the fund expected returns are given in the question.
Question
Consider a USD 1 million portfolio with an equal investment in two funds, Alpha and Omega, with the following annual return distributions:
Fund Volatility
Alpha 20% Omega 25%
Fund Expected Return
Alpha 5% Omega 7%
Assuming the returns follow the normal distribution and that there are 252 trading days per year, what is the maximum possible daily 95% Value-at-Risk (VaR) estimate for the portfolio?
Explanation: This question tests that the candidate understands correlation in calculating portfolio VaR. From the table, we can get daily volatility for each fund:
Fund Alpha volatility: 0.20 / 2520.5 = 1.260% Fund Omega volatility: 0.25 / 2520.5 = 1.575%
Portfolio variance:
0.52 * 0.012592 + 0.52 * 0.015742 + 2 x 0.5 x 0.5 x 0.01259 x 0.01574 x ρ Portfolio volatility = (portfolio variance)0.5Portfolio volatility is least when ρ = -1 → portfolio volatility = 0.1575% Portfolio volatility is greatest when ρ = 1 → portfolio volatility = 1.4175% Therefore, 95% VaR maximum is 1.645 x 0.014175 x 1,000,000 = USD23,316
This is a question from a Garp practice exam.
Why in this question can we not use the sum of absolute VAR for Alpha and absolute VAR for Omega to calculate the maksimum possible VAR for portfolio. The maximum possible daily VAR is then based on a correlation(p) = 1 between Alpha and Omega.
Absolute VAR Alpha (10.263) + Absolute VAR Omega (12.814) = Maximum VAR for the portfolio (23.077) (where p =1 between the 2 portfolios)
Relative VAR Alpha (10.363) + Relative VAR Omega (12.953) = Maximum VAR for portfolio (23.316) -which is same as GARP answer
The GARP answer follow a different approach, but the question is based on a Relative VAR for Omega and Alpha although the fund expected returns are given in the question.
Question
Consider a USD 1 million portfolio with an equal investment in two funds, Alpha and Omega, with the following annual return distributions:
Fund Volatility
Alpha 20% Omega 25%
Fund Expected Return
Alpha 5% Omega 7%
Assuming the returns follow the normal distribution and that there are 252 trading days per year, what is the maximum possible daily 95% Value-at-Risk (VaR) estimate for the portfolio?
- USD 16,587
- USD 23,316
- USD 23,459
- USD 32,973
Explanation: This question tests that the candidate understands correlation in calculating portfolio VaR. From the table, we can get daily volatility for each fund:
Fund Alpha volatility: 0.20 / 2520.5 = 1.260% Fund Omega volatility: 0.25 / 2520.5 = 1.575%
Portfolio variance:
0.52 * 0.012592 + 0.52 * 0.015742 + 2 x 0.5 x 0.5 x 0.01259 x 0.01574 x ρ Portfolio volatility = (portfolio variance)0.5Portfolio volatility is least when ρ = -1 → portfolio volatility = 0.1575% Portfolio volatility is greatest when ρ = 1 → portfolio volatility = 1.4175% Therefore, 95% VaR maximum is 1.645 x 0.014175 x 1,000,000 = USD23,316
