FRM Part II · FRM Exam Part II · Portfolio Performance Evaluation
A fund has an active risk (tracking error) of 3% per year relative to its benchmark. Assuming active returns are normally distributed with a mean of zero, what is the approximate one-year 95% relative VaR (using z = 1.645)?
Relative VaR at 95% one-tailed equals 1.645 times the 3% tracking error, about 4.94%. This means the portfolio is expected to underperform its benchmark by more than that amount in only 5% of years, given zero mean normal active returns.
- A3.00%
- B4.94%Correct
- C5.88%
- D1.82%
Explanation
Relative VaR = 1.645 x 3% = 4.935%, approximately 4.94%. 5.88% uses z = 1.96 (two-sided 95%), which is the wrong quantile for a one-tailed VaR. 3.00% ignores the multiplier; 1.82% divides by z.
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