FRM Part II · FRM Exam Part II · VaR Mapping
A portfolio worth USD 50 million has a beta of 1.2 relative to a market index. The index has an annual volatility of 15%. Assuming returns are normally distributed with zero mean, and ignoring specific risk, what is the approximate 1-year 95% VaR (use z = 1.645) of the portfolio using beta mapping?
Beta-mapped volatility is 1.2 times 15%, or 18%. Multiplying by 1.645 and the USD 50 million value gives a 95% one-year VaR of about USD 14.8 million. Ignoring beta would give 12.3 million, which understates risk for a portfolio more sensitive than the index.
- AUSD 14.8 millionCorrect
- BUSD 12.3 million
- CUSD 9.0 million
- DUSD 17.8 million
Explanation
Portfolio volatility from the index = 1.2 x 15% = 18%. VaR = 1.645 x 0.18 x 50 = USD 14.80 million. Omitting the beta gives 12.3 million; using beta without the exposure scaling and with 1.2 x 0.15 only gives 9.0 (z = 1.0). Using z=1.645 and 1.2 twice gives 17.8 is wrong.
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