FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A portfolio has two positions: Asset A with USD 6 million and annual volatility 10%, and Asset B with USD 8 million and annual volatility 5%. The correlation of returns is 0.5. Using the delta-normal approach with z = 1.645 and zero mean, what is the approximate one-year 95% VaR?
Combining the two positions with correlation 0.5 gives a portfolio standard deviation of about USD 0.872 million, so the 95% VaR is about USD 1.43 million, closest to USD 1.45 million. Simply adding standalone VaRs would overstate risk.
- AUSD 1.17 millionCorrect
- BUSD 1.45 million
- CUSD 0.97 million
- DUSD 0.71 million
Explanation
Position sigmas: A = 0.6 million, B = 0.4 million. Variance = 0.36 + 0.16 + 2(0.5)(0.6)(0.4) = 0.76; sigma = 0.8718 million. VaR = 1.645 × 0.8718 = 1.434 million. Recheck: 0.36+0.16+0.24 = 0.76, so 1.434 million, which corresponds to the listed 1.45 option.
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