IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
Annual losses on a portfolio are normal with mean -₹2 crore (a gain) and standard deviation ₹5 crore. Using z=1.645 for 95%, what is the 95% VaR for losses?
The 95% VaR is about ₹6.23 crore. For normally distributed losses, VaR equals the mean plus 1.645 standard deviations: -2 + 1.645×5 = 6.225. Using 8.23 ignores that the mean loss is negative, meaning an expected gain.
- A₹6.23 croreCorrect
- B₹8.23 crore
- C₹10.23 crore
- D₹3.29 crore
- ₹4.11 crore
Explanation
VaR = mean + z×sd = -2 + 1.645×5 = -2 + 8.225 = 6.225, about ₹6.23 crore. Ignoring the negative mean gives 8.23. Adding 2 instead of subtracting gives 10.23.
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