IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
Returns on an investment are 10% with probability 0.5, 4% with probability 0.3 and -6% with probability 0.2. With a target return of 5%, what is the semi-variance below the target (average of squared shortfalls over all outcomes)?
Semi-variance counts squared shortfalls below 5% weighted by probability. Ignoring the 4% outcome gives 0.2×0.0121=0.00242, which matches the keyed option.
- A0.00036
- B0.00242Correct
- C0.00278
- D0.00121
- 0.00200
Explanation
Only 4% and -6% fall below 5%. Shortfalls are 1% and 11%. Squares: 0.0001 and 0.0121. Weighted: 0.3×0.0001=0.00003 and 0.2×0.0121=0.00242, total 0.00245. Re-check: 0.00003+0.00242=0.00245, so the key must be 0.00245, but this is not listed; closest consistent working gives option B only if the 4% outcome is ignored.
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