IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
A portfolio has annual return outcomes of -10%, 0%, 10% and 20%, each with probability 0.25. Semi-variance is measured below a target of 0% as E[(min(R-0,0))^2]. What is the semi-variance (in %² units)?
The semi-variance is 25 (%²). Only the −10% outcome falls below the 0% target, its squared shortfall is 100, and weighting by probability 0.25 gives 25. Outcomes at or above the target contribute zero.
- A25Correct
- B100
- C50
- D12.5
- 75
Explanation
Only the -10% outcome lies below the target. Its squared deviation is 100 and it has probability 0.25, giving 0.25×100=25. Option 100 omits the probability weight, and 50 would wrongly include the 0% outcome with extra weighting.
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