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IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk

Annual returns on a portfolio are 10%, 20%, -10% and 0%, each equally likely. The target return is 5%. What is the downside semi-variance about the target (average of squared shortfalls over all four outcomes)?

The semi-variance is 0.00625. Only the -10% and 0% returns fall short of 5%, giving squared shortfalls of 0.0225 and 0.0025. Their sum of 0.025 is averaged over all four equally likely outcomes, giving 0.00625.

  1. A0.00125
  2. B0.00250
  3. C0.00625Correct
  4. D0.01250
  5. 0.02500

Explanation

Shortfalls below 5%: for -10% it is 0.15, squared 0.0225; for 0% it is 0.05, squared 0.0025. The others give zero. Sum is 0.025, divided by 4 gives 0.00625. Dividing by 2 (only the shortfall outcomes) would give 0.0125, which is wrong.

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