IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
In a single-index model, a security has beta 1.2, market standard deviation 15% and residual standard deviation 20%. What is the security's total standard deviation (to the nearest 0.1%)?
Total variance is 1.44 × 0.0225 = 0.0324 plus residual variance 0.04, giving 0.0724. The square root is about 26.9%. Standard deviations cannot be added directly because systematic and specific components are uncorrelated.
- A18.0%
- B20.0%
- C26.9%Correct
- D32.4%
- 35.0%
Explanation
Systematic variance = 1.2² × 0.15² = 1.44 × 0.0225 = 0.0324. Specific variance = 0.04. Total variance = 0.0724, so standard deviation = 26.9%. Adding standard deviations (18% + 20% = 38%) is wrong, and 32.4% is just the systematic variance misread.
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