IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
A stock has beta 1.5 and residual standard deviation 6% in a single-index model. The market return has standard deviation 10%. What is the total variance of the stock's return?
Total variance is 0.0261. Systematic variance is beta squared times market variance, 2.25 × 0.01 = 0.0225, and specific variance is 0.06 squared = 0.0036. Adding them gives 0.0261.
- A0.0261Correct
- B0.0225
- C0.0036
- D0.0225 plus 0.0060
- 0.0261 divided by 1.5
Explanation
Systematic variance = 1.5² × 0.10² = 2.25 × 0.01 = 0.0225. Residual variance = 0.06² = 0.0036. Total = 0.0261. The option 0.0225 omits specific risk; 0.0036 omits systematic risk.
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