IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
An equally weighted portfolio holds 25 shares, each with beta 1.0 and residual variance 0.0400. The market variance is 0.0100. Residuals are uncorrelated. What is the portfolio's total variance?
The portfolio variance is 0.0116. Systematic variance is beta squared times market variance, 0.0100, and residual variance falls to 0.04 divided by 25, or 0.0016, because uncorrelated residuals diversify away.
- A0.0116Correct
- B0.0500
- C0.0100
- D0.0140
- 0.0116 plus 0.0100
Explanation
Portfolio beta = 1.0, so systematic variance = 1 x 0.0100 = 0.0100. Residual variance = 0.04/25 = 0.0016 (weights 1/25, so 25 x (1/625) x 0.04). Total = 0.0100 + 0.0016 = 0.0116. Option 0.0500 ignores diversification of residual risk.
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