IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
A two-factor model for a fund's return is R = 2% + 0.9 F1 + 0.5 F2 + e, where F1 is the surprise in market return and F2 is the surprise in change in interest rates (both with mean zero), Var(F1)=0.0100, Var(F2)=0.0064, Cov(F1,F2)=0.0020 and Var(e)=0.0009. What is the variance of the fund's return?
The variance is 0.0124, from factor variances, the covariance term and residual variance. Among the listed values none matches exactly, so this question is flawed.
- A0.0090
- B0.0099
- C0.0113
- D0.0126Correct
- 0.0135
Explanation
Var = 0.81×0.0100 + 0.25×0.0064 + 2×0.9×0.5×0.0020 + 0.0009 = 0.0081 + 0.0016 + 0.0018 + 0.0009 = 0.0124. Checking: 0.0081+0.0016=0.0097; +0.0018=0.0115; +0.0009=0.0124. None of the options equals 0.0124 exactly, so the nearest check is needed.
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