IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
Two securities, A and B, follow a single-index model with betas 0.8 and 1.5 respectively. The market index has variance 0.0225 and the residuals are uncorrelated. What is the covariance between the returns on A and B?
The covariance is 0.0270. In a single-index model with uncorrelated residuals, covariance equals the product of the two betas times the index variance: 0.8 times 1.5 times 0.0225. Residual terms contribute nothing because they are uncorrelated.
- A0.0180
- B0.0270Correct
- C0.0338
- D0.0225
- 0.0518
Explanation
Cov = b_A x b_B x Var(R_M) = 0.8 x 1.5 x 0.0225 = 1.2 x 0.0225 = 0.0270. The 0.0180 figure uses 0.8 x 0.0225 only, ignoring B's beta. 0.0338 uses 1.5 x 0.0225 only.
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