IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
Two stocks, X and Y, follow a single-index model with market variance 0.04. Beta of X is 0.8 and beta of Y is 1.5. Residuals are uncorrelated. What is the covariance between X and Y?
The covariance is the product of the two betas and the market variance: 0.8 × 1.5 × 0.04 = 0.048. Residual terms are uncorrelated, so they contribute nothing to the covariance between the two stocks.
- A0.0480Correct
- B0.0320
- C0.0120
- D0.0600
- 0.0024
Explanation
Under the model Cov(X,Y) = b_X × b_Y × σ_M² because residuals are uncorrelated. That is 0.8 × 1.5 × 0.04 = 0.048. Leaving out the market variance gives 1.2, and using only one beta gives 0.032 (0.8×0.04).
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