IAI Actuarial Core Principles · Economic Modelling · Single and multifactor models for investment returns
Two shares, A and B, follow a single-index model with betas 0.8 and 1.5 respectively. The market return variance is 0.0225. What is the covariance between the returns of A and B?
Covariance equals beta A times beta B times the market variance: 0.8 x 1.5 x 0.0225 = 0.0270. Residual terms are uncorrelated across securities, so they contribute nothing to the covariance.
- A0.0180
- B0.0270Correct
- C0.0225
- D0.0300
- 0.0338
Explanation
Under the single-index model the covariance is beta_A x beta_B x market variance = 0.8 x 1.5 x 0.0225 = 1.2 x 0.0225 = 0.0270. Residuals are uncorrelated so they add nothing. Using 0.0225 x 1.5 alone gives 0.0338, which ignores beta A.
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