IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory
Two assets have standard deviations of 10% and 20%. Their correlation coefficient is 0.5. A portfolio holds 50% in each. What is the portfolio variance?
The portfolio variance is 0.0175. Using weights of one half, the variance terms contribute 0.0025 and 0.01, and the covariance term, twice the product of weights and a covariance of 0.01, adds 0.005. Summing gives 0.0175.
- A0.0225Correct
- B0.0175
- C0.0250
- D0.0325
- 0.0150
Explanation
Variance = 0.25(0.01) + 0.25(0.04) + 2(0.5)(0.5)(0.5)(0.10)(0.20) = 0.0025 + 0.01 + 0.005 = 0.0175 ... check covariance: 0.5 x 0.1 x 0.2 = 0.01; 2 x 0.25 x 0.01 = 0.005. Total = 0.0025 + 0.01 + 0.005 = 0.0175.
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