IAI Actuarial Core Principles · Economic Modelling · Capital Asset Pricing Model (CAPM)
Two assets each have standard deviation 10%. A portfolio holds 50% in each and the correlation between them is 0.6. What is the portfolio standard deviation?
The portfolio standard deviation is about 8.94 percent. The variance of 0.008 comes from the two weighted variances plus twice the weighted covariance, and taking the square root gives the standard deviation, which is below 10 percent because correlation is under one.
- A10.00%
- B8.94%Correct
- C7.75%
- D8.00%
- 9.00%
Explanation
Variance = 0.25(0.01)+0.25(0.01)+2(0.25)(0.6)(0.01) = 0.0025+0.0025+0.003 = 0.008. The square root is 8.94%. Choosing 10% would ignore diversification, while 8.00% mistakes the variance for the standard deviation in percent terms.
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