Suppose you have two assets, A and B. Over the past 3 periods, A has returned 8%, 2%, and 6%, while B has returned 11%, -5%, and 20%. What is the return covariance between assets A and B?
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A. B. C. D.B
First we must find the expected returns for A and B. These are 5.33% and 8.67%. Second, we find the difference between each observation and the average: (8%
- 5.33%), (2% - 5.33%), and (6% - 5.33%) for A, and (11% - 8.67%), (-5% - 8.67%), and (20% - 8.67%) for B. Next, we multiply these together and sum them: (8%
- 5.33%)*(11% - 8.67%) + (2% - 5.33%)*(-5% - 8.67%) + (6% - 5.33%)*(20% - 8.67%). The sum of these is 59.33%. The covariance is the probability weighted average of these cross products, so we divide by 3 to get 19.78%%. Note, we could have divided each cross product by 3 rather than the sum of the cross products. If the observations did not have the same probability or frequency, we would need to treat each cross product separately rather than divide at the end.