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18 Jul 2020, 08:51
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You have two mutual funds X and Y. You know E(X) = E(Y). If you are given $1, how would you allocate your $1 between X and Y?
If p_x is the proportion of the $1 that you allocate to X, then expected earnings is p_xE(X) + (1-p_x)E(X) = E(X) since E(X) = E(Y).
In the standard solution, your risk profile depends on your variance. Your earnings are (p_x)X + (1-p_x)Y, and so the standard solution seeks to minimize Var((p_x)X + (1-p_x)Y).
If p_x is the proportion of the $1 that you allocate to X, then expected earnings is p_xE(X) + (1-p_x)E(X) = E(X) since E(X) = E(Y).
In the standard solution, your risk profile depends on your variance. Your earnings are (p_x)X + (1-p_x)Y, and so the standard solution seeks to minimize Var((p_x)X + (1-p_x)Y).
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