Suppose X & Y are two independent stocks' returns with:

E(X) = E(Y) =15% and V(X) = 144,
V(Y) = 256

Problem 1. Buy half X and half Y, so
w1 = w2 = 0.5 and Z = (X+Y)/2

Note: The answer says that the variance is 100 but I thought it would be 200. Since I would be adding half each of the variances of X & Y. Thus getting X=72 and Y=128 or 200.

Why is it 100? I am confused.

To calculate the variance of Z, let's first calculate the expected value of Z:

E(Z) = E((X+Y)/2) = (E(X) + E(Y))/2 = (15% + 15%)/2 = 15%

Now, let's calculate the variance of Z using the formula:

V(Z) = V((X+Y)/2) = (1/4) * (V(X) + V(Y) + 2 * Cov(X,Y))

Since X and Y are independent, Cov(X,Y) = 0. Therefore:

V(Z) = (1/4) * (V(X) + V(Y) + 2 * 0) = (1/4) * (144 + 256) = (1/4) * 400 = 100

So, the variance of Z is indeed 100, not 200. This is because when you add independent random variables, the variances add up, but only if the weights are equal. In this case, since we are buying half of each stock, the weights are equal (w1 = w2 = 0.5).