Consider the formula for the variance of the portfolio of two assets discussed in class:

s_p² = w_A² s_A² + w_B² s_B² + 2 w_A w_B r s_A s_B

Recall that w_A denotes the portfolio weight of asset A (proportion of funds invested in A) and w_B denotes the portfolio weight of asset B, with w_A + w_B = 1 . The coefficient r -1 r 1 measures the correlation between the returns of assets A and B.

(a) Rewrite the above formula as a function of w_A only (recall that w_A + w_B = 1)

(b) Find the portfolio weight w*_A which minimizes portfolio variance.

(c) Suppose that s_A =12 and s_B = 20. Find the variance minimizing portfolio weight of asset A for each of the following values of the correlation coefficient: r = 0 and r = 0.3.