Stocks x, y, and z have expected returns of 7%, 6%, and 10%, respectively, and the following

x y z
x .01 .001 .001
y .001 .04 -.04
z .001 -.04 .08
(a) determine the fraction of the portfolio to hold in each stock so as to minimize the variance of the

portfolio subject to a minimum expected return on the portfolio of 8%. (profolio variance)

(b) can the variance of the portfolio be smaller than the variance of any individual stock? explain.

(c) use the lagrange multiplier information to estimate what would happen to the variance of the

optimal portfolio if the minimum expected return were raised to 9%. compare your estimate with

the actual by resolving the model.