Stocks x, y, and z have expected returns of 7%, 6%, and 10%, respectively, and the following
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Mathematics, 01.11.2019 02:31 M1CK3Y
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.
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