Smith buys 14 securities of Company Y. Securities for Company X are the same price, however, the variance of the price of X is 40 and the variance of the price of Y is 40.
According to market research, the price of X goes up when the price of Y goes down, with a covariance of -8. How many of X should be purchased to minimize the variance of his portfolio?
A. 3
B. 4
C. 10
D. 6
E. 9
Variance of portfolio = w^2 * 40 + (1-w)^2 * 40 - 2 * w(1-w) * 8
TO minimize, we take the derivative of
40 w^2+40(1-w)^2 - 16w+16w^2 =0
or
80w -80(1-w) -16 +32w = 0
80w+80w-80-16+32w=0
192w=96
w=0.5
It meand that no. of securites of X = No. of securities of Y
Hence, equal number of securites should be purchase.
Smith buys 14 securities of Company Y. Securities for Company X are the same price, however,...
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