Question

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

Answer 1

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.