Question: Consider formulas (B.32) and (B.33). Let X stand for the rate of retur

Question

Question: Consider formulas (B.32) and (B.33). Let X stand for the rate of return on a security, say, IBM, and Ythe rate of return on another security, say, General Foods. Let Let sk = 16, = 9, and r=-08. What is the variance of (X + Y) in this case? Is it greater than or smaller than var (X) + var (Y)? In this instance, is it better to invest equally in the two securities (i.e., diversify) than in either security exclusively? This problem is the essence of the portfolio theory of finance. (See, for example, Richard Brealey and Stewart Myers, Principles of Corporate Finance, McGraw-Hill, New York, latest edition.) Myers, Principles of Corporate Finance, McGraw-Hill, New York, atest edition.)

Explanation / Answer

given var(x) = 16 and var(y) = 9.and correlation coefficient r = -0.8

stndrd deviation of x = 4,y= 3.

var(x+y) = 16 + 9 - 2X0.8X12 = 25 - 19.2 = 5.8 < var (x) +var(y)

it is better to invest in both X and Y securities

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