Question

If Stock A is 25% of your portfolio with a beta of 1.4, and stock B is 45% of your portfolio with the remainder of the portfolio made up of the risk free asset; what is the beta of stock B if the portfolio beta is 1.2

A. 1.89

B. 1.98

C. 1.5

D. 1.3

Answer 1

Beta of portfolio is computed as:

βP = WA x βA + WB x βB +. . .... + WN x βN

βP = Portfolio beta

WA, WB … WN are weight of investment A, B …   N etc.

βA, βB … βN are beta of investment A, B …   N etc.

Beta of risk-free assets is zero.

Hence the portfolio beta is sum of products of weight and beta of stock A and B only.

1.2 = 0.25 x 1.4 + 0.45 x βB

1.2 = 0.35 + 0.45 x βB

0.45 x βB = 1.2 – 0.35 = 0.85

βB = 0.85/0.45 = 1.888889 or 1.89

Beta of stock B is 1.89

Hence option “1.89” is correct answer.