friend is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolioShe is highly risk averse and has asked for your adviceThe three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the marketPotential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75However, Stock A's standard deviation of returns is 12% versus 8% for Stock BWhich stock should this investor add to his or her portfolio, or does the choice not matter?
A) Stock A.
B) Stock B.
C) Neither A nor B, as neither has a return sufficient to compensate for risk.
D) Add A, since its beta must be lower.
E) Either A or B, i.e., the investor should be indifferent between the two.

Question

Quizplus · Accepted Answer

The investor in this case is highly risk-averse, meaning they prioritize risk reduction over high returns. With all three current stocks having a beta of 1.0 and a perfect positive correlation with the market, adding a fourth stock with a high standard deviation (Stock A) would increase the overall portfolio risk. Therefore, it is better to add Stock B, which has a lower standard deviation and will not significantly increase the portfolio risk. Both Stock A and Stock B have the same expected return and correlation with the market, so the choice is made solely on the basis of risk.

Friend Is Considering Adding One Additional Stock to a 3-Stock