1.) A highly risk-averse investor is considering adding one additional stock to

Question

1.) A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio, to form a 4-stock portfolio. The three stocks currently held all have b = 1.0, and they are perfectly positively correlated with the market. Potential new Stocks A and B both have expected returns of 15%, are in equilibrium, and are equally correlated with the market, with r = 0.75. However, Stock A's standard deviation of returns is 12% versus 8% for Stock B. Which stock should this investor add to his or her portfolio, or does the choice not matter?

Either A or B, i.e., the investor should be indifferent between the two.

Stock A.

Stock B.

Neither A nor B, as neither has a return sufficient to compensate for risk.

Add A, since its beta must be lower.

Explanation / Answer

Option - Stock B

Either of the stocks if added in same proportion of portfolio, would yield same expected return for the overall portfolio.

However, the expected standard deviation for portfolio will be lower when stock B is added to portfolio as it has lower standard deviation on a standalone basis.

So, for same level of expected return of the new portfolio, portfolio with stock B would have lower risk or volatility or standard deviation of portfolio.

Hence, Sharpe's ratio will be higher for portfolio with stock B. In simple words, portfolio with stock B is more risk return efficient.

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