You have a portfolio with a standard deviation of 24% and an expected return of

Question

You have a portfolio with a standard deviation of 24% and an expected return of 16%. You are considering adding one of the two stocks in the following table if after adding the stock you will have 30% of your money in the new stock and 70% of your money in your existing portfolio, which one should you add? Expected Standard Correlation with Return Deviation Your Portfolio's Returns Stock A Stock B 13% 13% 25% 16% 0.2 0.6 Standard deviation of the portfolio with stock A is 1% Round to two decimal places.

Explanation / Answer

1) Addition of Stock A: Expected return = 13*0.3+16*0.7 = 15.10% SD of the new portfolio = (0.3^2*25^2+0.7^2*24^2+2*0.3*0.7*25*24*0.2)^0.5 = 19.72% 2) Addition of Stock B: Expected return = 13*0.3+16*0.7 = 15.10% SD of the new portfolio = (0.3^2*16^2+0.7^2*24^2+2*0.3*0.7*16*24*0.6)^0.5 = 20.05% 3) The expected return is the same 15.10% for combinations with A and B. But SD for combination with Stock A is lower, signifying that it has lower risk for the same return. Hence, combination with Stock A is to be chosen: ie: Stock A should be added.

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