You have a portfolio with a standard deviation of 20% and an expected return of

Question

You have a portfolio with a standard deviation of 20% and an expected return of 19%. You are considering adding one of the two stocks in the following table. If after adding the stock you will have 20% of your money in the new stock and 80% of your money in your existing portfolio, which one should you add?

Standard deviation of the portfolio with stock A is ____%?
Stock B is ____%?
Which stock would you add to your portfolio?

Expected Return Standard Deviation Correlation w/your portfolio's returns Stock A 15% 22% 0.3 Stock B 15% 17% 0.7

Explanation / Answer

a. The standard deviation of the portfolio with Stock A is: sqrt(w1^2*sd1^2 + w2^2*sd2^2 + 2*w1*w2*corr*sd1*sd2)

where w1 = 0.8, w2=0.2, sd1=0.20,sd2=0.22,corr =0.3

The standard deviation of the portfolio with Stock A is = sqrt(0.8^2*0.2^2 + 0.2^2*0.22^2 + 2*0.8*0.2*0.3*0.22*0.2) = 0.1782 = 17.82%

b.

he standard deviation of the portfolio with Stock B is: sqrt(w1^2*sd1^2 + w2^2*sd2^2 + 2*w1*w2*corr*sd1*sd2)

where w1 = 0.8, w2=0.2, sd1=0.20, sd2=0.17, corr =0.7

The standard deviation of the portfolio with Stock A is = sqrt(0.8^2*0.2^2 + 0.2^2*0.17^2 + 2*0.8*0.2*0.7*0.17*0.2) = 0.1854 = 18.54%

c. We would add stock B since it has a correlation makes it different from the portfolio and gives it the advnatage of diversification

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