Question

You have a portfolio with a standard deviation of 28% and an expected return of 17%. 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 Return 16% 16% Standard Deviation 21% 16% Correlation with Your Portfolio's Returns Stock A Stock B 0.3 0.7 Standard deviation of the portfolio with stock Ais %. (Round to two decimal places.)

Answer 1

Standard deviation of Portfolio = 28%

Expected Return = 16%

Adding one of the Stock will have money in 30% in new Stock & 70% in existing portfolio.

Since, Both Stock A and Stock B have same expected Return, we are indifferent in choosing in ters of Expected returns.

Evaluating which stock to choose by calcualting Standard Deviation of new portfolio:

- Standard Deviation of Stock A = 21%

Correlation with portfolio = 0.3

Calculating SD of Portfolio with Stock A-

SD= V(W) * (0)ả + (W) *(0)} + 2WAWpRARPPAP

SD = V(0.302 (21)2 + (0.70)(28)2 + 2 *0.30 * 0.70 * 21 * 28 *0.3

SD = V39.69 + 384.16 + 74.088 = 497.938

SD of portfolio with Stock A is 22.31%

- Standard Deviation of Stock B = 16%

Correlation with portfolio = 0.7

Calculating SD of Portfolio with Stock B-

SD= V(W)*(0)8 +(W) * (0)} + 2WBWpRBRppbp

SD = 0.302(16)2 + (0.70)(28)2 + 2 *0.30 * 0.70 * 16 * 28 * 0.7

SD = 23,04 + 384.16+ 131.712 = 538.912

SD of portfolio with Stock B is 23.21%

As, SD of portfolio with Stock A is less volatile, we should choose STock A.

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