Your client has $95,000 invested in stock A. She would like to build a two-stock

Question

Your client has $95,000 invested in stock A. She would like to build a two-stock portfolio by investing another $95,000 in either stock B or C. She wants a portfolio with an expected return of at least 14.5%

and as low a risk as possible, but the standard deviation must be no more than 40%. What do you advise her to do, and what will be the portfolio expected return and standard deviation?

Expected Return

Standard Deviation

Correlation with A

A

17%

50%

1.00

B

12%

39%

0.18

C

12%

39%

0.34

The expected return of the portfolio with stock B is         %   (Round to one decimal place.)

The expected return of the portfolio with stock C is         %   (Round to one decimal place.)

The standard deviation of the portfolio with stock B is %. (Round to one decimal place.)

The standard deviation of the portfolio with stock C is    %(Round to one decimal place.)

Which stock would you advise your client to choose because it will produce the portfolio with the lower standard deviation.

Expected Return

Standard Deviation

Correlation with A

A

17%

50%

1.00

B

12%

39%

0.18

C

12%

39%

0.34

Explanation / Answer

Answer)

Expected return of porfolio = (Return of stock 1 * Weight of stock 1) + (Return of stock 1 * weight of stock 1)

Expected return of portfolio with stock B = 0.5*0.17 +0.5*0.12 = 14.5%

Expected return of portfolio with stock C =0.5*0.17 +0.5*0.12 = 14.5%

Standard deviation of Portfolio =

[(St.deviation of stock 1 * weightof stock 1)^2 + (St.deviation of stock 2 * weightof stock 2)^2 + (2* weight stock 1 * weight stock 2 * correlation stock 1 & 2) ]^(1/2)

Standard deviation od portfolio with stock B = 0.0625 + 0.038025+0.01755 = [(0.118075)]^(1/2)

= 0.34362043 or 34.36%%

Standard deviation od portfolio with stock C = 0.0625+0.038025+0.03315=[0.133675]^(1/2)

= 0.3656159 or 36.56%

We will advise a portfolio of a with combination of B as it has the lowest st. deviation

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