Question

Your client has $ 99 comma 000 invested in stock A. She would like to build a​ two-stock portfolio by investing another $ 99 comma 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?

Answer 1

Portfolio Returns = 14% for Stock B

Portfolio Returns = 14% for Stock C

Portfolio Standard Deviation for Stock C = 34.9%

Portfolio Standard Deviation for Stock B = 32.8%

Here, we can see that, in both stocks expected return rate is same but the portfolio standard deviation for Stock B is lesser than Stock C. So, I advise her to invest in Stock B.

Step-by-step explanation:

First of all, let be clear to you that, this question is incomplete and lacks data essential data. I have found similar question on the internet and I am going to share that data with you. Hope, the purpose of solving this question will be fulfilled.

Expected Return . Standard Deviation . Correlation with Stock A

Stock A = 15% 49% 1.00

Stock B = 13% 38% 0.12

Stock C = 13% 38% 0.28

Now, we have complete data. Let's solve this problem.

Condition: If my client invest in Stock B

then,

Expected Returns of stocks A & B will be as follows:

Expected Return of Stock A (R1) = 15%

Expected return of Stock B (R2) = 13%

and Standard Deviation of Stocks A & B will be as follows:

SD of Stock A (SD1) = 49%

SD of Stock B (SD2) = 38%

and weights depending on the amount of money invested on stocks A & B will be as follows:

Weight of Stock A (W1) = 50%

Weight of Stock B (W2) = 50%

Note: Weights are 50% each because, same amount of money is invested in two stocks i.e 99000 USD in Stock A and 99000 USD in Stock B.

So, for all of these data, our correlation with Stock A will be as follows:

Correlation of Stock B with Stock A = 0.12

Now, as we have all the data ready to be plugged into the formula. Let's write down the formula for portfolio return:

Portfolio Returns = W1xR1 + W2xR2 = (0.15x0.50) + (0.13x0.50) = 0.14 x 100 = 14%

Portfolio Returns = 14%

Now, it's time to calculate the Portfolio Standard Deviation:

Portfolio Standard Deviation = (W1² * SD1² + W2² * SD2² + 2*(W1)*(W2)*Correlation* SD1* SD2)^(1/2)

Portfolio Standard Deviation = [(50%² X 49%²) + (50%² X 38%²) + (2 X 50% X 50% X 0.12 X 49% X 38%)]^(1/2)

Portfolio Standard Deviation = 32.8%

Condition: If my client invest in Stock C

then,

Expected Returns of stocks A & C will be as follows:

Expected Return of Stock A (R1) = 15%

Expected return of Stock C (R3) = 13%

and Standard Deviation of Stocks A & C will be as follows:

Standard Deviation of A (SD1) = 49%

Standard Deviation of C (SD3) = 38%

and weights depending on the amount of money invested on stocks A & C will be as follows:

Weight of A (W1) = 50%

Weight of C (W3) = 50%

So, for all of these data, our correlation with Stock A will be as follows:

Correlation of Stock C with Stock A = 0.28

Now, as we have all the data ready to be plugged into the formula. Let's write down the formula for portfolio return:

Portfolio Returns = W1R1 + W3R3 = (0.15*0.50%) + (0.13*0.50) = 0.14 X 100 = 14%

Now, it's time to calculate the Portfolio Standard Deviation:

Portfolio Standard Deviation = (W1² * SD1² + W3² * SD3² + 2*(W1)*(W2)*Correlation* SD1* SD3)^(1/2)

Portfolio Standard Deviation= [(50%² X 49%²) + (50%² X 38%²) + (2 X 50% X 50%X 0.28 X 49% X 38%)]^(1/2)

Portfolio Standard Deviation = 34.9%

Here, we can see that, in both stocks expected return rate is same but the portfolio standard deviation for Stock B is lesser than Stock C. So, I advise her to invest in Stock B.