If Mary decides to invest 10 percent of her money in Firm A's common stock and 90 percent in Firm B's common stock, what is the expected rate of return and the standard deviation of the portfolio return? b. If Mary decides to invest 90 percent of her money in Firm A's common stock and 10 percent in Firm B's common stock, what is the expected rate of return and the standard deviation of the portfolio return? c. Recompute your responses to both questions a and b, where the correlation between the two firms' stock returns is negative 0.50. d. Summarize what your analysis tells you about portfolio risk when combining risky assets in a portfolio.

Part c: The return of portfolio is 10.5% and standard deviation is 4.911% for case a while the return of portfolio is 14.5% and standard deviation is 10.51% for case b.

Part d: By changing the investment from firm A to firm B, the return is increased however the risk is also increased.

Explanation:

As the complete data is not available in the question, thus by referring the question found by google matching the context.

Following is the additional data

Firm A

Expected Return: 0.15

Standard Deviation: 0.12

Firm B

Expected Return: 0.10

Standard Deviation: 0.06

Correlation Coefficient=0.50

Part a:

The investment value is WA=10%=0.1 and WB=90%=0.9 so

[tex]E_{portfolio}=[W_A \times E_A]+[W_B \times E_B]\\E_{portfolio}=[0.1 \times 0.15]+[0.9 \times 0.1]\\E_{portfolio}=0.105 =10.5 \%[/tex]

The standard deviation is given as

[tex]\sigma_{portfolio}=\sqrt{(W_A \times \sigma_A)^2+(W_B \times \sigma_B)^2+(2 \times W_A \times W_B \times CC \times \sigma_A \times \sigma_B)}\\\sigma_{portfolio}=\sqrt{(0.1 \times 0.12)^2+(0.9 \times 0.06)^2+(2 \times 0.1 \times 0.9 \times 0.5 \times 0.12 \times0.06)}\\\sigma_{portfolio}=0.06089 =6.089\%[/tex]

So the return of portfolio is 10.5% and standard deviation is 5.089%.

Part b:

The investment value is WA=90%=0.9 and WB=10%=0.1 so

[tex]E_{portfolio}=[W_A \times E_A]+[W_B \times E_B]\\E_{portfolio}=[0.9 \times 0.15]+[0.1 \times 0.1]\\E_{portfolio}=0.145 =14.5 \%[/tex]

The standard deviation is given as

[tex]\sigma_{portfolio}=\sqrt{(W_A \times \sigma_A)^2+(W_B \times \sigma_B)^2+(2 \times W_A \times W_B \times CC \times \sigma_A \times \sigma_B)}\\\sigma_{portfolio}=\sqrt{(0.9 \times 0.12)^2+(0.1 \times 0.06)^2+(2 \times 0.1 \times 0.9 \times 0.5 \times 0.12 \times0.06)}\\\sigma_{portfolio}=0.1111 =11.12\%[/tex]

So the return of portfolio is 14.5% and standard deviation is 11.12%.

Part c:

Now the correlation coefficient is -0.5 so

Calculation for part a now yields

The investment value is WA=10%=0.1 and WB=90%=0.9so

The value of return will remain same i.e. 10.5%

Whereas the standard deviation is given as

[tex]\sigma_{portfolio}=\sqrt{(W_A \times \sigma_A)^2+(W_B \times \sigma_B)^2+(2 \times W_A \times W_B \times CC \times \sigma_A \times \sigma_B)}\\\sigma_{portfolio}=\sqrt{(0.1 \times 0.12)^2+(0.9 \times 0.06)^2+(2 \times 0.1 \times 0.9 \times -0.5 \times 0.12 \times0.06)}\\\sigma_{portfolio}=0.04911=4.911\%[/tex]

So the return of portfolio is 10.5% and standard deviation is 4.911%.

Calculation for part a now yields

The investment value is WA=90%=0.9 and WB=10%=0.1 so

The value of return will remain same i.e. 14.5%

The standard deviation is given as

[tex]\sigma_{portfolio}=\sqrt{(W_A \times \sigma_A)^2+(W_B \times \sigma_B)^2+(2 \times W_A \times W_B \times CC \times \sigma_A \times \sigma_B)}\\\sigma_{portfolio}=\sqrt{(0.9 \times 0.12)^2+(0.1 \times 0.06)^2+(2 \times 0.1 \times 0.9 \times -0.5 \times 0.12 \times0.06)}\\\sigma_{portfolio}=0.1051 =10.51\%[/tex]

So the return of portfolio is 14.5% and standard deviation is 10.51%.

Part d:

It is evident from the example that by changing the investment from firm A to firm B, the return is increased however the risk is also increased.

For the first investment scenario(A:10% B:90%), (part:a), The return is 10.5% with a risk of 5.089%

For the second investment scenario(A:90% B:10%), (part:b), The return is 14.5% with a risk of 11.12%

Here is clearly visible that higher rate of return also increases the risk. In this case for an increase of 4% in the return, there is a rise of 6.031%

The effect of negative correlation coefficient is however minimal as indicated in part c.

For the first investment scenario, the risk is reduced from 5.089% to 4.911%

For the second investment scenario, the risk is reduced from 11.12% to 10.51%

This is not a significant effect.