Question

Please answer fast

7. The average return for Firm A is calculated as 0.05 (5%) with a standard deviation of 0.03 (3%). The average return for Firm B is calculated as 0.15 (15%) with a standard deviation of 0.06 (6%). The covariance between returns in Firms A and B is equal to -0.0005. The return on the risk-free asset is 1%.

Find the missing values in the table below and plot the portfolio frontier on a graph with portfolio expected returns on the vertical axis and portfolio standard deviation on the horizontal axis. Draw the “Sharpe line” on your graph (make sure your line intersects the vertical axis in the right spot) and identify the point on the portfolio frontier that maximizes the Sharpe ratio.

Share in firm A	Share in firm B	Portfolio expected returns	Portfolio standard deviation	Sharpe ratio
100%	0%	5%	3%
80%	20%
50%	50%
20%	80%
0%	100%	15%	6%

Since you can't directly fill in the table above as you might be able to on a paper exam, consider formatting your final answers for each portfolio as follows:

Portfolio: (100%, 0%)

Expected return: 5%

Portfolio standard deviation: 3%

Sharpe ratio: ____

Portfolio: (80%, 20%)

Expected Return: ____

Portfolio Standard Deviation: ____

Sharpe ratio: ____

And so on...

To increase your chance of getting partial credit, please show your work for all calculations.

Answer 1

1.)
Portfolio: (100%, 0%)
Expected return: 5%
Portfolio standard deviation: 3%
Sharpe ratio = ( 0.05-0.01)/0.03 = 1.333

2.) Portfolio: (80%, 20%)
Expected return= 0.8*0.05 + 0.2*0.15 = 0.07=7%
Portfolio standard deviation= [(0.8*0.03)^2 + (0.2*0.06)^2 + 2*0.8*0.2*(-0.0005)]^(0.5) = 0.0236 = 2.36%
Sharpe ratio = ( 0.07-0.01)/0.0236 = 2.5423

3.) Portfolio: (50%, 50%)
Expected return= 0.5*0.05 + 0.5*0.15 = 0.1=10%
Portfolio standard deviation= [(0.5*0.03)^2 + (0.5*0.06)^2 + 2*0.5*0.5*(-0.0005)]^(0.5) = 0.0295= 2.95%
Sharpe ratio = ( 0.1-0.01)/0.0295= 3.0508

4.) Portfolio: (20%, 80%)
Expected return= 0.2*0.05 + 0.8*0.15 = 0.13=13%
Portfolio standard deviation= [(0.2*0.03)^2 + (0.8*0.06)^2 + 2*0.2*0.8*(-0.0005)]^(0.5) = 0.0466 = 4.66%
Sharpe ratio = ( 0.13-0.01)/0.0466 = 2.5751

5.) Portfolio: (0%, 100%)
Expected return= 0*0.05 + 1*0.15 = 0.15=15%
Portfolio standard deviation= [(0*0.03)^2 + (1*0.06)^2 + 2*0*1*(-0.0005)]^(0.5) = 0.06 = 6.00%
Sharpe ratio = ( 0.15-0.01)/0.06 = 2.3333