The one-month riskfree rate is 0.4%. Risky asset A has a mean return of 1.50% a
ID: 2613259 • Letter: T
Question
The one-month riskfree rate is 0.4%. Risky asset A has a mean return of 1.50% a month and a standard deviation of 10%. Risky asset B has a mean return of 0.8% a month and a standard deviation of 5%. The correlation between the returns of A and B is 0.4. Use excel and form 11 portfolios of stocks A and B as follows: Portfolio 1 has weight of 1 on A and 0 on B. Portfolio 2 has weight of 0.9 on A and 0.1 on B. Etc. Portfolio 11 has weight of 0 on A and 1 on B. For each portfolio compute the expected return and standard deviation of its returns. What is the portfolio with the highest Sharpe ratio? Plot the returns and the standard deviations of each portfolio on a graph with expected returns on the y-axis and standard deviations on the x-axis.
Explanation / Answer
First we need to prepare a Table of the 11 Portfolios in the following manner to calculate the expected Return from the portfoio's based on the Wieghtage of Stock A & B
Portfolio Number
Weight of A
Weight of B
Expected Return from A
Expected Return from B
Total Expected Return
1
2
3
4
5
6
1
1
0
1.50
0.00
1.50
2
0.9
0.1
1.35
0.08
1.43
3
0.8
0.2
1.20
0.16
1.36
4
0.7
0.3
1.05
0.24
1.29
5
0.6
0.4
0.90
0.32
1.22
6
0.5
0.5
0.75
0.40
1.15
7
0.4
0.6
0.60
0.48
1.08
8
0.3
0.7
0.45
0.56
1.01
9
0.2
0.8
0.30
0.64
0.94
10
0.1
0.9
0.15
0.72
0.87
11
0
1
0.00
0.80
0.80
Column 4 is expected return from A x Weight of A
Column 5 is expected return from B x Weight of B
Column 6 is total expected return of the Portfolio.
In order to calculate the Standard Deviation of each portfolio we use the formula for calculating Standard Deviation in Excel which is =STDEV(number)
Below is the Table of Standard Deviation using above formula
In order to caluclate the Sharpe Ratio we calculate the Excess Return over and above the Risk Free Rate of Return of 0.4% and then use the formula for Sharpe Ratio = Average of Excess Return over Risk Free Return divided by the Standard Deviation of the Portfolio
Below is the Table prepared on the basis of above formula
The Highest Sharpe Ratio is of Portfoio No. 7 which is 8.01 and which has 40% Wieght of A & 60% Wieght of B
Portfolio Number
Weight of A
Weight of B
Expected Return from A
Expected Return from B
Total Expected Return
1
2
3
4
5
6
1
1
0
1.50
0.00
1.50
2
0.9
0.1
1.35
0.08
1.43
3
0.8
0.2
1.20
0.16
1.36
4
0.7
0.3
1.05
0.24
1.29
5
0.6
0.4
0.90
0.32
1.22
6
0.5
0.5
0.75
0.40
1.15
7
0.4
0.6
0.60
0.48
1.08
8
0.3
0.7
0.45
0.56
1.01
9
0.2
0.8
0.30
0.64
0.94
10
0.1
0.9
0.15
0.72
0.87
11
0
1
0.00
0.80
0.80
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