ou are constructing a portfolio of two assets, Asset A and Asset B. The expected
ID: 2735170 • Letter: O
Question
ou are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 10 percent and 14 percent, respectively. The standard deviations of the assets are 34 percent and 42 percent, respectively. The correlation between the two assets is .51 and the risk-free rate is 4.8 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your Sharpe ratio answer to 4 decimal places and Probability answer to 2 decimal places. Omit the "%" sign in your response.)
ou are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 10 percent and 14 percent, respectively. The standard deviations of the assets are 34 percent and 42 percent, respectively. The correlation between the two assets is .51 and the risk-free rate is 4.8 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 5 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your Sharpe ratio answer to 4 decimal places and Probability answer to 2 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
Return
SD
Weight age
Calculation
Stock A
10%
34%
0.4474
Stock B
14%
42%
0.5526
1
Correlation
0.51
Risk free rate
4.80%
Expected return
10%*0.4474 + 14%*0.5526
12.25%
Expected Standard Deviation
0.3343
SQRT((0.34*0.44)^2+(0.42*0.55)^2+2*0.34*0.42*0.447*0.5526*0.51))
Optimal Sharpe ratio = (12.25%-4.80%)/0.3343
0.22285
Probability of 2.5% corresponds to z-value od 1 sigma (SD)
Smallest expected loss
-0.33652
(12.25%-1)*0.3343
Return
SD
Weight age
Calculation
Stock A
10%
34%
0.4474
Stock B
14%
42%
0.5526
1
Correlation
0.51
Risk free rate
4.80%
Expected return
10%*0.4474 + 14%*0.5526
12.25%
Expected Standard Deviation
0.3343
SQRT((0.34*0.44)^2+(0.42*0.55)^2+2*0.34*0.42*0.447*0.5526*0.51))
Optimal Sharpe ratio = (12.25%-4.80%)/0.3343
0.22285
Probability of 2.5% corresponds to z-value od 1 sigma (SD)
Smallest expected loss
-0.33652
(12.25%-1)*0.3343
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