1. You are constructing a portfolio of two assets, Asset A and Asset B. The expe
ID: 2749731 • Letter: 1
Question
1. You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 13 percent and 16 percent, respectively. The standard deviations of the assets are 39 percent and 47 percent, respectively. The correlation between the two assets is 0.61 and the risk-free rate is 5.3 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 1 percent? (Negative amounts should be indicated by a minus sign. Round your Sharpe ratio answer to 4 decimal place & Probabilityanswer to 2 decimal places. Omit the "%" sign in your response.)
1. You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 13 percent and 16 percent, respectively. The standard deviations of the assets are 39 percent and 47 percent, respectively. The correlation between the two assets is 0.61 and the risk-free rate is 5.3 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 1 percent? (Negative amounts should be indicated by a minus sign. Round your Sharpe ratio answer to 4 decimal place & Probabilityanswer to 2 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
SHARPE RATIO
HERE WEIGHTAGE OF THE ASSETS IN THE PORTFOLIO IS NOT GIVEN SO WE CAN ASSUME THE WEIGHT FOR EACH ASSTER IS 50%.
PORTFOLIO ASSETS WEIGHT RETURN WEIGHTED RETURN
ASSET A 0.50 13% 6.5%
ASSET B 0.50 16% 8.0%
AVERAGE RETURN 14.5%
STANDARD DEVIATION OF THE PORTFOLIO
SQUARE ROOT OF[(W A *SD A)2+(W B *SD B)2 +2(W A *SD A)(W B *SD B)COR A B]
SQUARE ROOT OF[(0.5 * 0.39)2+(0.5 * 0.47)2+2(0.5 * 0.39)(0.5 * 0.47)0.61]
SQUARE ROOT OF[0.038025 + 0.055225 + 0.0559065]
0.3862
38.62%
WA= WEIGHT OF A
SD A= STANDARD DEVIATION OF A
W= WEIGHT OF B
SD B= STANDARD DEVIATION OF B
COR AB= CORELATION OF A & B
SHARPE RATIO=( RETURN OF PORTFOLIO - RISK FREE RETURN) / STANDARD DEVIATION OF PORTFOLIO
=(14.5 - 5.3) / 38.62
=0.2382
I DON'T KNOW CALCULATION OFSMALEST EXPECTED LOSS.
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