Problem 13-18 You are constructing a portfolio of two assets, Asset A and Asset
ID: 2751841 • Letter: P
Question
Problem 13-18
You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 12 percent and 16 percent, respectively. The standard deviations of the assets are 29 percent and 37 percent, respectively. The correlation between the two assets is .41 and the risk-free rate is 3.4 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 2.5 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.)
You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 12 percent and 16 percent, respectively. The standard deviations of the assets are 29 percent and 37 percent, respectively. The correlation between the two assets is .41 and the risk-free rate is 3.4 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 2.5 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
Asset A: Asset B:
Expected Return = 12% Expected Return = 16%
Standard deviation = 29% Standard deviation = 37%
Risk-free rate = 0.41% Risk-free rate = 3.4%
Asset A:
Sharpe ratio = (Expected Return (P) Risk-free rate)/Standard deviation (P)
= (15% - 0.41%) / 29%
= 0.5031
Asset B:
Sharpe ratio = (Expected Return (P) Risk-free rate)/Standard deviation (P)
= (16% - 3.4%) / 37%
= 0.3405
What is the smallest expected loss for this portfolio over the coming year with a probability of 2.5 percent
Expected return of a portfolio:
E(RP,T) = E(RP) × T
Standard deviation of a portfolio:
P,T= P× T
Value at risk:
Prob[RP,T E(Rp) × T – 1.96PT] = 2.5%
Asset A:
Prob[RP,T E(Rp) × T – 1.96PT] = 2.5%
Prob[RP,T 12% × 1 – 1.96(0.29)1] = 2.5%
Prob[RP,T -44.84 % ] = 2.5%
Asset B:
Prob[RP,T E(Rp) × T – 1.96PT] = 2.5%
Prob[RP,T 16% × 1 – 1.96(0.37)1] = 2.5%
Prob[RP,T -56.52 % ] = 2.5%