You are constructing a portfolio of two assets, Asset A and Asset B. The expecte

Question

You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 11 percent and 14 percent, respectively. The standard deviations of the assets are 35 percent and 43 percent, respectively. The correlation between the two assets is .53 and the risk-free rate is 3.8 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 1 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 11 percent and 14 percent, respectively. The standard deviations of the assets are 35 percent and 43 percent, respectively. The correlation between the two assets is .53 and the risk-free rate is 3.8 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 1 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

Step 1: Calculate Weights of the securities in Portfolio Wa = [(Ra-Rf)SDb^2 - (Rb-Rf) SDa *SDb *r(a,b)] /[ (Ra-Rf)SDb^2 + (Rb-Rf) SDa^2 ) - (Ra-Rf+Rb-Rf)SDa *SDb *r(a,b)] Where, Wa = Weight of Security A Ra = Return on Security A Rb = Return on security B Rf = Risk Free rate of Return SD = Standard Deviation r(a,b) = Correlation coefficient between a and b Wa =[(0.11-0.038)*0.43^2 - (0.14-0.038)*0.35*0.43*0.53] / [(0.11-0.038)*0.43^2 + (0.14-0.038)*0.35^2 - (0.11-0.038+0.14-0.038)*0.35*0.43*0.53        =0.434 Wb =1-0.434 = 0.566 Step 2: Expected Return on Portfolio = Ra*Wa+Rb*Wb                                                      =.11*.434+.14*.566                                                      =12.70% Step 3: Standard Deviation of portforlio(SDp) SDp = Wa^2*SDa^2 + Wb^2*SDb^2 + 2*SDa * SDb * Wa*Wb*r(a,b)         =0.434^2*0.35^2 + 0.566^2*0.43^2 + 2*0.35*0.43*0.434*0.566*0.53         =0.207 Shape Ratio = [Return of Portfolio - Risk Free Rate of Return] / Standard Deviation of Portfolio                       =[12.7%-3.8%]/20.7%                       =0.43 Smallest Expected Loss Prob(R0.127 - 2.326(.207))=1% Prob(R - 0.3549) = 1% -35.49%

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.