You are given the following information concerning three portfolios, the market portfolio, and the riskfree asset:
Portfolio  R_{P}  σ_{P}  β_{P}  
X  16.0  %  32  %  1.90 
Y  15.0  27  1.25  
Z  7.3  17  0.75  
Market  11.3  22  1.00  
Riskfree  5.8  0  0  
What are the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio? (A negative value should be indicated by a minus sign. Leave no cells blank  be certain to enter "0" wherever required. Do not round intermediate calculations. Round your ratio answers to 5 decimal places. Enter your alpha answers as a percent rounded to 2 decimal places.)

Answer
Calculation of Sharp Ratio, Treynor Ratio and Jensen's Alpha
Portf olio 
Return on Portfolio(%) (A) 
Risk free Return(%) (B) 
σ_{P(%)} _{(C)} 
β_{P} _{(D)} 
CAPM (E) 
Sharp Ratio= (AB)/C 
Treynor Ratio= (AB)/D 
Jensen's Alpha= (AE) 
X  16  5.8  32  1.90  16.25  0.31875  5.3684  0.25 
Y  15  5.8  27  1.25  12.675  0.3407  7.36  2.325 
Z  7.3  5.8  17  0.75  9.925  0.0882  2.00  2.625 
Sharp Ratio= Return on portfolio Risk free rate/ Standard deviation of portfolio
Treynor ratio= Return on portfolio Risk free rate/ Beta of portfolio
Jensen's alpha= Return on portfolio CAPM return
CAPM return= Risk free rate+Beta (Retuen on market portfolio Risk free rate)
X= 5.80+1.90(11.305.80) =16.25
Y=5.80+1.25(11.305.80)= 12.675
Z=5.80+0.75(11.305.80)= 9.925
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