Question

# You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset:...

You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset:

 Portfolio RP σP βP X 16.0 % 32 % 1.90 Y 15.0 27 1.25 Z 7.3 17 0.75 Market 11.3 22 1.00 Risk-free 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.)

 Portfolio Sharpe Ratio Treynor Ratio Jensen's Alpha X % Y % Z % Market %

Calculation of Sharp Ratio, Treynor Ratio and Jensen's Alpha

 Portf olio Return on Portfolio(%) (A) Risk free Return(%) (B) σP(%) (C) βP (D) CAPM Return (E) Sharp Ratio= (A-B)/C Treynor Ratio= (A-B)/D Jensen's Alpha= (A-E) 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(11.30-5.80) =16.25

Y=5.80+1.25(11.30-5.80)= 12.675

Z=5.80+0.75(11.30-5.80)= 9.925