You are given the following information concerning three portfolios, the market

Question

You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio 32% 27 17 1.90 1.25 0.75 1.00 16.0% 15.0 Market Risk-free5.8 11.3 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 "O" 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 Market

Explanation / Answer

Portfolio Sharpe Ratio Treynor's Ratio Jensen's Alfa X           0.32           0.05 -0.25% Y           0.34           0.07 2.33% Z           0.09           0.02 -2.63% Market 0.00% Working: Sharpe Ratio = Rp-Risk Free return/Standard deviation of Portfolio Sharpe Ratio: X = (16.0%-5.8%)/32% =           0.32 Y = (15.0%-5.8%)/27% =           0.34 Z = (7.3%-5.8%)/17% =           0.09 Treynor's Ratio = Rp-Risk Free return/Beta of Portfolio Sharpe Ratio: X = (16.0%-5.8%)/1.90 =           0.05 Y = (15.0%-5.8%)/1.25 =           0.07 Z = (7.3%-5.8%)/0.75 =           0.02 Jensen's Alfa = Rp-expected Return as per CAPM CAPM = Capital Asset Pricing Model Expected Return as per CAPM = Rf+Beta*(Rm-Rf) Where, Rf = Risk Free Return Expected Return as per CAPM: Rm = market Return X = 5.80% +           1.90 x ( 11.30% - 5.80% ) = 16.25% Y = 5.80% +           1.25 x ( 11.30% - 5.80% ) = 12.68% Z = 5.80% +           0.75 x ( 11.30% - 5.80% ) = 9.93% Market = 5.80% +           1.00 x ( 11.30% - 5.80% ) = 11.30% Jensen's Alfa: X 16.00% - 16.25% = -0.25% Y 15.00% - 12.68% = 2.33% Z 7.30% - 9.93% = -2.63% Market 11.30% - 11.30% = 0.00%

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