Question

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				%

Answer 1

Answer

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