Answer to Question #173971 in Management for ParagB

Question

Compare the following portfolios on performance using Sharpe, Treynor and Jensen’s measure and rank them.

Portfolio

Avg. returns

Std. deviation

Beta

X

15%

0.25

1.25

Y

12%

0.30

0.75

Z

10%

0.20

1.20

Market Index

12%

0.20

1.00

 

Risk free rate – 7%.       

Answer 1

X

Y

Z

Market index

Portfolio return

15%

12%

10%

12%

Standard deviation

0.25

0.30

0.20

0.20

beta

1.25

0.75

1.20

1.00

Risk-free rate 7%

i)       Treynor Measure= PR−RFR​/β

Where: PR=portfolio return

RFR=risk-free rate

β=beta

X = 0.15- 0.07/1.25 = 0.064

Y= 0.12-0.07/0.75= 0.067

Z=0.10-0.07/1.20= 0.025

Market= 0.12-0.07/1.00= 0.05

The higher the Treynor ratio the better, X and Y are better because they are above the market index.

ii)      Sharpe ratio=PR−RFR​/SD

Where: PR=portfolio return

RFR=risk-free rate

SD=standard deviation

               X=0.15-0.07/0.25=0.32

               Y= 0.12-0.07/0.30=0.17

               Z=0.10-0.07/0.20=0.15

               Market=0.12-0.07/0.20=0.25

X portfolio is better because it has a superior risk-adjusted return

iii)    Jenson’s alpha=PR−CAPM

Where: PR=portfolio return

CAPM=risk-free rate+β (return of market- risk-free rate of return)

 CAPM for X = 0.07+1.25(0.12-0.07) = 13.25%

       Jenson’s alpha (JA) = 15-13.25= 1.75%

CAPM for Y= 0.07+0.75(0.12-0.07) = 10.75%

                                       JA= 12-10.75= 1.25%

CAPM for Z = 0.07+1.20(0.12-0.07) = 13%

                                       JA= 10-13= -3%

X did well.