Answer to Question #194829 in Management for Vishakha Dhoka

Question

1.        Compare the following portfolios on performance using Sharpe, Treynor and Jensen’s measure and recommend a suitable portfolio for investment.                                              (10 Marks)

 

 

 

Portfolio

Avg. returns

Std. deviation

Beta

A

15%

0.35

1.20

B

12%

0.15

0.85

C

10%

0.25

1.25

Market Index

12%

0.25

1.00

 

Risk free rate – 6%.

Answer 1

A

B

C

Market index

Portfolio return

15%

12%

10%

12%

Standard deviation

0.35

0.15

0.25

0.25

Beta

1.20

0.85

1.25

1.00

Risk-free rate 6%

i)       Sharpe ratio=PR−RFR​/SD

Where: PR=portfolio return

RFR=risk-free rate

SD=standard deviation

               A= (0.15-0.06)/0.35= 0.25

               B= (0.12-0.06)/0.15=0.4

               C= (0.10-0.06)/0.25=0.16

               Market= (0.12-0.06)/0.25=0.24

A portfolio is better because it has a superior risk adjust return

ii)      Treynor Measure= PR−RFR​/β

Where: PR=portfolio return

RFR=risk-free rate

β=beta

A = (0.15- 0.06)/1.20 = 0.075

B= (0.12-0.06)/0.85= 0.071

C= (0.10-0.06)/1.25= 0.032

Market= (0.12-0.06)/1.00= 0.06

The higher the Treynor ratio the better, A and B are better because they are above the market index.

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 A= 0.06+1.20(0.12-0.06) = 13.2%

       Jenson’s alpha (JA) = 15-13.2= 1.8%

CAPM for B= 0.06+0.85(0.12-0.06) = 11.1%

                                       JA= 12-11.1= 0.9%

CAPM for C= 0.06+1.25(0.12-0.06) = 13.5%

                                       JA= 10-13= -3.5%

A did well.