Question

1. The risk free rate is currently 3%, market return is 9% Rate of return Standard deviation of return Beta Portfolio A 14.8% 13% 1.4 Portfolio B 13.6% 12.50% 1.3 a. Calculate the Sharpe's ratio for the two portfolios (4 marks) b. Calculate the Treynor's ratio for the two portfolios (4 marks) c. Calculate the Jensen's measure for the two portfolios (4 marks) d. On the basis of your previous findings, which portfolio has better performance? (2 marks)

Answer 1

1. Sharp ratio of portfolio

Portfolio A: .9077

Portfolio B: .848

Sharp ratio =

Rate of return-risk free rate Standard Deviation of the return

Sharp ratio of portfolio A

Sharp ratio =

Rate of return-risk free rate Standard Deviation of the return

Rate of return =14.80%

Risk free rate = 3%

Standard deviation of the return =13%

Sharp ratio =

                        =.9077

                       

Sharp ratio of portfolio B

Sharp ratio =

Rate of return-risk free rate Standard Deviation of the return

Rate of return =13.60%

Risk free rate = 3%

Standard deviation of the return =12.50%

Sharp ratio =

                        =.848

2. Treynor’s Ratio of Portfolio

Portfolio A: 8.4286

Portfolio B: 8.1538

Treynor’s Ratio =

Rate of return-risk free rate Beta

Treynor’s Ratio for portfolio A

Rate of return =14.80%

Risk free rate = 3%

Beta =1.4

Treynor’s Ratio = (14.80 - 3) ÷ 1.4

                        = 8.4286

Treynor’s Ratio for portfolio B

Rate of return =13.60%

Risk free rate = 3%

Beta =1.3

Treynor’s Ratio = (13.60 - 3) ÷ 1.3

                        = 8.1538

3. Jenson Measure for the portfolio

Portfolio A: 3.4

Portfolio B: 2.8

Jenson Measure = Rate of return – ((Risk free rate + Beta (Market return – Risk free rate)

Jenson Measure for Portfolio A

Rate of return =14.80%

Risk free rate = 3%

Beta =1.4

Market Return = 9%

Jenson Measure = 14.8% - (3% + 1.4(9% - 3%)

                             =14.8-11.4

                             = 3.4

Jenson Measure for Portfolio B

Rate of return =13.60%

Risk free rate = 3%

Beta =1.3

Market Return = 9%

Jenson Measure = 13.6% - (3% + 1.3(9% -3%)

                        =13.6-10.8

                        =2.8

4. Selection of the portfolio

Portfolio	Sharp ratio		Treynor’s Ratio		Jenson Measure
	Ratio	Rank	Ratio	Rank	Ratio	Rank
A	.9077	1	8.4286	1	3.4	1
B	.8480	2	8.1538	2	2.8	2

Since all measure rank portfolio A as rank 1, select portfolio A

Note: Sharp ratio, Treynor’s Ratio and Jenson Measure are higher the better.