Question

The following table provides information about the portfolio performance of three investment managers: Manager Return Standard Deviation Beta A 25% 22% 2.1 B 21% 19% 1.5 C 15% 10% 0.8 Market (M) 15% 12% Risk Free Rate = 5% Complete the following table: Manager Expected Return Sharpe Ratio Treynor Ratio Jensen’s Alpha A B C Rank

Answer 1

1) expected return of Manager 1 = risk free rate + beta (market return - risk free rate)

= 5% + 2.1 (15% - 5%)

= 5% + 2.1 (10%)

= 5% + 21%

= 26%

expected return of manager 2= risk free rate + beta (market return - risk free rate)

= 5% + 1.5 (15% - 5%)

= 5% + 1.5 (10%)

= 5% + 15%

= 20%

expected return of manager 3= risk fre rate + beta (market return - risk free rate)

= 5% + 0.8 (15%-5%)

= 5% + 0.8 (10%)

= 5% + 8%

= 13%

2) Sharpe ratio of manager 1 = manager return - risk free rate / standard deviation

= 25% - 5% / 22%

= 20% / 22%

= 0.91

sharpe ratio of manager 2= manager return - risk free rate / standard deviation

= 21% - 5% / 19%

= 16% / 19%

= 0.84

sharpe ratio of manager 3= expected return - risk free rate / standard deviation

= 15% - 5% / 10%

= 10% / 10%

= 1

As per the sharpe ratio the rank of the managers are as follows

1) manager 3

2) manager 1

3) manager 2

3) Treynor ratio of manager 1= manager return - risk free rate / beta

= 25% - 5% / 2.1

= 20% / 2.1

= 9.52

Treynor ratio of manager 2 = 21% - 5% / 1.5

= 16% / 1.5

= 10.67

Treynor ratio manager 3 = 15% - 5% / 0./8

= 10%/0.8

= 12.5

As per treynor ratio rank of the managers are as follows:-

1) manager 3

2) manager 2

3) manager 1

4) Jensen alpha of manager 1 = actual return - expected return

= 25% - 26%

= -1%

Jensen alpha of manager 2= actual return - expected return

= 21% - 20%

= 1%

Jensen alpha of manager 3= actual return - expected return

= 15% - 13%

= 2%

As per jensen alpha rank of the managers are

1) manager 3

2) manager 2

3) manager 1