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**

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

Please use the following information on the portfolio and its
benchmark (S&P 500 index) to calculate
Portfolio
S&P 500
Average Annual Return
12%
10%
Standard Deviation
18%
15%
Beta
1.2
1
Risk-free rate =
2%
Sharpe ratio for the portfolio and S&P 500 index
Treynor ratio for the portfolio and S&P 500 index
Jensen’s alpha based on Capital Asset Pricing Model.

You are given the following information concerning three
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RP
σP
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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
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Paragraph

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