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In 2011-2015, mutual fund manager, Diana Sauros produced the following percentage rates of return for the...

In 2011-2015, mutual fund manager, Diana Sauros produced the following percentage rates of return for the Mesozoic Fund. Rates of return on the market index are given for comparison.

2011 2012 2013 2014 2015
Fund −1.3 +24.2 +40.2 +11.2 +0.4
Market index −0.7 +14.0 +31.2 +10.5 −0.5

Calculate (a) the average return on both the Fund and the index, and (b) the standard deviation of the returns on each.

Solutions

Expert Solution

a. The average return on both the Fund and the index

The average return on the Fund = Sum of all returns / number of years

= (-1.3 + 24.2 + 40.2 + 11.2 + 0.4)/5

= 74.7 /5 = 14.94

The average return on the index = Sum of all returns / number of years

= (-0.7 + 14 + 31.2 + 10.5 -0.5)/5

= 54.5 /5 = 10.90

  1. The standard deviation of the returns on each

The standard deviation of the returns = SQRT [Sum of (return – average return) ^2/number of years]

Year

Fund

(Return - Avg. Return)

(Return - Avg. Return)^2

Market index

(Return - Avg. Return)

(Return - Avg. Return)^2

2011

-1.3

-16.24

263.74

-0.7

-11.60

134.56

2012

24.2

9.26

85.75

14

3.10

9.61

2013

40.2

25.26

638.07

31.2

20.30

412.09

2014

11.2

-3.74

13.99

10.5

-0.40

0.16

2015

0.4

-14.54

211.41

-0.5

-11.40

129.96

Average Return

14.94

10.90

Sum

1212.95

686.38

Sum/number of years

242.59

137.28

Standard Deviation

15.58

11.72

The standard deviation of the returns on fund = 15.58

The standard deviation of the returns on index = 11.72

Formulas used in excel calculation –


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