In: Finance
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.
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
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 |
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Sum |
1212.95 |
686.38 |
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Sum/number of years |
242.59 |
137.28 |
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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 –