Question

In a recent 5-year period, mutual fund manager Goldie Touch produced the following percentage rates of return for the Mesozoic Fund. Rates of return on the market index are given for comparison. Calculate:

1. the average return on both the fund and the index
2. the standard deviation of the returns on each.
3. Did Ms. Goldie Touch do better or worse than the market index on these measures?   

   	1	2	3	4	5
   Fund	-1.2	+24.8	+40.7	+11.1	+0.3
   Market Index	-0.9	+16.0	+31.7	+10.9	-0.7

Answer 1

Goldie Touch Fund

Average return = sum of all return / no. of return

= -1.2% + 24.8% + 40.7% + 11.1% + 0.3 / 5

= 75.7% / 5

= 15.14%

Standard deviation= √ sum of all (return - average return) ^2 / n - 1

= √ (-0.012 - 0.1514)^2 + (0.248 - 0.1514)^2 + (0.407 - 0.1514)^2 + (0.111 - 0.1514)^2 + (0.003 - 0.1514)^2 / 5 - 1

= √ (0.1634)^2 + (0.0966)^2 + (0.2556)^2 + (-0.0404)^2 + (-0.1484)^2 / 4

= √ 0.027 + 0.00933 + 0.0653 + 0.001632 + 0.0220 / 4

= √ 0.125262 / 4

= √ 0.0313155

= 0.1769 or 17.69%

Market Index

Average return= sum of all return / no. of return

= -0.9% + 16% + 31.7% + 10.9% - 0.7% / 5

= 57 % / 5

= 11.4%

Standard deviation= √sum of all (return - average return)^ 2 / n - 1

= √ (-0.009 - 0.114)^2 + (0.16 -0.114)^2 + (0.317 - 0.114)^2 + (0.109 - 0.114)^2 + (-0.007 - 0.114)^2 / 5 - 1

= √ (-0.123)^2 + (0.046)^2 + (0.203)^2 + (-0.005)^2 + (0.121)^2 / 4

= √ 0.015129 + 0.002116 + 0.041209 + 0.000025 + 0.014641 / 4

= √ 0.07312 / 4

= √ 0.01828

= 0.1352 or 13.52%

On the basis of these measures, Goldie touch performed better than market index, as the average return is more than market index average return , and also coefficient of variation of Goldie touch fund is less than that of market index.