Question

In a recent 5-year period, 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.
1 2 3 4 5

Fund −1.2 23.8 41.7 10.7 0.3
Market index −0.8 14.0 31.2 9.7 −0.6

Required:
1. Calculate (a) the average return on both the Fund and the index, and (b) the standard deviation of the returns on each.
2. Did Ms. Sauros do better or worse than the market index on these measures?

Answer 1

Answer:

Average return :

Funds = 15.06

Index = 10.70

Standard deviation :

Funds = 16.0457

Index = 11.765

2.) Funds is doing better

Explanation:

Given :

Fund −1.2 23.8 41.7 10.7 0.3

Market index −0.8 14.0 31.2 9.7 −0.6

A.)

Average return : total sum over 5 years / number of years

Average return on funds (a) :

(-1.2 + 23.8 + 41.7 + 10.7 + 0.3) / 5 = 15.06

Average return on market index (b) :

(−0.8 + 14.0 + 31.2 + 9.7 + −0.6) /5 = 10.70

B.)

Standard deviation =sqrt[Σ(x - mean)²/n]

Funds :

[(-1.2 - 15.06)^2 + (23.8 - 15.06)^2 + (41.7 - 15.06)^2 + (10.7 - 15.06)^2 + (0.3 - 15.06)^2] / 5

= √1287.332 / 5

= √257.4664

= 16.0457

Market index :

Sqrt([(-0.8 - 10.70)^2 + (14.0 - 10.70)^2 + (31.2 - 10.70)^2 + (9.7 - 10.70)^2 + (-0.6 - 10.70)^2] / 5)

= sqrt(692.08 / 5)

= sqrt(138.416)

= 11.765

2.) obtain the Coefficient of variation :

Standard deviation / mean

Funds = 16.0457 / 15.06 = 1.065

Market index = 11.765 / 10.70 = 1.0995

Funds is doing better due to its lesser Coefficient of variation than market index.