Question

If an investor purchases shares in a no-load mutual fund for $36.00, received cash distributions of $1.00 and redeems the shares after one year for $42.00 what is the percentage return on the investment?

Mutual fund A earned 10% while B earned 8%. The standard deviations of the returns were 10% and 7%, respectively. According to the Sharpe Ratio, which fund performed better?

Answer 1

1). Purchase price P0 = $36

year end cash received D = $1

price after 1 year P1 = $42

So, percentage return on the investment = (P1 - P0 + D)/P0 = (42 - 36 + 1)=36 = 19.44%

2). Sharpe Ratio = (E(rp) - Rf)/SD(p)

So, for mutual fund A, sharpe ratio = (10 - Rf)/10

Similarly, sharpe ratio of mutual fund B = (8 - Rf)/7

So, this comparision can not be performed without risk free rate. If risk free rate is available, substitute in the formula and compute sharpe ratio and compare it.