Question

A no–load mutual fund had NAV per share of $24.00 on January 1. On December 31 of the same year the fund's NAV was $26.49. Income distributions were $1.15 and the fund had capital gain distributions of $1.95. Without considering taxes and transactions costs, what rate of return did an investor receive on the fund last year?  

What is the geometric average return of a stock that returned 39%, -30%, 48%, -15% and 36% over the last 5 years?

Answer 1

1.Rate of return=(Closing NAV-Opening NAV) +income distribution+Capital distribution/Opening NAV
=(26.49-24) + 1.15 +1.95 / 24

=23.29%

2.
Geometric avergae return = [(1+r1)* (1+r2)*....(1+r5) ]^1/n ] - 1

= [(1+.39) * (1+ (-.30)) * (1+.48)* (1+ (-.15)) * (1+.36) ]^ 1/5] -1

=[1.39 * .70 * 1.48*.85 *1.36 ]^1/5 - 1

= [1.66468 ^ 1/5 ] - 1

= 1.1073021 -1

= .1073 or 10.73%