Wally invests 5800 dollars in a mutual fund on January 1 On

Wally invests 5800 dollars in a mutual fund on January 1. On June 1, his fund balance is 4000 dollars. Wally doesn\'t notice the decline, and invests an additional 1400 dollars. On September 1, his fund balance is 7900 dollars. He then withdraws 1500 dollars. On the following January 1, his fund balance is 7500 dollars. What is Wally\'s time-weighted rate of return? Answer =

Solution

The first period return, from January 1 to June 1, would be calculated as follows:

Return = ($4,000 - $5,800) / $5,800 = -31.034%

The second period return, from June 1 to September 1, would be calculated as:

Return = ($7,900 - ($4,000 + $1,400)) / ($4,000 + $1,400) = 46.30%

The third period return, from September 1 to January 1, would be calculated as:

Return = ($7,500 - ($7,900 - $1,500)) / ($7,900 - $1,500) = 17.19%

The time-weighted over the two time periods is calculated by geometrically linking these two returns as follows:

Time-weighted return = (1 + (-31.034%) x (1 + 46.30%) x (1 + 17.19%) - 1 = 18.24%