Question

(1 pt) Your grandmother gives you 2200 dollars for your birthday, which you invest in a mutual fund on January 1. On June 1, your fund balance is 7000 dollars, and you then deposit 1500 dollars (which you received for your high school graduation). On the following January 1, you calculate that your dollar-weighted rate of return for the year was 41 percent. What was your time-weighted rate of return for the year? Answer = percent.

Can use excel as long as answer is correct.

Answer 1

Compound fund balance of $2200 as on Jan 1 at 41% for 5 months = $2200 * (1+41%)^(5/12) = $2,538.617743

Fund balance as on 31 December = ($2,538.617743 + $1500) * 1.41^(7/12)
= $4,934.887213

Rate of return for Jan 1 to June 1 = ($7000 - $2200) / $2200 = 218.1818%

Rate of return for June 1 to December 31 = ($4,934.887213 - ($7000 + $1500)) / ($7000 + $1500) = -41.9425%

Time weighted return = [(1+rate of return upto June 1)*(1+rate of return from June 1 to Dec 31)]-1

= (1 + 2.1818) * (1 - 0.419425) - 1

= 1.8473 - 1

= 84.73%