Question

A pension fundbegins with $500,000 earns 15%the first six monthsand 10% the second six months. At the beginning of the second six months, the clients contributeanother $300,000.

A) The annual dollar-weighted rate of return was

B) The annual time-weighted rate of return was

(the anwser is supposed to be .265. unsure how to get there)

Answer 1

A)

value at the beginning(t = 0) = 500,000

earnings in first 6 months = 15%

value after 6 months = 500,000 *(1 + 15%) = 575,000

contribution(t = 0.5) = 300,000

so total value at the beginning of second 6 - months = 575,000 + 300,000 = 875,000

return = 10%

value at end (t = 1) = 875,000 *(1.10) = 962,500

dollar weighted return:

above return is 6 months return to find annual return :

annual return = (1 +11.95%)^2 1 = 0.2533 or 25.33%

B)

annual time weighted return = [(1+ earning rate in first 6 months) *(1 + earning rate in second 6 months)] - 1

= [(1+15%) * (1 + 10%) ] - 1

= 0.265 or 26.5%