Question

A fund has 10,000 at the start of the year. Six months later, the fund has a value of 15,000 at which time, Stuart removes 5,000 from the fund. At the end of the year, the fund has a value of 11,000. Calculate the exact dollar weighted rate of return less the time weighted rate of return

NO EXCEL

EXCEL= THUMBS DOWN

FORMULAS/ SHOW WORK = THUMBS UP

Answer 1

step - 1 :

Calculation of dollar weighted rate of return:

cash flow stream

at t = 0 cash flow = -10,000

at t = 0.5 cash flow = 5000

at t = 1 cash flow = 11,000

let x be dollar weighted rate of return

equation will be

-10,000 = 5000 / (1 + x)^0.5 + 11,000 / (1 + x)

solving for x by trail and error method (or can use financial calculator )

x = 76.41%

so dollar weighted rate of return = 76.41%

Step - 2:

calculating time weighted rate of return

at t = 0 value = 10,000

at t = 0.5 value = 15,000

return = (15,000 - 10,000) / 10,000 = 50%

after withdrawing 5000 balance = 15,000 -5000 = 10,00

at t = 0.5 value = 10,000

at t = 1 value = 11,000

gain = (11000 - 10000) / 10,000 = 10%

time weighted return = [(1+50%)*(1+10%)] - 1

= 65%

Dollar weighted return - time weighted retun = 76.41% - 65%

= 11.41%