# Annual Time Weighted Return Question (it seems simple, but I can't answer it)

Quarter Value at beginning of quarter Cash Inflow/outflow Value at end of quarter 1 2 .2 2.4 2 2.4 .4 2.6 3 2.6 (.2) 3.2 4 3.2 1 4.1 The annual Time Weighted return is closest to: A. 8% B. 27% C. 32% D. 60% **note, I understand that Time weighted return would take the geometric return of each quarter’s HPR, and multiply each quarter’s geometric return to give you the annual time weighted. This question seems simple, but I can’t seem to get to the right answer. thanks

yancey, haven’t done the actual calcs, but just a though. Did you remember in the end to multiply the rate of return by 4, since those are quarterly cash flows and you need an annual number?

that didn’t come out too well value at beginning of quarter cash inflow/outflow end of quarter value 2 .2 2.4 2.4 .4 2.6 2.6 (.2) 3.2 3.2 1 4.1

again it cam out horribly. I know the answer is: 31.85% according to the answer, the geometric returns are: 1.0909 x .9286 x .1.3333 x 9762 = 1.3185 1.3185 -1 = .3185 however, I find that the HPR for the first quarter is: (2.4 - 2)/2 = .2 and the second quarter is (2.6 - 2.4) / 2.4 = 8.3333 my first and second quarters are different from their returns. Yes, I’m confused.

1 2 .2 2.4 2 2.4 .4 2.6 3 2.6 (.2) 3.2 4 3.2 1 4.1 You have to take into account the inflow/outflow at the beginning of the period. The most accurate way would be to have daily values, but that takes too long without a computer. So for Q1, the return is (2.4/2.2)-1, Q2 (2.6/2.8)-1, etc. I remember that description of calculating returns in the CFAI books was kinda worded akwardly.

To malnoll, Many thanks. I have been studying for about a year now. I just took a practice exam from CFAI, and got 58%, which tells me I’m close…just need to be sharper, and put it all together. With your imput I see how to answer this question now: basically end price / beginning price + or - cash inflows, minus 1

1st Period return +1 = (2.4-0.2)/2=1.1 2nd period return +1 = (2.6-0.4)/2.4= 0.92 3rd period return +1 = (3.2+0.2)/2.6= 1.31 4th period return +1 = (4.1-1)/3.2= 0.97 (1.1 x 0.92 x 1.31 x 0.97)^0.25 = 1.064 Annual time weighted return = (1.064 - 1) x 4 = 26% I choose B

the answer is C. for the first quarter the formula is: (2.4 / 2.2) - 1, the same for all the other quarters. Then, multiply them by each other to arrive at 31.8%

I think I interpreted the cash inflow and outflow which happened at the end of each period, while actually the answer is at the beginning. One more question, why is the geometric mean simply the multiplication of each quarter return? (in stead of (1+r)).