# time-weighted return

I just finished a practice test and am thoroughly confused on computing time-weighted returns. In the CFA textbook, you calculate the holding period returns: Ending Value- Beginning Value/ Beginning Value. Then you annualize it by calculating geometric mean. However, in a practice test from the CFA Institute, they calculated holding period return as follows: Ending Value/Beginning Value+cash flows Any suggestions? Which way do you use? Not sure if I can post the exact question.

typically HPR = (EV - BV + CF) / BV

cpk123, that’s what I thought. But, here is the type of question I am looking at: An analyst gathered the following information (\$ millions) about the performance of a portfolio: Quarter Value at Beginning of Quarter Cash Inflow (Outflow) at beginning of Quarter Value at end Of Quarter 1 2.0 0.2 2.4 2 2.4 0.4 2.6 3 2.6 (0.2) 3.2 4 3.2 1.0 4.1 The portfolio’s annual time-weighted rate of return is closest to: A. 8% B. 27% C. 32% D. 60& On other question I have: when do you NOT raise the calculation on geometric mean to 1/N? Do you not raise it to 1/N when calculating ANNUAL returns?

2nd question first yes you do not raise it to 1/N if it is quarterly data e.g. so product of quarterly data information would give you the annual TWR. The above problem has been solved before. The CF is at the beginning of the quarter. So you need to add to the beginning amt to get the actual amt… and then calculate HPR as below: So Q1 2.4 / 2.2 = 1.0909 Q2 2.6 / 2.8 = .9286 Q3 3.2/2.4 = 1.3333 Q4 4.1 / 4.2 = .9761 So TWR = 1.3183 So 32% Choice C

bigfin Wrote: ------------------------------------------------------- > On other question I have: when do you NOT raise > the calculation on geometric mean to 1/N? Do you > not raise it to 1/N when calculating ANNUAL > returns? Right. You only raise it to the power for the number of years. These are the little tricks that the CFA throws in. If they give you 4 quarterly returns then there is no need to raise it to any power at all. Think about what they are asking for…“The portfolio’s annual time-weighted rate of return”…There is no need to annulized the returns by raising them to any power because you only have 4 quarter (1 years) returns. But if you had 8 quarters of retuns it would be ^1/2. Edit: Beat to the punch

Ok, but Holding-period return is calculated: Value at end- Value at beginning/ Value at Beginning. Therefore, it seems that the calculations should be,and this would be taking into account the cashflows: 1. 2.4-2.2/2.2= .0909 2. 2.6-2.8/2.8= -.0714 3. 3.2-2.4/2.4= .3333 4. 4.1-4.2/4.2= -.0238 Maybe I’m missing something, but in the CFA text, it is pretty clear about calculating Holding period return. Am I just not getting it and should just go onto the next question? Ha!

in all of those the CF is at the end of the period… because it is a dividend at the end of the year. In this case, the dividend is happening at the beginning of the year. That is the difference. I have done above what you have done exactly, only not subtracted the 1… essentially 2.4/2.2 = 1.0909 and what you have is (2.4-2.2)/2.2 = 0.0909 I have not subtracted the one here, because you need to add it back later… to do the (1+r1)(1+r2)… for the TWR calculation

You still have me lost. I don’t understand why you wouldn’t subtract the beginning value from the ending value, even if the dividend is at the beginning. The first one definitely resembles your answer, but then the other three don’t if I stick to the formula of Vend-Vbeg/Vbeg. In other words, why do you just do: Vend/Vbeginning?

Look at it (vend - vbeg)/vbeg = r or vend/vbeg -1 = r so by doing vend / vbeg = (1+r) do you see that now? Quarter 1 2.0 0.2 2.4 vbeg = 2.2, vend = 2.4 2 2.4 0.4 2.6 vbeg = 2.8, vend = 2.6 3 2.6 (0.2) 3.2 vbeg = 2.4, vend = 3.2 4 3.2 1.0 4.1 vbeg = 4.2, vend = 4.1 HTH CP

That’s exactly what I needed. It now makes sense…finally.