# Annual time weighed rate based on quaterly cash flow

Column 1 is Quarter Column 2 is “Value at Beginning of Quarter (prior to inflow or outflow)” Column 3 is " Cash Inflow (Outflow) at Beginning of Quarter" Column 4 is “Value at End of Quarter” 1 2 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%

Is it C? I got like 32.66%

I got C as well

C is correct, but accurate number is 31.85%. How?

27%

ah, that’s more tricky than I thought!

Dreary Wrote: ------------------------------------------------------- > ah, that’s more tricky than I thought! Dreary, can you show the process please…I am getting confused

Time value ignores inflows and outflows of cash. I thought that in this case the ending value is affected by the flow of cash, so at first I deducted the inflows, added the outflows back to reflect the value of ending without accounting for inflows/outflows, what the value would have been simply with growth. (2.4-0.2-2)/2=10% (2.6-0.4-2.4)/2.4=-8.33% (3.02+0.2-2.6)/2.6=30.77% (4.1-1-3.2)/3.2=-3.13% Then I calculated the weighted retun for the quarter: (2*10-2.4*8.33+2.6*30.77-3.2*3.13)/(2+2.2+2.6+3.2)=6.99% (1+6.99%)^4-1=31.0767%, correction to my initial value

No, answer is 1.0909 x 0.9286 x 1.3333 x 0.9762 -1 = 0.3185.

How do you get 9.09% for the first quarter??

I don’t know. That’s why you see this question here.

Look at it again…there is no way you can get 9.09% from the numbers given.

Oh I was so off:)) I thought those are 4 investments in the same quarter:))

1.0909=2.4/(2.0+0.2) Since the cash inflow occurred at the beginning of the quarter, you have to include that in the beginning balance.

9.09%, -7.14%, 33.3% and -2.38% Makes sense, but aren’t we supposed to ignnore additions/withdrawals when calculating time-weighted?

Yes, there is. At the beginning of the quarter, the value is 2, and a 0.2 inflow is made. At the end of the quarte, the value is 2.4 (2.4-2.2)/2.2 =9.09 At the beginning of the second, the value is 2.4 but an inflow is made to 2.8 at at the end of the term it gets down to 2.6 (2.6-2.8)/2.6=-7.69 At the beginning of the third, the value is 2.6 but an outflow is made reducing the beginning value to 2.4, ending value 3.2 (3.2-2.4)/2.4=33.333 At the beginning of the fourth, the value is 3.2 but an intflow is made increasing the beginning value to 4.02, ending value 4.1 (4.1-4.2)/4.2=-2.381 Geometric mean it, and you have it.

vbcfa Wrote: ------------------------------------------------------- > 1.0909=2.4/(2.0+0.2) Since the cash inflow > occurred at the beginning of the quarter, you have > to include that in the beginning balance. Thanks Vb. This part is clear. But 1.0909 x 0.9286 x 1.3333 x 0.9762 -1 = 0.3185. Is this supposed to be annual TWR? Since the holding period is quarter, instead of year.

I thought that too.

Dreary Wrote: ------------------------------------------------------- > 9.09%, -7.14%, 33.3% and -2.38% > > Makes sense, but aren’t we supposed to ignnore > additions/withdrawals when calculating > time-weighted? The HPY’s that you are taking the mean of do account for inflows and outflows (dividends for example): HPY=(p1+D1/p0)-1

> (2.6-2.8)/2.6=-7.69 I got -7.14%, same as indicated in the answer.