Studying the Level I Curriculum and I finished reading Time Weighted Return & Money Weighted Return. I am very aware of the difference in calculations between the two, however the way the curriculum defines them confuses me a bit. Here’s what I am able to extract to support my question:

Money Weighted Return (IRR): Rate of return generated by an investment.

Over the period of the investment, you will realize a compound rate of return equivalent to IRR (assuming re-investment at IRR).

Time Weighted Return: The compound rate of growth of the initial investment.

So I decided to solve the example using both approaches: You buy a share for $200 at t = 0. At t = 1 you buy another share for $225 & earn a dividend of $5 (which you keep and don’t reinvest into portfolio)… At t = 2 you sell both shares for $235 each and earn dividends of $10.

Money Weighted Return

The way the curriculum interprets this is the following: PV(outflows) = PV(inflows), find the ® that makes this possible: $200 is an outflow (t =0) $225 is an outflow (t=1) $5 is an inflow (t = 1) $10 is an inflow (t = 2) $470 is an inflow (t = 2) Netting them, the curriculum gets: t0 = -200 t1 = -220 t2 = 480 IRR = 9.39% Then it proceeds to explain what happened during the yea. It says we divide each period (t0, t1, t2) with in between HPR: HPR (t0 - t1) = (225 - 200 + 5)/200 => 15% HPR (t1-t2) = (470 + 10 - 450 )/ 450 => 6.7% Then the curriculum ends by saying that 6.7% was of greater emphasis as more money was invested in second year. From my point of view, I do not see any money invested in the second year, all we did was sell both of our shares for $235 eachand earned a $10 dividend. Also, where is the mathematical proof that we put more emphasis on it? Curriculum ends its explanation here. Going back to the definition and our cash flow sets, we see that: 200*(1+9.39%)^{2} <=> -220*(1+9.39%) + 480

Time Weighed Return

Jumps straight into HPRs so: HPR1: (225-200+5)/200 => 15% HPR2: (480-450+10)/450 => 6.67% TWR = SQRT(1+15%)(1+6.67%) - 1 => 10.76% Going back to the definition we see: 200*(1+10.76%)^{2} => $245

HPR is (End Value - Beg Value)/Beg Value. In this case your beg value is 225 and since you have two shares you have 450. The reason we don’t take 200 as beg value coz you have already counted your return for that 200 in first HPR. Can’t doubble dip it :).

where is the mathematical proof that we put more emphasis on it? Curriculum ends its explanation here.

If we have same weights in both periods then the return would be just an simple avg of 15% and 6.7% but that’s not the case here. Since you made $20 in first period and $30 in second period you have to put more weights on second period. It’s MONEY WEIGHTED return so first period has weight of 40% and second period has weight of 60% based on amount of money earned during that period and return is calculated based on these.

200*(1+10.76%)^{2} => $245

Don’t forget you bought one more share in period two. You can breakdown the two period to see if math checks out.

Period 1 - 200 @ 10.76 = 222 is end value

Period - 2 (222-5+225) @ 10.76% = 490 (and less $10 for div) is $480.

Thank you for all your input. May I ask a few follow up questions?

Can someone show me when I find the TWR of a portfolio, how the TWR leads me from a beginning value to an ending value: Q1 Q2 Q3 Q4 Beginning Value 4,000,000 6,000,000 5,775,000 6,720,000 Deposit/Withdrawal 1,000,000 (500,000) 225,000 (600,000) Amount Invested 5,000,000 5,500,000 6,000,000 6,120,000 Ending Value 6,000,000 5,775,000 6,720,000 5,508,000 TWR = 27% --> 4,000,000*(1+27%) => does not lead me to 5,508,000.

Alright. Let’s start with assumption that your deposit/withdrawal and investment happens at Beg of the period. So all your amount invest is Beginning Value and Deposits and withdrawals are your Capital Add/Dividends. To cal the Gain/Loss End Val+Divs-Beg Val (same as yod did for first exaple on top) and you can calculate the return based on these. It should all tie back.

Thank you for your input, sorry I am a bit confused.

How does my portfolio start with 5,000,000 ; receive a deposit of 1,000,000; and take a gain of 2,000,000 and have an ending value of 6,000,000? Shouldnt my ending value be (5M + 1M + 2M) = 8M? In my example I had a beginning value of 4M + 1M deposit + 1M capital gain and had an ending value of 6M which made sense.

And how can you assume that your capital gains/dividends are deposits/withdrawals (in a sense cant investors push money into the account and have that count as a deposit)?

Also using your numbers how did your HPR1 turn out to be 20%?

How are you saying you received a negative return in year 2 if your beginning value is 5,500,000 and your ending value is 5,575,000.

Magician - I tried to remove the interim cash flows as you said and it is still not working:

I took my initial $4,000,000(1+27%) = 5,080,000 and attempted to add/remove my deposits and withdrawals but it still wont work.

When you removed the deposits and withdrawals, did you also remove the effects on the returns?

For example, in year 1 you earned $1,000,000 on an initial investment of $5,000,000. If you remove the deposit, then your initial investment is only $4,000,000, so your earnings would be only $800,000 (= 4/5 × $1,000,000) and your ending value would be only $4,800,000 (= 4/5 × $6,000,000).

May I ask how or why we do (4/5) * 6,000,000 is it a way to obtain the real return (w/o the effect of the deposit on the ending value)? Is there some sort of rate I am not aware of?

So are you saying I am supposed to do:

[(Initial Investment w/o deposit)/(initial Investment w deposit)] x [Capital Gain & Dividends)?

I’m just trying to set this up in a logical fashion:

Q1 Q2 Q3 Q4

Beginning Value w/o deposit 4,000,000 5,000,000 5,275,000 5,995,000 Capital Gain 1,000,000 275,000 720,000 -612,000 End value 5,000,000 5,275,000 5,995,000 5,383,000

The TWR should be the compound rate that takes us from 4,000,000 to 5,383,000 … this is really nerve wracking.