Subject 3. Dollar-weighted and Time-weighted Rates of Return

The dollar-weighted rate of return is essentially the internal rate of return (IRR) on a portfolio. This approach considers the timing and amount of cash flows. It is affected by the timing of cash flows. If funds are added to a portfolio when the portfolio is performing well (poorly), the dollar-weighted rate of return will be inflated (depressed).

The time-weighted rate of return measures the compound growth rate of $1 initial investment over the measurement period. Time-weighted means that returns are averaged over time. This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement.

Example

Jayson bought a share of IBM stock for $100 on December 31, 2000. On December 31, 2001, he bought another share for $150. On December 31, 2002, he sold both shares for $140 each. The stock paid a dividend of $10 per share at the end of each year.

To calculate the dollar-weighted rate of return, you need to determine the timing and amount of cash flows for each year, and then set the present value of net cash flows to be 0: - 100 - 140/(1 + r) + 300/(1 + r)2 = 0. You can use the IRR function on a financial calculator to solve for r to get the dollar-weighted rate of return: r = 17%.

To calculate the time-weighted rate of return:

  • Split the overall measurement period into equal sub-periods on the dates of cash flows. For the first year:

    • beginning price: $100
    • dividends: $10
    • ending price: $150

    For the second year:

    • beginning price: $300 (150 x 2)
    • dividends: $20 (10 x 2)
    • ending price: $280 (140 x 2)

  • Calculate the holding period return (HPR) on the portfolio for each sub-period: HPR = (Dividends + Ending Price)/Beginning Price - 1. For the first year, HPR1: (150 + 10)/100 - 1 = 0.60. For the second year, HPR2: (280 + 20)/300 - 1 = 0.

  • Calculate the time-weighted rate of return:

    • If the measurement period < 1 year, compound holding period returns to get an annualized rate of return for the year.
    • If the measurement period > 1 year, take the geometric mean of the annual returns.

User Contributed Comments 34

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synner: how do you use IRR function on a TI BAII plus?
jimmymh: IRR is a function of CF, input your CF then Push IRR then compute.
rche: Can anyone tell me the exact key stroke to solve for the 17% in the IBM example using the BA II Plus?
Evgenia1: CF
C01=-100
F01=1
C02=-140
F02=1
C03=300
IRR CPT
Result: 16.82
yly13: shouldn't it be -100-150/(1+r)+300/(1+r)2
HBomb: yly13

There is a $10 Dividend after the first year also which you add to the $-150. This gives you $-140 instead.
KenSemer: How do you compute the Time Weighted Rate of Return using BA II Plus?
clyde: Hi,
Can anyone tell me for Time-Weighted, in 2nd yr, the beginning price is 300(150x2)? Yr1 has ending $150. Where does the other 150 come from. Many thanks
akanimo: clyde, jayson bought a second IBM share at the end of the year which combines with the initial purchase to give 2 shares, both the new share and the old share will be valued at this same new price i.e. 150 x 2
sdivietr: how do I calculate the Time wrr if period < 1 year? Compounding of individual HPR means?????
Taimoor: If the return Time Weighted Rate of Return is less than 1 year the compounded annual return is calculated as follows:

e.g a weekly return of 0.2%

(1.002)^52 - 1 = 0.1095 or 10.95%

note: 52 is used as a power because the return is weekly and their are 52 weeks in a year.
achu: Geometric Mean formula used with TIME wtd returns, the preferred measure of performance!
HaTran: What is different betweent money - weighted and dollar - weighted rates of return???
vinnybozz: Dollar Weighted Solution is:

t=0 first purchase: -100
t=1 dividend on 1st share: +10
2nd purchase: -150
t=2 dividend on 2 shares: +20 (10+10)
sale: +280 (140*2)

So at t=0, Solve r:
-100 + (+10-150)/(1 + r) + (+20+280)/(1 + r)2=0
<=> - 100 - 140/(1 + r) + 300/(1 + r)2=0
Gooner7: is there a way to do time-weighted calculation on TI BA II+ ?
DonAnd: There is a similar example for calculating Money-Weighted(Dollar-Weghted)rate of return on p.246 in the text.
LONG: For dollar-weighted rate of return I can TI BAII as following and get the same result 16.8154%:
CFo=-100
C01=-140
C02=300
IRR=16.8154

and same as:
CFo=0
C01=-100
C02=-140
C03=300
IRR = 16.8154
poomie83: Long, could you explain why 140 is negative? Also why is the cash flow at end of year 2 $300 when that is the value at end of year 1? And don't we account for the dividends?
TiredHand: $140 is negative because the dude paid $150 for a second IBM share (unwise) which is -$150, but he received a $10 dividend.
$-150 + $10 = $-140.

Not that I could do that question in an exam.
niyongana: in which situation liquidity and maturity cannot be investment constraint illustration by using numerical example
ran123: Can someone please show how the dollar weighted return example was calculated manually(step by step)?

Thanks
jonan203: can you rephrase your question?
tshepi: van you share how to do it on the HP12c
Callie2: HP12C:
100[CHS][g][CF1] (price of 1st share)
140[CHS][g][CF1] (price of 2nd share - $10 div)
300[g][CF1] (proceeds plus two $10 div)
[f][IRR]
=16.8154
bschmitt: For BAII Plus, what is F01 and F02 in the calculation please?
schweitzdm: F01 and F02 refer to the frequency of cash flows.

If it only happens once, leave it at 1.
Inspector: HPR = (Ending price - beginning price + dividends) / beginning price so why do the notes say HPR = (Ending price + dividends)/ beginning price... wtf

HPR = ((MV1 - MV0 + D1 - CF1)/MV0)


Where: MV0 = beginning market value, MV1 = ending market value,
D1 = dividend/interest inflows, CF1 = cash flow received at period end (deposits subtracted, withdrawals added back)
littlecow: @Inspector: you missed the -1 part. The notes says HPR = (Dividends + Ending Price)/Beginning Price - 1, this is exactly the same as what you have: HPR = (Ending price - beginning price + dividends) / beginning price
ajshittu: HP 12c Platinum Financial Calculator - IRR Calculation
100(CHS)(g)(CF0)
140(CHS)(g)(CFj)
300(g)(CFj)
2(RCL)(n)
(f)(IRR)
kaichan91: Can someone elaborate on the part that talks about inflation/depression of the dollar-weighted rate of return? I'm a little confused about the mathematical relationship of the two.
Rudger: I dont understand how the square root of 1.06 is 1.26. I get 1.29. ANy help anyone?
khalifa92: in long time horizons situations?
gjohnub: Here's how I do it.
1.He buys $100 of share on Dec 31, 2000 : so beginning price = $100
2.He buys $150 of share on Dec 31, 2001: so ending value = $150
3. So HPR = (ending- beginning + dividend)/ beginning = (150 - 100 + 10) / 100 = 0.6
4. Then, he sold shares for $140 on Dec 31, 2002. so ending value = $140 and beginning value = $150 from previous year.
5. So HPR = (ending - beginning + dividend) / beginning = (140 - 150 + 10) /150 = 0
6. TWRR = [(1+0.6)(1+0)]^1/2 - 1 ( 1/2 because 2 years ) = 0.26
931129: Go over the calculations here.