How to calculate Time Weighted and Dollar Weighted return
About this lesson
In this video, we will discuss time-weighted and dollar-weighted returns. With a simple numeric example, I will also show how you can calculate and interpret these returns.
Two ways to measure a multi-year return
When money is added to or taken out of an investment over time, there are two common ways to measure its return:
- Time-weighted return: the return of the investment itself, ignoring when and how much money was added. It’s the standard for judging a fund manager.
- Dollar-weighted return (money-weighted, or the internal rate of return): the return you actually earned, given the timing and size of your deposits.
Example
- Year 0: buy 1 share at $50.
- Year 1: the share pays a $2 dividend; buy another share at $53.
- Year 2: each share pays a $2 dividend; sell both shares at $54.
Time-weighted return
Calculate each year’s return separately:
- Year 1: (53 − 50 + 2) ÷ 50 = 10.00%
- Year 2: (54 − 53 + 2) ÷ 53 = 5.66%
Arithmetic average: (10% + 5.66%) ÷ 2 = 7.83%
Geometric average: √(1.10 × 1.0566) − 1 = 7.81%
Dollar-weighted return
List the cash flows from your point of view:
| Year | Cash flow |
|---|---|
| 0 | −$50 (buy the first share) |
| 1 | −$53 + $2 = −$51 (buy the second share, less the dividend) |
| 2 | +$4 + $108 = +$112 (two dividends, plus selling two shares) |
Find the rate r that makes the present value of these cash flows zero:
−50 − 51 ÷ (1 + r) + 112 ÷ (1 + r)² = 0 → r = 7.12%
In Excel: =IRR(B2:B4) with the three cash flows in B2:B4.
Why they differ
The dollar-weighted return (7.12%) is lower than the time-weighted return (7.83%) because more money was invested in year 2, the weaker year. The dollar-weighted return gives more weight to periods when more money is invested.