freebirdcapitalAnyone who regularly deposits or withdraws has not one return but two. The time-weighted return measures the strategy, the internal rate of return the result for the money invested. In my example one is plus 5 %, the other minus 10 % — in the same portfolio, in the same year.
Why one number is not enough
A portfolio of €10,000 rises to €12,000 in the first half of the year. On 1 July another €20,000 is added, then the market falls, and at year-end the portfolio stands at €28,000. €30,000 was invested; €2,000 is missing. Did the strategy fail? No: it returned 20 % in the first half and lost 12.5 % in the second. Only the timing of the large deposit was unlucky — and the investor decides that, not the strategy.
| Period | Value at start | Value at end | Sub-period return |
|---|---|---|---|
| 1 Jan to 1 Jul | €10,000 | €12,000 | +20.0 % |
| 1 Jul to 31 Dec (after a €20,000 deposit) | €32,000 | €28,000 | −12.5 % |
| time-weighted: 1.20 × 0.875 − 1 | +5.0 % | ||
| internal rate of return of the cash flows | −9.9 % |
Time-weighted return: the measure of the strategy
The time-weighted return splits the period at every deposit and withdrawal, calculates the return for each sub-period and chains them. Cash flows therefore do not change the result. That is why it is the standard when funds and asset managers report performance, and the only return that can be fairly compared with an index — an index has no deposits.
time-weighted = (1 + R₁) × (1 + R₂) × … × (1 + Rₙ) − 1
Internal rate of return: the measure of your own money
The internal rate of return is the rate at which all deposits, withdrawals and the final value balance out. It weights every euro by the time it was invested. Large deposits before a price fall push it down, deposits before a rise lift it. For the question "what became of my money?" it is the honest answer. In controlling it is familiar from investment appraisal: it is the same method used to evaluate a new machine or a plant extension.
Which number for what
| Question | Measure |
|---|---|
| Is my stock selection better than an index fund? | time-weighted return |
| Has my rulebook proved itself over the years? | time-weighted return |
| What return did my invested money earn? | internal rate of return |
| Was the timing of my deposits favourable? | the difference between the two |
Four pitfalls
- Dividends are not deposits. If they stay in the portfolio, they are part of its value. If paid out to the current account, they are a withdrawal.
- Use the value before the cash flow. The time-weighted return needs the value immediately before each deposit or withdrawal. Monthly statement values suffice as long as cash flows fall at month-end.
- Do not annualise short periods. Three good months extrapolated to a year produce fantasy numbers.
- Treat taxes and fees consistently. Either both returns after costs or both before — otherwise you compare apples and oranges.
The performance calculator computes both returns from any number of dates — pre-filled with this example.
Foundations: the time-weighted return is the standard of the CFA Institute's Global Investment Performance Standards (GIPS) for reporting investment results; the internal rate of return is the standard method of dynamic investment appraisal. Example with own figures.
