Money-weighted vs time-weighted return
The money-weighted return is the internal rate of return on the investor's own cash flows, so it rewards good timing of deposits. The time-weighted return chains the returns between cash flows, so it ignores their size and timing. Use time-weighted to judge a manager who does not control the flows.
Before this: Holding period return, Arithmetic, geometric and harmonic mean returns
On the exam
- Compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures
Compare money-weighted and time-weighted returns and evaluate performance with them. Expect one calculation (usually the time-weighted return, sometimes a two-period money-weighted return) and one "which is appropriate" question.
What is the money-weighted return?
It is the discount rate that makes the present value of everything the investor put in equal to the present value of everything taken out, including the ending value. In other words, it is the IRR of the investor’s cash flows.
The money-weighted return is an internal rate of return applied to a portfolio. Contributions are negative flows, withdrawals and the ending value are positive flows, and the rate solves net present value = 0.
More money was invested in year 2 than in year 1, so year 2’s weaker return counts for more.
You buy 1 share at USD 100. A year later it is USD 120 and you may buy more. At the end of year 2 you sell everything.
MWR < TWR: more money was invested in the weaker year.
Show working
MWR: solve -100 − 120/(1 + r) + 260/(1 + r)² = 0 → r = 12.05% (calculator: CF0 = -100, C01 = -120, C02 = 260, IRR CPT)
TWR: (1.20 × 1.0833)1/2 − 1 = 14.02% a year
What is the time-weighted return?
It measures how the assets performed, ignoring how much money was in them at each point. Split the period at every external cash flow, find the return of each piece and chain them.
- Split at every external cash flow.
- Compute the holding period return of each sub-period.
- Chain them: .
- If the total is longer than a year, take the geometric mean to annualize.
The result is the time-weighted return .
The money-weighted return (12.05%) is below the time-weighted return (14.02%) because the investor added money just before the weaker year.
Which one should you use?
Use the time-weighted return to judge a manager who does not control the flows. Use the money-weighted return when the investor, or a manager, does control the timing of flows.
| Money-weighted | Time-weighted | |
|---|---|---|
| What it measures | The investor’s actual experience, including timing of deposits | The manager’s skill per unit invested |
| Affected by size and timing of flows | Yes | No |
| Needs a valuation at each flow | No | Yes |
| Use when | The investor (or a manager) controls the flows, as in private equity | The manager does not control the flows. Required by GIPS |
Exam tip Timing of cash flows affects the money-weighted return. If an answer says it affects the time-weighted return, it is the trap.
Go deeper Dividends in a money-weighted return
Dividends and interest are part of the investor’s cash flows, so they enter the IRR calculation. A dividend of USD 2 paid at t = 1 simply adds 2 to the flow at t = 1 (so −120 becomes −118) and the IRR is solved again with the same calculator keys. No other step changes. The principle is simple, and it is the same for every pattern of flows. List every dollar that crosses the boundary between the investor and the portfolio, with its date, and solve for the rate that sets net present value to zero.
Go deeper Why the time-weighted return needs so many valuations
To chain sub-period returns, you must know the portfolio’s value just before every external cash flow. Daily pricing makes that easy for a mutual fund, but it is a heavy requirement for assets that are valued rarely, such as property. Approximations exist, for example the Modified Dietz method, which weights each flow by the fraction of the period it was invested and avoids the interim valuations. It is mentioned here only so you recognize the name. It is not examinable in this module.
Go deeper When there is more than one IRR
Because the money-weighted return is an IRR, it inherits the IRR’s quirks. When the cash flows change sign more than once, for example money in, money out, then money in again, the equation can have more than one solution, or none. That is unusual for a typical portfolio, but it appears in project finance and private investments. The capital allocation module returns to this, together with the net present value rule that avoids the problem. For the exam, the practical advice is short: if a question gives a conventional pattern of one outflow followed by inflows, trust the single answer, and if the signs flip back and forth, expect the question to be about the caveat itself rather than the number.
Exam traps
- Not annualizing a multi-year time-weighted return (or annualizing one shorter than a year).
- Starting the next sub-period from the beginning value instead of the beginning value plus the contribution.
- Saying the time-weighted return is affected by the timing of cash flows. It is the money-weighted return that is.
Checkpoint
3 exam-style questions. About 90 seconds each.
1A pension fund's external managers do not control when the sponsor adds or withdraws money. To evaluate the managers, the sponsor should most appropriately use the:
2A portfolio is worth USD 1,000,000 at the start of the year. Just before a USD 500,000 contribution mid-year it is worth USD 1,100,000. It ends the year at USD 1,500,000. The time-weighted return for the year is closest to:
3An investor's money-weighted return will exceed the time-weighted return when the investor:
Key takeaways
- Money-weighted return = IRR of the investor's cash flows. It reflects the investor's timing.
- Time-weighted return = chained sub-period returns. It ignores timing and is the standard for judging managers.
- More money in before a good period: MWR > TWR. Before a bad period: MWR < TWR.
Where this comes back
- Capital Investments and Capital Allocation Corporate Issuers
- Introduction to the Global Investment Performance Standards (GIPS) Ethical and Professional Standards
Questions candidates ask
What is the difference between money-weighted and time-weighted return?
The money-weighted return is the IRR of the investor's cash flows, so it depends on when money went in and out. The time-weighted return chains the returns of each sub-period between flows, so it does not. The first describes the investor's experience, the second the manager's performance.
Is money-weighted return the same as IRR?
Yes. The money-weighted return is the internal rate of return of the investment's cash flows: the discount rate at which contributions, withdrawals and the ending value have a net present value of zero. Any dividends count as flows in the calculation.
Why does GIPS use time-weighted return?
Firms report performance to prospective clients, and the manager usually does not control when clients add or withdraw money. The time-weighted return strips out that timing, so different managers can be compared fairly on what they did with the assets.
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