Lesson 8 of 9
Two answers to how did I do
A fund can report zero over two years while the investor in it lost 41 percent a year. Both figures are correct and they answer different questions.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- A time-weighted return measures the manager, because it removes the effect of when money was added or taken out.
- A money-weighted return measures the investor, because the size of the position at each moment is the whole point.
- The two can differ enormously, and the difference is entirely the investor's own timing.
"How did I do" is two questions. One asks how the strategy performed. The other asks how much money you ended with. When deposits and withdrawals happen in between, the two answers can be almost unrelated.
One portfolio, two years, two returns
- Time-weighted, per year0%
- Money-weighted, per year−41.74%
The example
Start with 1,000. In year one it doubles, to 2,000. Pleased with that, you add 8,000 at the start of year two, making 10,000. Year two halves it, to 5,000.
Time-weighted. Chain the period returns and ignore the cash you moved. Up 100 percent, then down 50 percent: 2.0 multiplied by 0.5 is exactly 1.0. The strategy returned zero over the two years, and zero a year.
Money-weighted. This is an IRR on your own cash flows. You paid 1,000 at the start, 8,000 a year later, and ended with 5,000 a year after that. The rate that sets that stream to zero is minus 41.74 percent a year.
Which is which, and why
The time-weighted figure exists because a manager does not choose when clients deposit. Judging a strategy by a return that a client's deposit timing can move would be judging the wrong person, which is why published fund returns are time-weighted almost everywhere.
The money-weighted figure exists because the investor does choose. It weights each period by how much money was exposed to it, so a good year on a small balance counts for little and a bad year on a large one counts for a lot.
The uncomfortable part
Deposits are not random. They tend to follow good performance, which means they tend to arrive before the periods that give it back, and withdrawals tend to follow bad performance. A body of published work has measured this gap between fund returns and fund investors' returns, and the direction is consistent even where the size is disputed.
The measurement that matters for a private investor is the money-weighted one, because it is the only one that answers what happened to the money. The time-weighted one is the right way to judge a method that was applied consistently. Keep both, label both, and never compare one against the other.
Check yourself
A fund reports a time-weighted return of 10 percent a year. What has it not told you?
- How volatile the fund was
- How much money was invested during the good and bad periods
- Which securities it held
Show the answer
Answer: B.
Time weighting deliberately removes the effect of cash moving in and out. That is correct for judging the manager and it means the figure cannot describe any particular investor's outcome.A money-weighted return is computed as which of these?
- The arithmetic mean of the period returns
- The internal rate of return on the investor's own dated cash flows
- The compound growth of the fund's unit price
Show the answer
Answer: B.
It is an IRR, which is why it inherits both the usefulness and the failure modes of the previous lesson.In the example, why is the money-weighted return so far below the time-weighted one?
- The fund charged high fees
- Most of the money was present only for the losing year
- The time-weighted calculation is wrong
Show the answer
Answer: B.
One thousand was exposed to the doubling and ten thousand was exposed to the halving. Money weighting counts that, which is exactly what it is for.Sources
- Damodaran, Investment Valuation: the distinction between dollar-weighted and time-weighted returns and the reporting conventions that follow from it.
- Williams, The Theory of Investment Value, 1938: the present-value identity that a money-weighted return solves.
What this leaves out
- The two-year example is invented arithmetic, chosen so both answers can be recomputed by hand.
- The claim that investor returns tend to trail fund returns is a direction reported in published work, not a figure computed here, and the size of the gap is contested.
- Neither measure adjusts for risk, and neither is a forecast.
- Nothing here is advice about any security.