Time-Weighted Return (TWR)

A time-weighted return is a way of measuring investment performance that removes the influence of the size and timing of money moving into and out of an account. The Global Investment Performance Standards, the voluntary reporting standards published by CFA Institute, define it as "a method of calculating period-by-period returns that reflects the change in value and negates the effects of external cash flows." Because it answers what the investment did rather than what the investor's money did, it is the fair way to compare two funds, or a fund against its benchmark, and the wrong way to answer "how did I do?"

The companion measure is the money-weighted return, which deliberately keeps the effect of cash-flow timing and therefore reports the investor's own experience. Neither one is more correct. They answer different questions, and a statement that shows both is showing you two facts rather than a discrepancy.

The mechanics follow from the goal. If you want a number the investor's deposits cannot move, you have to stop measuring whenever a deposit happens. So the period is cut at every external cash flow, a separate return is computed for each sub-period using the account value immediately before and after the flow, and the sub-period returns are then multiplied together, not averaged. Multiplying is what makes the result independent of how much money was present in each piece.

The GIPS standards spell this out as a requirement rather than a suggestion. For the portfolios in a composite, a firm claiming compliance must calculate returns at least monthly; must, if it is not calculating daily returns, calculate sub-period returns at the time of all large cash flows and adjust for daily-weighted external cash flows on the flows that are not large; and must "geometrically link periodic and sub-period returns." Geometric linking is the multiplication step. A firm that added the sub-period returns instead would produce a number that drifts further from the truth the more volatile the account is.

Time-weighting is also embedded in how funds are allowed to advertise. Under SEC Rule 482 (17 CFR 230.482), a mutual fund advertisement quoting performance for a fund other than a money market fund is limited to specified figures, including "average annual total return for one, five, and ten year periods," computed by the method prescribed in Form N-1A. That computation starts from a single hypothetical investment held for the whole period, which is a time-weighted construction by design: it has to be, because the fund cannot know when any particular shareholder bought.

The practical consequence is the one that surprises people. A fund can report a strong ten-year record while most of the dollars that were ever invested in it did worse, simply because money tends to arrive after good stretches. That is not a criticism of the fund's number, which is measuring the fund. It is a reason not to read the fund's number as a report on the investor.

Three steps. Cut the measurement period at every deposit and withdrawal. Compute a plain percentage return for each resulting sub-period. Multiply the growth factors together and subtract one.

A hypothetical illustration, built so the arithmetic is easy to check. An account starts the year with $100,000. In the first half it gains 25 percent, so it is worth $125,000 at the end of June. The investor then deposits $400,000, bringing the account to $525,000. In the second half the market falls 20 percent, leaving $420,000 at year end.

The two sub-period growth factors are 1.25 and 0.80. Multiplied, they give exactly 1.00, so the time-weighted return for the year is 0 percent. That is a true statement about the investment: a dollar left alone for the whole year ended the year where it started.

It is not a true statement about the investor. She put in $100,000 and then $400,000, a total of $500,000, and finished with $420,000. She is down $80,000. Nothing has gone wrong with the calculation. The 0 percent figure was built to ignore the fact that four fifths of her money only showed up in time for the fall, and the money-weighted return is the measure that puts that back in.

Strengths

• It is the only fair basis for comparing a manager or a fund against a benchmark or against a rival, because neither one controls when clients send money.
• It is reproducible. Two firms following the same standard on the same portfolio should produce the same figure.
• It is what almost every published performance table already contains, so it is the number that makes external comparisons possible.

Limits

• It does not tell an investor how their own money did, and it is routinely read as though it does.
• It can diverge sharply from the investor's experience precisely when the divergence matters most, which is after a large contribution ahead of a fall.
• Computing it properly requires an account valuation at every significant cash flow, which is why the daily-priced version is a custodian's job rather than something to reconstruct from a year-end statement.
• It says nothing about risk. Two funds with the same time-weighted return can have reached it through very different drawdowns.