Time-Weighted Versus Money-Weighted Returns

A fund starts the year with $100 under management. In month one it returns +20%, growing to $120. Right after that, an investor — encouraged by the strong first month — adds $880, bringing the account to $1,000. In month two the fund drops 10%, ending the year at $900. The manager's own skill produced two clean, independently reportable moves: up 20%, then down 10%. But the investor opened the year with $100 and ends with $900 having contributed $880 of new money along the way — in raw dollar terms they are down relative to what they put in and out, and if you calculate their personal rate of return it comes out clearly negative, even though the manager's decisions in each month were exactly as good or bad on their own terms. Both descriptions are correct. They're answering different questions, and reporting the wrong one to the wrong audience is the actual failure mode this concept exists to prevent.

Two different questions, two different answers

Time-weighted return (TWR) answers "how good was the manager's skill, independent of when money moved in and out." It does this by breaking the period into sub-periods at every cash-flow date, computing the return on each sub-period using only the money actually invested during it, then compounding those sub-period returns together. Because each sub-period's return is measured on its own capital base, a large deposit right before a bad month doesn't drag down the reported number — it only affects performance from the moment it entered.

Money-weighted return (MWR), also called the internal rate of return on the cash flows, answers "how did the investor's own money actually do, given when it went in and out." It's the single discount rate that makes the present value of all contributions and withdrawals equal the ending value. Because it weights each period by how much capital was actually at risk during it, a large deposit right before a bad month drags the reported number down hard — which is exactly appropriate if the question is "how did this investor do," and exactly wrong if the question is "was this manager skilled."

Worked example: the numbers from the opening paragraph

Time-weighted: month one return is (120 − 100)/100 = +20%. Month two's return is measured only on the capital actually invested during that month, $1,000, ending at $900: (900 − 1000)/1000 = −10%. Compound the two sub-period returns: (1.20)(0.90) − 1 = +8% time-weighted for the year. This is the number that isolates the manager's decisions from the investor's timing.

Money-weighted: the investor's actual cash flows were −$100 at the start (an outflow from their pocket into the fund), −$880 one month in, and +$900 received at the end. Solve for the rate $r$ that sets the present value of those flows to zero — equivalently, find $r$ such that $100(1+r) + 880 = 900(1+r)^{-1}$-style balancing holds across the two months. Working it through gives a money-weighted return of roughly −1.4% for the year: the investor's own dollars, weighted by how much was actually exposed and when, lost a little money, even though the fund's time-weighted return was a healthy +8%.

Measure	Answers	Result	Sensitive to investor's timing?
Time-weighted	How good was the manager	+8%	No
Money-weighted	How did this investor's money do	≈ −1.4%	Yes

Neither number is wrong. The GIPS performance standard requires funds to report time-weighted returns to prospective investors specifically because it isolates skill from any one investor's particular contribution history — a fund's reported track record shouldn't depend on when its existing clients happened to add or withdraw money.

Doing it properly

Report time-weighted returns when evaluating a manager or comparing strategies against each other, since that's the number that isolates decisions from client-specific cash-flow timing — this is why GIPS mandates it for track records. Report money-weighted returns when the question is about an individual account's actual outcome, including for internal reviews of whether a specific client's experience matched expectations. And when the two diverge sharply, as in the example above, treat that gap itself as information: it usually means large flows are arriving at systematically bad times, which is worth investigating whether it's driven by investor behavior, by the manager gating subscriptions around performance, or by something structural in how the strategy attracts capital.