Money-Weighted Return

The calculation begins with a timeline of every cash movement between the investor and the account, dated to the period in which it occurred. Beginning value and subsequent contributions are treated as outflows from the investor's perspective and carry one sign; withdrawals, distributions and the ending market value carry the opposite sign, with the terminal value placed at the final date. The money-weighted return is then the single periodic discount rate at which the present value of that entire series equals zero.

There is no closed-form solution beyond very simple cases, so the rate is found iteratively, either by a financial calculator's cash flow and IRR routines or by trial and error. Two mechanical points matter. Cash flows must be assigned to evenly spaced periods, with zeros entered for periods that saw no activity, or the timeline is distorted. And the rate produced is a periodic rate: a monthly or quarterly solution must be compounded to an annual figure, not simply multiplied.

The result is a dollar-weighted average of the returns earned in each subperiod, where each subperiod's weight depends on how much capital was actually invested during it. A period in which the account held a large balance contributes heavily to the solution; a period in which the balance was small barely moves it. This is why two investors holding an identical fund over an identical horizon, and therefore experiencing identical fund performance, can report materially different money-weighted returns.

The consequence is that the measure blends two distinct effects that cannot be separated after the fact: the return generated on invested capital and the allocation decision of when to put capital in and take it out. It answers what the investor's money earned, which is precisely why it is informative about the investor's experience and unreliable as a comparison of managers who received cash on different schedules.

Wealth management reporting relies on it whenever the question is what a specific client actually earned, since clients fund and withdraw on their own schedule. Retirement account statements, pension contribution analyses and any evaluation of a savings plan use dollar-weighted logic for the same reason.

In private markets, the since-inception internal rate of return is the standard headline figure for closed-end funds. The general partner calls capital when opportunities arise and returns it when assets are exited, so the timing of flows is part of the investment decision rather than noise imposed by outside investors. Practitioners pair the since-inception IRR with multiples such as total value to paid-in capital, because an IRR computed over a short early period, or one dominated by a single quick exit, can look spectacular without much value having been created. Interim IRRs also depend heavily on how unrealized holdings are valued.

Expect to be handed a short series of purchases, sales, dividends and an ending price and asked for the money-weighted return. Set out the timeline, keep the sign convention consistent, include the terminal value as a final inflow, and let the calculator solve. Verify that the answer is plausible: it should fall inside the range of the individual subperiod returns and lean toward the periods in which the balance was largest.

Equally important is the comparison question. Given the same data, you should be able to compute both the money-weighted and the time-weighted return, state which is appropriate for judging the manager and which describes the investor's outcome, and explain the direction of the gap from the timing of the flows. Also be alert that unusual patterns of sign changes in a cash flow series can produce multiple internal rates of return or none at all.