Money-Weighted Return (MWR)

A money-weighted return is a measure of investment performance that keeps the effect of cash-flow timing rather than removing it, so the answer describes the investor's own money. The Global Investment Performance Standards, published by CFA Institute, define it as "the return for a period that reflects the change in value and the timing and size of external cash flows." It is also called a dollar-weighted return, and in its exact form it is an internal rate of return, meaning the one constant rate that reconciles every cash flow with the ending balance.

Its counterpart is the time-weighted return, which deliberately negates cash-flow effects so that funds and managers can be compared on equal terms. Neither measure is a corrected version of the other. A statement showing both is reporting the performance of the investment and the performance of the account, which are separate facts.

Think of an account as a series of dated cash amounts: money in on the days it went in, money out on the days it came out, and the closing balance treated as a final withdrawal. The money-weighted return is the discount rate that makes those amounts balance. There is no closed-form solution, so software solves for it by trial and improvement, which is why this number appears on a statement rather than being something a reader computes by hand.

Two approximations are common. The simple Dietz method assumes every flow happened at the midpoint of the period. The Modified Dietz method weights each flow by the fraction of the period it was actually invested, which is far more accurate when the flows are lumpy, and it is the version most performance systems use for short periods. The exact internal rate of return is preferred when the flows are large relative to the balance.

Professional reporting treats the two measures asymmetrically, and the reason is control. Under the 2020 GIPS Standards for Firms, a compliant firm "must present time-weighted returns unless certain criteria are met, in which case the firm may present money-weighted returns." Money-weighted reporting is permitted only if the firm "has control over the external cash flows" and the portfolio or fund is closed-end, has a fixed life, has a fixed commitment, or has "illiquid investments as a significant part of the investment strategy." Where a manager decides when to call and return capital, as in private equity or private credit, the timing is part of the manager's job and belongs in the score. Where the client decides, it does not. The same standards require that a money-weighted return be calculated as an annualized since-inception figure, which is why private-market track records are quoted since inception rather than year by year.

For an individual, the useful reading is diagnostic. A money-weighted return well below the time-weighted return over the same window usually means large amounts arrived shortly before weak stretches. That can be pure coincidence, since most people contribute on a payroll schedule they did not choose, and it can also be the signature of buying after a run. The number tells you the pattern existed. It does not tell you which of the two caused it.

Every cash flow is dated, weighted by how long it was invested, and the return is the rate that reconciles the whole set with the ending balance.

A hypothetical illustration using the Modified Dietz method, chosen because the arithmetic can be checked by hand. On 1 January an investor opens an account with $10,000. On 1 July she adds another $10,000. On 31 December the account is worth $21,000.

The gain is the ending value minus everything put in: $21,000 minus $20,000, which is $1,000. The weighted average capital is the starting balance plus each flow multiplied by the fraction of the year it was invested: $10,000 plus $10,000 times six twelfths, which is $15,000. The money-weighted return is $1,000 divided by $15,000, or 6.67 percent.

Now suppose the account had been worth $10,800 on 30 June, just before the deposit. The first half returned 8 percent, and the second half took $20,800 to $21,000, a gain of about 0.96 percent. Linking those two gives a time-weighted return of about 9.04 percent for the year. The investment did 9.04 percent; her money did 6.67 percent. The difference is entirely the fact that half her capital only arrived in time for the weaker half of the year.

Strengths

• It answers the question an individual investor is actually asking, which is what happened to their money.
• It is the right measure wherever the manager, not the client, controls the timing of capital, which is why private-market funds report it.
• It exposes contribution-timing patterns that a fund-level figure hides completely.

Limits

• It is useless for comparing managers or funds, because a large part of the answer is a decision the manager did not make.
• It is sensitive to a single large flow, so one deposit near a turning point can dominate a whole year's figure.
• It cannot be verified by hand from a year-end statement, since it needs the date and size of every flow.
• Reading a low money-weighted return as a personal failure is a mistake as often as it is a lesson, because most contributions follow a payroll schedule rather than a view about the market.