Two portfolios earn identical percentage gains. One looks great, one looks awful. The choice between money-weighted and time-weighted return decides which is which, and the weighting scheme an index uses can flip the sign of a market's reported return.
The two worked examples below calculate and compare the money-weighted and time-weighted rates of return on one identical set of cash flows, and each rate answers a different question.
The money-weighted return is the internal rate of return on every dollar that flows into and out of a portfolio. Initial value and contributions are outflows. Withdrawals and ending value are inflows. Solve for the rate that sets net present value to zero.
KEY: MWR rewards good timing and punishes bad timing. A client who adds money before a strong period lifts MWR. A client who adds money before a drawdown lowers MWR, even if the manager picked great securities.
The time-weighted return measures compound growth per dollar invested at the start of each sub-period, regardless of when the client adds or withdraws cash.
Common mistakes
- Reporting MWR for an open-ended fund. GIPS-compliant reports require TWR. Trap: MWR makes a mutual fund manager look good or bad based on client timing, not skill.
- Geometrically linking arithmetically. TWR is (1.22)(1.1167) − 1, not the sum 22% + 11.67% = 33.67%. The arithmetic answer is off by ~1.4 percentage points.
- Forgetting to subtract 1. After multiplying, candidates report 1.3624 instead of 36.24%, or 1.1672 instead of 16.72% annualized.
Bottom line
- MWR = IRR of all portfolio cash flows. Reflects the investor's dollar-weighted experience and rewards or punishes the manager for client timing decisions.
- TWR geometrically chains sub-period returns, stripping out cash flow timing. It is the GIPS-required measure for manager comparison.
- Price-weighted (DJIA): sum of prices divided by a divisor adjusted for splits and constituent changes. High-price stocks dominate.
- Market-cap weighted (S&P 500): weight proportional to (usually float-adjusted) market cap. Rebalances passively as prices move.
Exam shortcut
For MWR vs TWR: "Money follows money (timing matters), Time strips time (timing removed)." Manager evaluation = TWR. Investor experience = MWR. For weighting, remember PEMF: Price, Equal, Market-cap, Fundamental. Price-weighted is dominated by the highest-price stock; cap-weighted by the largest company; equal-weighted by the smallest names. On a price-weighted index, just sum the prices and divide by the divisor. Splits adjust the divisor, not the index level.
The full lesson (about 1,851 words, 12 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- benchmarking returns
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