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.
You judge a portfolio against a benchmark in two steps. First you calculate the portfolio's own return. Once the client adds or withdraws cash, you compare the money-weighted and time-weighted rates of return, because they answer different questions. Then you calculate the value and the returns of the index it is measured against.
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.
Common mistakes
- Reporting MWR for an open-ended fund. Clients, not the manager, control an open-ended fund's cash flows, so 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 understates the cumulative return, and it is off by about 2.57 percentage points.
- Forgetting to subtract 1. After multiplying, candidates report 1.3623 instead of 36.23%, 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. GIPS generally requires it for manager comparison, with MWR allowed only where the manager controls cash flows.
- Price-weighted (DJIA): sum of prices divided by a divisor. After a split, new divisor = post-split sum of prices / pre-split index value.
- Market-cap weighted (S&P 500): index value = total (usually float-adjusted) market cap / divisor. 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 weighting gives the highest-price stock the largest weight, and cap weighting gives the largest company the largest weight. Equal weighting gives every stock the same target weight, which lifts small companies relative to cap weighting.
The full lesson (about 3,733 words, 25 min read) adds 10 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- benchmarking returns
Browse all free CFA Level I lessons or jump into free CFA Level I practice questions.