Money-weighted vs time-weighted return: 18.02% or 21.83%

Quantitative Methods·August 22, 2026·5 min read

An investor buys one share at 50, adds a second share a year later at 65, and sells both at 70 after the second year, collecting a 2 per share dividend each year. The money-weighted return is 18.02% a year. The time-weighted return is 21.83% a year. Same portfolio, same dividends, two different answers, and a question asking how well the manager did wants the second one.

The two measures answer different questions

The money-weighted return is the portfolio's internal rate of return. Set the present value of every cash flow to zero and solve for the discount rate. Because a bigger balance dominates the calculation, the measure loads the periods when the most money was invested, and the investor is usually the one who decided when that money arrived.

The time-weighted return ignores the size of the balance entirely. Break the horizon at every external cash flow, compute a holding period return inside each subperiod, then chain them geometrically.

Time-weighted return = [(1 + HPR_1) × (1 + HPR_2) × ... × (1 + HPR_n)] − 1

Every subperiod gets the same weight in that product no matter how much money sat in the account. That is the whole point. A client who wires in a deposit the week before a bad quarter has not made the manager worse at picking securities, so the measure used to judge the manager should not react to the deposit at all.

Working the 50 and 65 example

Year one holds one share bought at 50. It ends the year worth 65 with a 2 dividend already in hand. Year two holds two shares worth 130 at the start, sold for 140 with 4 of dividends collected.

HPR_1 = (65 + 2 − 50) / 50 = 17 / 50 = 34.00%

HPR_2 = (140 + 4 − 130) / 130 = 14 / 130 = 10.77%

Linked return = (1.3400 × 1.1077) − 1 = 48.43% over two years

Time-weighted return = (1.4843)^(1/2) − 1 = 21.83% a year

Now the money-weighted version. The cash flows are 50 out at time zero, 63 out at the end of year one (65 paid for the share, less the 2 dividend received), and 144 in at the end of year two (140 from the sale plus 4 of dividends).

−50 − 63 / (1 + r) + 144 / (1 + r)² = 0, so r = 18.02%

Both numbers are correct. The gap opens because the second share was bought right before the weaker year: year two put 130 to work against a 10.77% return, while year one had only 50 riding on a 34.00% one. Weighting by money penalises the 34.00% year for being small. The money-weighted return reports what the investor's wallet did. The time-weighted return reports what a unit of money left alone would have done.

The distractors on either side

Averaging the two holding period returns gives (34.0000% + 10.7692%) / 2 = 22.38%, which sits close enough to 21.83% to look like a rounding difference rather than a wrong method. It is the arithmetic mean of returns being used where the geometric mean belongs, and the two only coincide when every subperiod return is identical.

The other trap is quoting 48.43% as the answer. That is the correct linked return, but it covers two years. A question asking for an annual figure wants the square root taken.

Then there is the reversal: computing the money-weighted return correctly and offering it as the manager's performance. The GIPS standards are voluntary, but a firm claiming compliance with them must present time-weighted returns, and may present money-weighted returns instead only when it controls the external cash flows and the portfolio is closed-end, has a fixed life, has a fixed commitment, or holds illiquid investments as a significant part of the strategy. Both halves have to hold. Private-market strategies are the common home for that exception; a separately managed account where the client deposits and withdraws at will fails the control test before the rest is even reached.

Quick reference

Read the verb before touching the calculator. "Evaluate the manager" and "calculate the return earned by the investor" point at different formulas, and both formulas are usually sitting in the answer choices. The arithmetic is short; identifying which measure the question asked for is the part worth slowing down on.

The same reflex shows up in two-asset portfolio risk, where averaging the inputs feels natural and is wrong for a structural reason rather than an arithmetic one.

Charter5m is an independent study tool and is not affiliated with CFA Institute. CFA Institute does not endorse, promote, or warrant the accuracy or quality of this content. CFA® is a registered trademark of CFA Institute.