Time-Weighted vs Money-Weighted Return (CFA Level 1)

Two portfolios, same manager, same holdings, same period — and two different reported returns. Both are correct. They are answering different questions, and Level 1 tests whether you know which question is being asked.

The core distinction

Time-weighted return (TWR) measures how one unit of currency invested at the start would have grown, regardless of what money came in or went out along the way. It is the return on the strategy.

Money-weighted return (MWR) is the internal rate of return on the portfolio's actual cash flows. It reflects what the investor actually experienced, given the amounts they had invested at each point.

The difference exists entirely because of external cash flows — contributions and withdrawals the manager does not control. If no money enters or leaves during the period, the two are identical.

How each is calculated

Time-weighted return

Break the period into sub-periods at every external cash flow. Compute the holding period return for each sub-period. Link them geometrically:

TWR = [(1 + R₁) × (1 + R₂) × ... × (1 + R_n)] − 1

Because each sub-period return is computed on the portfolio value at the start of that sub-period, the size of any cash flow is irrelevant to the result. That is the whole point.

For multi-year figures, annualise by taking the nth root of the linked product.

Money-weighted return

Set the present value of all cash inflows equal to the present value of all outflows and solve for the discount rate. It is an IRR calculation, and on the exam it is done on your calculator's cash flow function.

Sign convention matters: money going into the portfolio is a negative cash flow from the investor's perspective; withdrawals and the ending value are positive.

A worked example

An investor puts $100 into a fund at the start of year 1. The fund returns 50% in year 1, so the position is worth $150. Pleased, the investor adds $900 at the start of year 2, giving a $1,050 portfolio. Year 2 returns −20%.

Time-weighted return: (1.50 × 0.80) − 1 = 1.20 − 1 = +20% over two years, or about 9.5% annualised.

Money-weighted return: the investor had $100 exposed to the good year and $1,050 exposed to the bad year. Ending value is $840, against $1,000 contributed. The IRR is substantially negative.

Both are right. The manager delivered a positive two-year strategy return. The investor lost money, because they committed most of their capital immediately before the loss.

This asymmetry is the entire subject, and exam questions are built to produce exactly this kind of divergence.

Which is higher, and why

The relationship is predictable once you see the mechanism, and questions frequently ask you to state it without calculating.

• Large contribution before a strong period → MWR > TWR. More money was exposed to the good returns.
• Large contribution before a weak period → MWR < TWR. More money was exposed to the losses — the example above.
• Large withdrawal before a strong period → MWR < TWR. Less money captured the gains.
• No external cash flows → MWR = TWR.

The rule underneath all four: money-weighted return rewards good timing of cash flows and punishes bad timing. Time-weighted return is blind to timing entirely.

When to use which

Use time-weighted return to evaluate a manager. A manager typically does not control when clients add or withdraw money. Judging them on money-weighted return would credit or blame them for decisions they did not make. This is why time-weighted return is the standard for performance presentation and why it underpins the GIPS standards — comparability across managers requires a measure independent of client cash flow behaviour.

Use money-weighted return when the manager controls the cash flows. Private equity is the standard example: the general partner decides when to call capital and when to distribute it, so timing is part of their skill and should be reflected in the measure. IRR is the industry convention in private markets for exactly this reason.

Use money-weighted return to measure an investor's own experience. If the question is "what return did this person actually earn on their money", it is money-weighted.

Recognition cues in a question

• "Evaluate the manager's performance" or "compare with a benchmark" → time-weighted
• "The investor's return" or "the return on the client's account" → money-weighted
• Any mention of GIPS or performance presentation → time-weighted
• Private equity, capital calls, distributions → money-weighted
• "The manager controls the timing of cash flows" → money-weighted

The behavioural footnote worth knowing

Across the industry, investors' money-weighted returns tend to lag the time-weighted returns of the funds they hold. The reason is timing: money flows in after good performance and out after bad, so more capital is exposed to the periods that follow strong runs.

That is representativeness bias expressed as a number — performance chasing, treating a short run of returns as a stable property. The gap between an investor's return and their fund's return is, in effect, the measurable cost of the bias, which is why the two topics reappear together at Level 3.

Common errors

Breaking sub-periods at the wrong points. Sub-periods are defined by external cash flows — money entering or leaving the portfolio. Dividends reinvested inside the portfolio are not external flows and do not create a break.

Adding sub-period returns instead of linking them. Returns compound. They are multiplied as (1 + R) factors, not summed.

Sign errors in the IRR. A contribution is a negative cash flow. Ending value is positive. Getting a sign wrong produces a plausible but wrong IRR.

Assuming higher MWR means better management. It usually means better cash flow timing by the investor, which the manager may have had nothing to do with.