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Contrast money-weighted with time-weighted rates of return

CFA® Level I · Quantitative Methods · Benchmarking Returns · QM.3.c

The idea

A money-weighted return is the internal rate of return of the portfolio's cash flows, so it is affected by when the investor added or withdrew money. A time-weighted return chains the returns of each sub-period and is unaffected by those flows. The distinction decides what is being measured: the manager does not control deposits and withdrawals, so time-weighted return is the fair basis for judging them and is what performance standards require. The investor's own experience, however, depends on having money invested when returns were good, and that is what the money-weighted return captures.

Formulas

Time-weighted rate of return

time-weighted return = (1 + r₁) × (1 + r₂) − 1

r₁, r₂
the holding period return of each sub-period, cut at every external cash flow

The manager's return, because breaking the period at each deposit and withdrawal removes the effect of when the client added money. The money-weighted return is an internal rate of return and does include it, which is why it is the client's return rather than the manager's.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which return measure is affected by the timing and size of client cash flows?

  1. The money-weighted return — correct
  2. The time-weighted returnWhy not: It is built to be immune to them: the period is broken at every cash flow and the sub-period returns chained.
  3. Neither is affected by cash flowsWhy not: One of them is, by design. The money-weighted return is an IRR over the actual flows, so their size and timing are inputs to it.

The money-weighted return is an internal rate of return over the actual cash flows, so a large deposit before a strong period raises it. The time-weighted return removes that effect.

A harder one

Why do performance standards require managers to report time-weighted returns?

  1. They are always higher than money-weighted returnsWhy not: Neither is systematically higher. Which one leads depends on whether clients added money before good periods or bad ones.
  2. They isolate the manager's decisions from client cash flows the manager does not control — correct
  3. They are simpler to calculateWhy not: They are more work: the period has to be split at every cash flow and the pieces chained. The money-weighted return is a single IRR.

A manager should not be credited or penalised for when clients happened to add money. Chaining sub-period returns removes that influence and makes managers comparable.

The hardest tier

An investor adds a large sum just before a sharp market fall. How will their money-weighted return compare with the fund's time-weighted return?

  1. Higher, because more capital was at workWhy not: More capital was at work during a *fall*, which magnifies the loss rather than the gain.
  2. Identical, because both measure the same portfolioWhy not: Same portfolio, different questions. One asks how the holdings performed, the other how this investor's money fared given when it arrived.
  3. Lower, because more capital was exposed to the poor period — correct

The money-weighted return weights each sub-period by the money invested in it, so a large balance during the fall drags it below the time-weighted figure. The fund's stated return is unchanged; the investor's experience is not.

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