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Performance Measurement: Time-Weighted vs. Money-Weighted Return

One-line definition

Time-weighted return (TWR) measures a manager's skill independent of when clients moved money in or out; money-weighted return (MWR, also called the dollar-weighted return or IRR) measures the investor's actual realized return on the capital they actually had at risk. They diverge whenever cash flows happen mid-period, and the divergence isn't a bug in either one — they're answering different questions.

Formula

TWR — geometrically link each sub-period's return (a sub-period ends every time an external cash flow happens): TWR = (1+r_1) * (1+r_2) * ... * (1+r_n) - 1

This repo already has this: pm.returns.cumulative_return computes exactly this geometric link — TWR isn't a new calculation, it's the existing function applied to sub-periods split at each cash flow.

MWR — the constant periodic rate r that sets the net present value of every cash flow (including the starting investment and ending value) to zero: sum(cash_flow_i / (1+r)^time_i) = 0

pm.returns.money_weighted_return(cash_flows, times) solves this numerically (bisection), since there's no closed form for more than two cash flows.

Why PMs care

GIPS (the industry-standard performance-presentation rules) requires time-weighted return for composite reporting precisely because it isolates manager skill from client-driven cash-flow timing — a manager shouldn't be credited or blamed for a client depositing right before a rally or right before a crash. But TWR is the wrong number for an investor asking "what did I actually earn on my money?" — that question is answered by MWR, which is exactly as sensitive to timing and size of contributions as the investor's own bank balance is. A PM reporting composite performance uses TWR; a PM explaining a specific client's actual realized experience uses MWR — conflating the two is a common, misleading mistake.

Worked example

The canonical case where they sharply diverge: an investor starts with $100. By the end of year 1, the portfolio doubles to $200 (period-1 return = +100%) — the investor then contributes another $200, bringing the total invested to $400. By the end of year 2, the portfolio falls back to $200 (period-2 return = -50%).

TWR = (1+1.00) * (1-0.50) - 1 = 0% — a wash, using cumulative_return.

MWR: cash flows of -100 (t=0, initial investment), -200 (t=1, additional contribution), +200 (t=2, ending value) — solving money_weighted_return gives r ≈ -26.79% (tests/test_returns.py::test_money_weighted_return_classic_twr_divergence_example).

The manager's skill (as TWR sees it) was neutral across the two years. But the investor's actual experience was strongly negative, because they had four times as much capital exposed during the losing year as during the winning one — MWR captures exactly that, TWR by design does not.

Why full GIPS composite construction isn't implemented in src/pm

GIPS composite requirements — asset-weighting individual portfolio returns into a firm-wide composite, minimum-size and significant-cash- flow policies, verification procedures, and the disclosure/presentation rules themselves — are a compliance and process framework layered on top of the return calculations above, not a new formula. cumulative_return and money_weighted_return are the actual computational core GIPS requires; the rest is organizational policy this repo's "small transparent function" style doesn't attempt to encode.

Common mistakes

  • reporting MWR when GIPS (or a mandate) requires TWR, because MWR "looks like" the more intuitive number — it answers a different question and isn't a substitute
  • assuming TWR and MWR only diverge in extreme cases — any mid-period cash flow at all creates some divergence; the classic example above is chosen to make it dramatic, not because dramatic divergence is rare
  • treating money_weighted_return's brentq solve as guaranteed to converge for any cash-flow pattern — it assumes a single real root (true for the typical one-sign-change pattern of contributions then a final withdrawal), which isn't guaranteed for cash flows with multiple sign changes

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