Modified Dietz vs true time-weighted return: when the approximation is fine, and when it lies

True time-weighted return has one inconvenient requirement: a portfolio valuation on every date money moves in or out. Most personal investors do not have that. Modified Dietz exists to fill the gap — it estimates a period's return by weighting each cash flow for the fraction of the period it was invested, so it needs no valuation at each flow. It is the workhorse beneath institutional performance reporting. It is also, used carelessly, capable of being wrong by eighteen percentage points. The difference between those two outcomes is worth understanding precisely.

This is the technical companion to our cornerstone on how investment return is actually calculated, and the written counterpart to our Modified Dietz calculator. The register here is deliberately rigorous; the conclusions are practical.

The formula, every term defined

The Modified Dietz return for a period is:

            EMV − BMV − C
R_MD  =  ─────────────────────
           BMV + Σᵢ (wᵢ · Cᵢ)

            EMV − BMV − C
R_MD  =  ─────────────────────
           BMV + Σᵢ (wᵢ · Cᵢ)

            EMV − BMV − C
R_MD  =  ─────────────────────
           BMV + Σᵢ (wᵢ · Cᵢ)

• BMV is the beginning market value; EMV the ending market value.

• C is the net external cash flow over the period (Σ Cᵢ), contributions positive, withdrawals negative.

• Cᵢ is the i-th external flow.

• wᵢ is the day-weight of flow i — the fraction of the period it was invested: wᵢ = (TD − tᵢ) / TD, where TD is the total days in the period and tᵢ the days from the period start to the flow.

The numerator is the gain net of contributed capital. The denominator, BMV + Σ wᵢ·Cᵢ, is the average capital employed over the period — the figure that makes the method work without interim valuations.[1] One convention to fix and keep: if a flow is treated as occurring at the start of its day it earns one extra day of weight (wᵢ = (TD − tᵢ + 1)/TD). State which you use; do not mix them. (Modified Dietz weights each flow by its actual day-count; the older Original Dietz assumed every flow occurred at the period midpoint — i.e. every wᵢ = ½ — which is simply the special case of Modified Dietz with no day-weighting.)

Its dual role — the source of most confusion

Modified Dietz does two different jobs, and conflating them is where people go wrong.

As a building block for time-weighted return. Compute a Modified Dietz return for each short sub-period — delineated by month-ends or by large flows — and geometrically link them. This "linked Modified Dietz" is classified as a time-weighted method and is how institutional-grade TWR is produced in practice when daily valuations are unavailable.[1] It is an approximation of true TWR, not an identity: true TWR requires actual valuations at each flow, which linking estimates instead.

As a money-weighted proxy. Run Modified Dietz over a single long period instead of chaining short ones, and it drifts toward the money-weighted answer — because the average-capital denominator bakes in how much money was present and when. Over one long window it behaves less like TWR and more like a dollar-weighted return.

Same formula, two jobs. Chained over sub-periods it approximates the investment's return; run over one long period it approximates the investor's. Knowing which job you are asking it to do is the whole discipline.

When the approximation is good — and when it lies

Modified Dietz uses simple-interest (linear) weighting. So it converges to true TWR when flows are small relative to the portfolio and intra-period returns are low (low volatility, short sub-periods). It diverges materially when a large flow coincides with large market moves inside the period.[2] Two verified illustrations make the range concrete:

In the good case the approximation is within a rounding error. In the poor case — a portfolio-doubling flow landing amid a violent reversal — Modified Dietz reports 22.67% against a true 4.00%, an error of more than eighteen points.[2] The lesson is not "Modified Dietz is unreliable." It is that the approximation degrades exactly when a large flow meets a volatile period, and that is precisely when you should either obtain a valuation at the flow date (and compute true TWR) or break the period at the flow (and link).

One edge case worth a guard rail: a large early outflow can drive the average-capital denominator toward zero or negative, producing a nonsensical figure. Any serious implementation handles that exception explicitly rather than returning the arithmetic.

A worked example on a realistic portfolio

Take the twelve-month rand portfolio from our cornerstone, treated as a single Modified Dietz period (28 Feb 2026 to 28 Feb 2027, 365 days):

• BMV = R500,000.00; EMV = R897,014.02

• C = net external flow = +R310,000 in contributions − R80,000 withdrawal = +R230,000.00

• Σ wᵢ·Cᵢ (each flow weighted by its remaining fraction of the year) = R150,602.74

• Average capital = 500,000 + 150,602.74 = R650,602.74

• R_MD = (897,014.02 − 500,000 − 230,000) / 650,602.74 = 167,014.02 / 650,602.74 = 25.6707%

That 25.6707% is instructive precisely because of where it lands. The same portfolio's true time-weighted return is 19.43%, and its money-weighted return (XIRR) is 25.90%.[3] The single-period Modified Dietz figure sits right next to the money-weighted number and far from the true TWR — a textbook demonstration of the "single long period drifts toward money-weighted" behaviour. Had this same portfolio's months been computed as separate Modified Dietz sub-periods and linked, the result would instead approximate the 19.43% TWR. One formula, one dataset, two answers — determined entirely by whether you chained sub-periods or ran one long window.

When it matters to you

For a personal investor the practical question is narrow: does the divergence change a decision? If your flows are modest relative to your portfolio and markets were not wild during the period, single-period Modified Dietz is within a fraction of a point of the truth and you can use it without ceremony. If you added or withdrew a large sum during a turbulent stretch, the single-period figure can mislead by enough to matter — and you should either source the valuation and compute true TWR, or chain sub-periods. The Modified Dietz calculator applies the day-weighting correctly and flags when your inputs put you in the territory where the approximation degrades.

The point

Modified Dietz is neither a poor cousin of time-weighted return nor a synonym for it. Chained over short sub-periods it is how true-to-life TWR gets built without daily valuations; run over one long period it quietly becomes a money-weighted proxy. Its accuracy is conditional and predictable: excellent when flows are small and markets calm, poor when a large flow meets a volatile period — 0.04 of a point in the good case, more than eighteen in the bad one. Use it knowing which job you have asked it to do, and knowing the conditions under which its answer is the truth and the conditions under which it merely resembles one.