The formula is one line and the Excel is two functions. The trap is what the number measures when a large flow lands mid-period.
The Modified Dietz return is the period's gain, ending value less beginning value less net external flows, divided by the beginning value plus each flow weighted by the share of the period it was invested. On an illustrative 200m mandate that receives 50m with 31 of 92 days left, it gives 3.25 per cent for the quarter, against a true time-weighted return of 1.52 per cent. The 1.73 point difference is the client's timing, not the manager's skill.
Worked in full in Asset Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Modified Dietz approximates the return of a period without valuing the portfolio on the day of each cash flow. The numerator is the investment gain, so contributions are taken out of it and withdrawals added back. The denominator is the average capital at work: the opening value plus each flow multiplied by its weight, the fraction of the period remaining after it arrived.
The same weighting applied to a private fund's annual accounts, where the gain comes from the statement of operations rather than from market values, is worked in how to calculate a private fund's annual return from its accounts. This page is about the other use: measuring a mandate between valuations, and what a large flow does to the answer.
RMD = (EMV − BMV − Σ CFi) / (BMV + Σ wi × CFi)
wi = (CD − Di) / CD, where CD is the days in the period and Di the days elapsed when flow i arrives
Excel: =(EMV-BMV-SUM(CF))/(BMV+SUMPRODUCT(CF,(CD-Di)/CD))
A fictional pension scheme runs a 200m equity mandate. The market falls through July and August, the scheme transfers 50m at the close of 30 August, and the market then rallies through September. The manager holds the index throughout, so any return difference is purely arithmetic.
| Input | Value |
|---|---|
| Beginning market value, 1 July | 200.0 |
| Return 1 July to 30 August | -6.0% |
| Contribution at the close of 30 August | 50.0 |
| Return 31 August to 30 September | 8.0% |
| Days in the quarter / days elapsed at the flow | 92 / 61 |
| Ending market value, 30 September | 257.04 |
The ending value is (200.0 × 0.94 + 50.0) × 1.08: the mandate is worth 188.0 just before the flow, 238.00 after it, and 257.04 at the quarter end.
Step 1, the gain. Take the flow out of the change in value: 257.04 less 200.0 less 50.0 is a gain of 7.04. Forgetting this step and reporting (257.04 − 200.0) / 200.0 gives 28.52 per cent, which is a statement about the client's bank transfer.
Step 2, the weight. The flow arrived at the close of day 61, so it was invested for the remaining 31 days of 92. Its weight is 31 / 92 = 0.3370, and it counts as 16.848 of average capital.
Step 3, the return.
Denominator = 200.0 + 0.3370 × 50.0 = 216.848
RMD = 7.04 / 216.848 = 3.2465%, or 3.25%
True TWR = 0.94 × 1.08 − 1 = 1.0152 − 1 = 1.52%
The true time-weighted return needs the valuation on 30 August, which Modified Dietz exists to avoid. Here we have it, because the case was built from it, and the two methods disagree by 1.73 points in a single quarter.
Modified Dietz is a money-weighted measure. It asks what the average capital earned, and in this quarter a quarter of the capital arrived at the bottom and caught all of the 8.0 per cent rally without suffering any of the 6.0 per cent fall. The time-weighted return removes the flows entirely: it is what one unit of money held from 1 July to 30 September earned, which is what the manager controlled. The manager did not choose when the scheme sent its 50m, so the 1.73 points belong to the scheme, not to the manager's track record.
Run the same market the other way round, a rise of 8.0 per cent before the flow and a fall of 6.0 per cent after it, and the gain shrinks to 0.04 and Modified Dietz to 0.02 per cent. The time-weighted return is 1.52 per cent in both orders. The money-weighted gap and the reasons it persists over years are worked in why the money-weighted return trails the time-weighted return.
| Flow | % of opening value | Ending value | Modified Dietz | True TWR | Gap, points |
|---|---|---|---|---|---|
| None | 0 | 203.04 | 1.52% | 1.52% | 0.00 |
| Contribution 10.0 | 5 | 213.84 | 1.89% | 1.52% | 0.37 |
| Contribution 20.0 | 10 | 224.64 | 2.24% | 1.52% | 0.72 |
| Contribution 50.0 | 25 | 257.04 | 3.25% | 1.52% | 1.73 |
| Contribution 100.0 | 50 | 311.04 | 4.72% | 1.52% | 3.20 |
| Withdrawal 50.0 | -25 | 149.04 | -0.52% | 1.52% | -2.04 |
The error is roughly proportional to the flow. With no flow, Modified Dietz is exact. A withdrawal before a rally does the reverse: the client took money out at the bottom and the measure shows a loss in a quarter in which the portfolio itself made 1.52 per cent. This is why the GIPS standards require a valuation at every large cash flow, with the threshold set by the firm, and why many performance teams value at every external flow and chain-link the sub-period returns. A flow of 10 per cent of the portfolio already moves this quarter by 0.72 point.
The chain-linking, the Dietz weights and the money-weighted solve for a five-year mandate are laid out cell by cell in the free workbook for this case.
Strictly it is a money-weighted return: it weights each flow by the time it was invested, so it approximates the internal rate of return of the period. It is used as a proxy for time-weighted return when sub-periods are short and flows small. In the worked quarter, a 50m flow equal to 25 per cent of the opening value pushes it to 3.25 per cent against a true time-weighted 1.52.
Simple Dietz assumes every flow arrived at the middle of the period and gives it a weight of 0.5. Modified Dietz uses the actual fraction of the period remaining after the flow. On the worked quarter the 50m arrived with 31 of 92 days left, a weight of 0.3370, so Modified Dietz gives 3.25 per cent and simple Dietz 3.13 per cent.
Whenever a flow is large relative to the portfolio, because the error grows with flow size. In the worked quarter the gap to the true time-weighted return is 0.37 point for a flow of 5 per cent of opening value, 1.73 points at 25 per cent and 3.20 points at 50 per cent. The GIPS standards require a valuation at each large cash flow, as the firm defines it.
This article is one calculation from Asset Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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