2

When money moves in or out

The simple formula breaks the moment money moves. Say a client adds 200,000 during the month. The account grows by 280,000, but the manager only earned 80,000 of that. The rest was just a deposit.

There are two fixes. First, take the flow out of the gain. Second, give the flow credit only for the days it was actually invested. Money that arrives on day 10 of a 30-day month worked for 20 days, so it counts as two thirds of a full-month balance. This is the Modified Dietz method.

RMD = EMV − BMV − CFBMV + w × CFw = (days in month − day of flow) ÷ days in month
In plain termsIf a friend drops 200 into your piggy bank, you didn't earn 200. And if they drop it in on the last day of the month, it had no time to earn anything for you.

Place the cash flow

Move the flow through the month and compare three ways of computing the return.

Day 0Day 15Day 30

Ignores the flow
Counts the deposit as profit
Subtracts the flow
Right gain, but ignores timing
Modified Dietz
Right gain, right timing
For practitionersModified Dietz approximates a true time-weighted return, and the approximation weakens when a flow is large relative to assets and markets move sharply in the month. Most firms set a large-cash-flow threshold (often around 10% of assets) above which they revalue on the flow date and chain the sub-periods. For composites, GIPS has required valuation at large external flows since 2010, and daily valuation makes the question moot. Also fix a convention: start-of-day and end-of-day flow treatment shift the weight by a day.

All numbers are illustrative. The models are simplified for teaching: annual coupons, Black-Scholes options, simplified fee mechanics and no intra-period trading. Real systems add transaction-based returns, daily valuation, tax and corporate action processing, and reconciliation to the official TWR.