The Modified Dietz Return

Computing a true time-weighted return requires a portfolio valuation on every single day money moves in or out, which many back-office systems simply don't have for older periods. The Modified Dietz method is the practical workaround: it approximates the time-weighted return using only the beginning value, ending value, and the size and date of each cash flow during the period, weighting each flow by the fraction of the period it was invested for.

$$R = \frac{V_1 - V_0 - \sum_i CF_i}{V_0 + \sum_i w_i \, CF_i}$$

In plain English: the numerator is the gain net of contributions and withdrawals, and the denominator is the starting capital plus each cash flow weighted by how much of the period it participated in — a flow on day one of a 30-day month gets weight $w_i = 1$, a flow on the last day gets weight close to $0$.

Worked example. A portfolio starts the month at $1,000,000, receives a $100,000 deposit exactly halfway through a 30-day month, and ends at $1,150,000. The deposit's weight is $w = 15/30 = 0.5$. So $R = (1{,}150{,}000 - 1{,}000{,}000 - 100{,}000) / (1{,}000{,}000 + 0.5 \times 100{,}000) = 50{,}000 / 1{,}050{,}000 \approx 4.76\%$ for the month.