The Modified Dietz Method
IRR and XIRR are accurate but require a computer's iterative calculation. In the era before that, the Modified Dietz method was how people found a fairly accurate return even by hand.
What is the Modified Dietz method
The Modified Dietz Method is a way to approximate the return by reflecting the 'timing' of the cash (deposits and withdrawals) that came in and went out during the investment period as weights.
The core formula is this. Return = (ending value − starting value − net cash flow) ÷ (starting value + weighted cash flow). The numerator means 'the money purely gained,' and the denominator means 'the average capital actually put to work.'
'Time weighting' is the key
The simple Dietz method lumps all deposits and withdrawals together as if they occurred 'in the middle of the period.' The Modified Dietz method weights each cash flow by 'how many days during the period it was invested.'
For example, money put in early in a year was invested for a long time so its weight is large (close to 1), while money put in at year-end was barely invested so its weight is small (close to 0). Doing this produces a result quite similar to XIRR with a single division, without iterative calculation.
The Modified Dietz method is one of the return-calculation methods recognized by GIPS (Global Investment Performance Standards), the international performance standard.
When it's useful
Because the Modified Dietz method is light to compute and intuitive, it has long been used in funds, pensions, and the like to quickly produce monthly and quarterly performance.
That said, it has the limit of being an approximation. When volatility during the period is very high or cash flows are concentrated at particular times, the error versus XIRR can widen. You can split usage: XIRR for precise individual performance, and Modified Dietz for a quick approximation.
よくある質問
Q. Which is more accurate, the Modified Dietz method or XIRR?
XIRR is more accurate. XIRR discounts each cash flow with exact compounding and solves the equation, whereas the Modified Dietz method approximates this with linear (proportional) weighting. That said, over short periods with small fluctuations, the difference between the two is negligible.
Q. Why is this method still used today?
Because it's simple to compute, it can produce performance for large numbers of accounts and funds consistently and quickly, and the results are easy to verify and reproduce. It's still used as a standard in institutions' performance reporting.
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