How This Calculator Works
This tool covers two different questions people mean when they ask for an "average return." The Cash Flow Method tab answers "what rate of return did my own money actually earn," accounting for every deposit and withdrawal on the exact date it happened — mathematically the same calculation as the XIRR function in a spreadsheet. The Multiple Period Returns tab answers a different question: given a series of already-known period returns (say, five years of annual performance), what's the properly compounded average, as opposed to a misleading simple average? Pick whichever matches the numbers you actually have on hand.
Money-Weighted Return: The Cash Flow Formula
The Money-Weighted Rate of Return (MWRR) is defined as the annualized rate r that makes the present value of every cash flow sum to zero — treating your starting balance and any deposits as money going in, and your withdrawals and ending balance as money coming out:
where t = days since the start date ÷ 365, for each cash flow's own date
There's no algebraic shortcut for r here — it has to be solved iteratively (this calculator uses the same bisection search used elsewhere on this site, verified independently against a second, separate root-finding method before shipping). The key detail this formula captures that a simple "ending minus starting, divided by starting" calculation can't: a dollar added early has more time to compound than a dollar added late, and a dollar withdrawn early stops earning sooner — so the exact date of every cash flow genuinely changes the answer.
Money-Weighted vs. Time-Weighted Return
Investment professionals draw a sharp line between two different return metrics, and mixing them up leads to real confusion. Money-Weighted Return (what the Cash Flow tab computes) reflects your actual, personal experience — it's sensitive to your own timing, so adding cash right before a rally lifts your number, and adding cash right before a downturn lowers it. Time-Weighted Return strips that out entirely by breaking the period into sub-periods around each cash flow and linking the sub-period returns together, which is why it's the standard fund managers and GIPS-compliant performance reports use — it isolates investment skill from an investor's contribution timing, which the manager doesn't control. Neither number is "wrong"; they just answer different questions. If you're asking "how did my money actually do," MWRR is the right tool. If you're asking "how good is this manager, independent of when clients added or pulled money," you want TWRR instead.
Arithmetic vs. Geometric Average
When you already have a series of period returns rather than raw cash flows, averaging them correctly still isn't as simple as adding and dividing. The arithmetic mean does exactly that — sum the percentages, divide by the count — but it silently assumes each period's return applies to the same starting amount, which isn't how compounding actually works. The geometric mean instead multiplies each period's growth factor (1 + return) together and takes the appropriate root over the total time elapsed, which is the rate that, applied consistently, would have produced the exact same ending balance from the same starting balance. The geometric mean is also known as the Compound Annual Growth Rate (CAGR) when applied this way, and it's very nearly always the more meaningful number for judging an actual investment's performance.
The geometric mean of a return series is the same number a CAGR calculator returns from just the opening and closing values — useful when you have the two endpoints but not the year-by-year figures.
Volatility Drag: A Worked Example
Suppose an investment returns +50% one year and −50% the next. The arithmetic average is exactly 0% — the two numbers cancel out. But that's not what actually happened to the money: $100 growing 50% becomes $150, and $150 falling 50% becomes $75. The investment actually lost 25% over the two years, and the geometric average correctly shows a loss of roughly 13.4% per year, because a 50% loss requires a 100% gain just to break even — an asymmetry the arithmetic mean can't see.
This gap between the arithmetic and geometric average is called volatility drag (or "variance drain"), and it grows with how much returns swing up and down — two investments with an identical arithmetic average return can end up with meaningfully different real, compounded growth if one is far more volatile than the other. It's a big part of why professional performance reporting leans so heavily on geometric, compounded figures rather than simple averages.
What This Calculator Doesn't Cover
The Cash Flow tab assumes every deposit and withdrawal you enter is complete and accurate — it can't detect a missing transaction, and a single missing or mistimed cash flow can meaningfully shift the solved rate. It also doesn't account for taxes, fees, or currency effects on the underlying cash flows themselves. The Multiple Period Returns tab takes each period's return as already correct and given — if those returns were themselves calculated incorrectly (for example, ignoring intra-period cash flows), the compounded average inherits that error. Neither mode adjusts for inflation; both describe nominal returns unless you've already entered inflation-adjusted figures yourself.
Frequently Asked Questions
What is the Money-Weighted Rate of Return (MWRR)?
MWRR is the annualized rate that reconciles every deposit, withdrawal, and your starting and ending balance — accounting for exactly when each cash flow happened. It's mathematically the same as XIRR in a spreadsheet, and it reflects the actual return your own money experienced, including the effect of your own timing decisions.
Why is my Money-Weighted Return different from the fund's advertised return?
Funds typically advertise a time-weighted return (TWRR), which strips out the effect of when investors added or removed money, so it reflects manager skill alone. Your MWRR includes the effect of your own deposits and withdrawals — adding money right before a rally lifts your MWRR, and adding money right before a downturn lowers it, even though the fund's TWRR wouldn't move at all.
Why are the arithmetic and geometric average ever different?
The arithmetic mean simply adds the percentages and divides — it ignores how compounding actually works. The geometric mean multiplies the growth factors together, which is what your money actually experienced. They match only when every period has an identical return; the gap widens the more volatile the returns are.
What is "volatility drag"?
It's the gap created purely by the ups and downs of returns, separate from their average level. A classic example: alternating +50% and −50% produces an arithmetic average of exactly 0%, but a 50% loss needs a 100% gain just to break even, so the actual (geometric) result is a loss — that gap is volatility drag.
Can a cash flow's exact date really change the answer?
Yes, meaningfully. Adding the same dollar amount a month earlier gives it more time to compound (or lose value) before the ending balance is measured, which shifts the solved rate. This is exactly why MWRR is computed from actual dates rather than assuming cash flows land in neat annual buckets.
Which number should I use to judge my own investment performance?
For your own lived experience — what rate actually explains how your balance grew given your own deposits and withdrawals — use the Money-Weighted Return (cash flow method). For comparing a fund manager's skill independent of your contribution timing, or for averaging a series of already-known period returns, the geometric average (second tab) is the more standard, comparable figure.
How is the Average Rate of Return (ARR) different from MWRR?
ARR, also called the accounting rate of return, is a simpler figure — typically total gain divided by the number of years and the original investment — that ignores the time value of money and the exact timing of cash flows entirely. It shows up mainly in capital-budgeting contexts for comparing projects at a glance. For judging how your own account actually performed, MWRR and the geometric average are both more accurate, since they properly account for compounding and when money moved.
This calculator provides estimates for general informational purposes only and is not financial or investment advice. Always verify important calculations against your own account statements or a financial professional.