What "Average Return" Really Means
An average return is the mathematical average of a series of returns over time — but there are two
honest ways to compute one, and they answer different questions. The first calculator above finds
the single annual rate at which a beginning balance, fed and drained by dated deposits and
withdrawals, lands exactly on the ending balance. Money that arrived early compounds longer, and
the rate knows it: the time value of money — a dollar today is worth more than a dollar tomorrow —
is built in. This is the money-weighted return, the right summary of your experience in an
account. The second calculator works when you don't have cash flows, only results: a list of
returns each earned over its own holding length. Those chain multiplicatively into a cumulative
return, which is then normalized over the total time into an average annual return — again with
timing accounted for, not averaged away.
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Not the accounting rate of return
The average rate of return (ARR), or accounting rate of return, averages the cash flow an
investment generates over its life — and stops there. It never discounts: year-ten dollars weigh
the same as year-one dollars, so ARR systematically flatters slow-paying investments. It's a
reasonable first glance at a big decision and a poor final answer; use it alongside measures (like
both calculators here, or IRR and NPV) that respect timing.
Cumulative return: the total, without the clock
Cumulative return is the aggregate gain or loss of an investment, as a sum or a percentage,
irrespective of how long it took. It contrasts with the annual return (one year's result) and with
the average annual return (the total, normalized per year). Because most financial figures are
quoted annualized, cumulative return is the less comparable of the three — a 40% cumulative return
is excellent over two years and mediocre over twenty. Quote it with its holding period attached, or
next to its annualized twin, as the results above do.
FAQ
My brokerage shows a different "average return" — why?
It may be showing a time-weighted return, which strips out the effect of your deposits and withdrawals to judge the investments themselves. The cash-flow calculator here is money-weighted: it judges your account, timing and all. Both are legitimate; they answer different questions.
Why chain returns instead of averaging them?
Because returns compound on each other. +10% then −10% averages arithmetically to 0% but actually leaves you at 0.99× — down 1%. Chaining (multiplying growth factors) is the only average that reproduces the ending value.
Can the cash-flow return be negative or fail to solve?
Negative, yes — if the ending balance trails what the flows alone would produce. It can fail to solve only in pathological cases (for instance, net withdrawals exceeding everything the account could have held); the calculator says so rather than inventing a number.
Disclaimer: This calculator provides estimates for educational purposes only and does not constitute financial
advice. Cash-flow returns use actual days over a 365-day year.