Average Return Calculator

This page holds two calculators. The first takes a starting balance, an ending balance, and every deposit and withdrawal in between, then works out the annual rate that ties them together. The second takes several returns with different holding lengths and reports the cumulative return and the average annual return across the lot. Both account for the time value of money, so a dollar that arrived three years ago is not treated the same as one that arrived last month.

What an average return is

An average return is the mathematical average of a series of returns over a period. That plain definition hides a trap, because there is more than one way to average returns and the answers differ sharply.

The arithmetic mean adds the returns and divides by how many there are. It is the number most people picture, and it overstates what actually happened whenever returns vary. Take a fund that gains 50% one year and loses 50% the next. The arithmetic mean is zero, so it looks like you broke even. In reality $100 became $150, then fell to $75. You lost 25%, and the honest annual figure is a geometric mean of −13.4% a year.

That gap is called volatility drag, and it grows with the size of the swings. A useful rule is that the geometric mean sits roughly half the variance below the arithmetic mean, so the wilder the ride, the more misleading the simple average becomes. Both calculators here use compounding rather than a plain average for exactly this reason.

The first calculator: return from your cash flows

When money moves in and out at irregular dates, no simple formula gives the return. What you need is the annual rate that discounts every cash flow back to the starting balance, which is the internal rate of return computed on actual dates, often called XIRR.

Enter the balance you began with, the balance you ended with, and each deposit or withdrawal with its date. The calculator finds the rate that makes the whole set balance out. With the default figures, $5,600 at the start of 2023, a $5,000 deposit in January 2024, a $1,500 withdrawal that June, a $3,800 deposit in January 2025, and $18,000 today, the answer is about 12.7% a year. Your own money in totals $12,900 against $18,000 at the end, a $5,100 gain, but the percentage matters more than the dollar figure because the money was not all working for the same length of time.

This kind of figure is a money-weighted return. It answers the question "what did I earn," and it is sensitive to when you added or removed money. Adding a large sum just before a strong run flatters the number; adding it just before a fall drags it down, even if the underlying investment never changed.

Money-weighted against time-weighted

The distinction matters when judging a fund manager rather than yourself. A time-weighted return chops the period at every cash flow, calculates the return of each segment, and links the segments together. Because it strips out the effect of when money arrived, it measures the investment's performance rather than the investor's timing. That is why the Global Investment Performance Standards require time-weighted returns for reported track records, and why a published fund return rarely matches what an individual holder actually earned.

Use a money-weighted return, like the one above, to judge your own outcome, and a time-weighted return to compare two funds or managers on equal terms.

Average rate of return, and what it leaves out

The average rate of return, also called the accounting rate of return, divides the average annual profit an investment produces by the initial outlay. It is quick and it appears in plenty of business-school capital budgeting problems, but it ignores the time value of money entirely. A project returning most of its cash in year one scores identically to a project returning the same total in year five, which is obviously wrong for anyone who has to fund the wait.

It also works from accounting profit rather than cash. Treat it as a rough screen, not a decision, and pair it with a discounted measure. Our IRR Calculator and ROI Calculator cover the two most common alternatives.

The second calculator: cumulative and average return

The second tool handles the case where you know the annual return of several holdings and how long each was held. Each Return you enter is an annual rate, and it compounds over that row's holding length rather than applying once.

Take the defaults: 10% a year for 1 year 2 months, then −2% a year for 5 months, then 15% a year for 2 years 3 months. Starting from $100, the first stretch produces $111.76, the second takes it to $110.82, and the third finishes at $151.78. Cumulative return is 51.78% across a total holding period of 3 years 10 months, and the average annual return is 11.50%.

Notice that 11.50% is not the average of 10, −2, and 15, which would be 7.67%. The calculator weights each return by how long it was held and compounds the result, which is what makes the figure comparable to any other annual rate.

Cumulative return

Cumulative return is the total gain or loss over the whole period, with no reference to how long that period was. It is straightforward to compute and easy to misread. A 51.78% cumulative return sounds impressive until you learn it took nearly four years, at which point it becomes 11.50% a year.

Because almost every published figure in finance is annualised, a cumulative number cannot be compared to anything without knowing the time span attached to it. It is genuinely useful for two things: describing exactly how much an investment grew in total, and comparing two investments held over the identical period. Outside those cases, annualise before you compare.

Annualising, and the trap in it

To annualise, take the growth factor and raise it to the power of one over the number of years: an ending balance of 1.5178 times the start over 3.8333 years gives 1.5178^1/3.8333 − 1, or 11.50%.

One warning. Annualising a short period assumes the same rate continues for a full year, which is fine as arithmetic and often nonsense as a forecast. A 4% gain in one month annualises to more than 60% a year. That figure is arithmetically correct and tells you nothing about the next eleven months, which is why reputable reporting shows periods under a year as plain cumulative returns rather than annualised ones.

Which measure to use

• Judging your own portfolio: the money-weighted return from the first calculator, since it includes the timing of your contributions.
• Comparing funds or managers: a time-weighted return, which removes the effect of cash flows you controlled.
• Comparing holdings of different lengths: the average annual return from the second calculator.
• Describing total growth: cumulative return, always quoted with the period alongside it.
• Quick capital-budgeting screens: the accounting rate of return, backed up by a discounted measure before anything is decided.

Whatever the measure, returns are backward-looking. They describe what happened, and they carry no obligation to repeat. For projecting forward from an assumed rate, use the Investment Calculator.