CAGR: how to calculate the average annual return correctly

Basics8 min read · updated 19 September 2026 · 8 sources

The CAGR (compound annual growth rate) is the average annual return including compounding: the one fixed interest rate at which the starting value would have grown to exactly the final value over the same period. It is the most important metric in any backtest, and it is almost always lower than the simple average of the annual returns.

How to calculate CAGR: the formula

You only need three numbers: the starting value, the final value and the number of years. Distributions count if they are reinvested (total return). The formula extracts the annual rate from the total growth, the exact reverse of a compound interest calculation, in which you derive the final value from an interest rate.

The number of years can also be a fraction. If a portfolio grows from €10,000 to €12,500 in two and a half years, the CAGR is 1.25^(1 / 2.5) − 1 = 9.34% a year. If you only have monthly returns, multiply all the factors (1 + return) together and take the root over the number of years.

Why the average of annual returns is misleading

Suppose a fund rises by 50% in the first year and falls by 50% in the second. The arithmetic average is 0%. That sounds like “nothing happened”. In reality, €10,000 first became €15,000 and then €7,500.

The more returns fluctuate, the larger the gap between the two averages. As a rule of thumb: geometric ≈ arithmetic − variance / 2. A portfolio with an average annual return of 8% and 20% volatility therefore only grows at around 6.0% a year. That is why lower fluctuation pays off even when the average return stays the same. The article volatility drag explains this in detail.

Which average is the right one? For the question “How much has my money grown?”, always the geometric one, i.e. the CAGR. For the question “What return do I expect in the next single year?”, the arithmetic one is the better estimator. When expectations are compounded over many years, the truth lies in between. This is a well-known point of contention in forecasts for pension plans.

Time-weighted or money-weighted?

A fund's CAGR describes the performance of one euro invested once. It is therefore called the time-weighted return: deposits and withdrawals play no part. How well your own money has done, by contrast, depends on when you invested how much. That is measured by the money-weighted return (internal rate of return).

The money-weighted return r here is the interest rate at which €10,000 × (1 + r)² + €10,000 × (1 + r) gives exactly €19,800. Differences like this are not a special case.

Dichev (2007) compared the returns of entire stock markets with the money-weighted returns of the investors in them. Because money tends to flow in after good years and out after bad ones, investors' returns were below the market's CAGR in almost all major markets. More on this in the article time-weighted return.

For advanced readers: log returns and the distribution

Mathematically, it is more convenient to work out the CAGR via log returns: ln(1 + r) can simply be added up across periods. The average log return times the periods per year is the continuous growth rate; e to the power of this value minus 1 gives the CAGR again. This also gives the rule of thumb above: if log returns are normally distributed, mean wealth grows at μ, but typical (median) wealth only at μ − σ² / 2.

This has an uncomfortable consequence: the average across many possible futures is pulled up by a few very good paths, and most investors experience less. Bessembinder (2018) shows this for individual stocks: over their lifetime, many individual US stocks returned less than short-term Treasury bills, and the wealth creation of the overall market came from comparatively few companies. For broadly diversified index funds this is an argument in their favour; for individual stocks, a warning.

Closely related is the diversification return: because a regularly rebalanced portfolio fluctuates less than its components, its geometric return can be above the weighted average of the individual geometric returns. Booth and Fama (1992) described this effect, and Fernholz and Shay (1982) derive it in stochastic portfolio theory. See also rebalancing.

And finally: if you want to maximise the CAGR, you maximise the expected log return. That is the core of the Kelly criterion. However, Samuelson (1971) showed that this is not the right objective for every long-term investor, because the strategy with the highest growth tolerates very large losses along the way.

What the research shows

Long series show how strongly the CAGR depends on the period. Dimson et al. (2002) compiled returns on equities, bonds and money market instruments in many countries over 101 years: equities came out ahead in the long run, but with decades in which bonds or even the money market did better. Siegel (2014) reaches a similar picture using US data over around two centuries. For your own planning, this means: a CAGR from 10 or 15 years is a sample, not a constant of nature.

In performance measurement practice, the CAGR is the standard for the annualised return (p.a.); Bacon (2008) summarises definitions and variants (for example for periods of less than a year).

CAGR, total return and savings plans

• Total return: the CAGR should always be calculated with distributions reinvested. Pure price indices (the DAX, for example, is already a performance index, while the S&P 500 is usually quoted as a price index) understate the return by the dividend yield.
• Nominal or real: if you deduct inflation, the CAGR becomes the real return.
• Savings plan: with regular contributions, the CAGR only describes the performance of one euro invested once. How well your own money has done is shown by the internal rate of return (money-weighted return), because later contributions are invested for a shorter time.
• Costs and taxes: the CAGR of an index contains no fund costs and no taxes. Even 0.5% costs a year make a noticeable difference to the final value over 30 years.

Reading CAGR correctly in a backtest

A high CAGR is only half the story. Two portfolios with an 8% CAGR can be very different: one with a maximum drawdown of 20%, the other with 55%. So always compare the CAGR together with risk metrics such as volatility, drawdown or the Sharpe ratio, and pay attention to the period: a CAGR from 2010 to 2021 says little about a decade of rising interest rates.

• Start and end point: if the test begins shortly before a crash or ends at a high, the CAGR shifts by several percentage points. Rolling returns over 5 or 10 years show how stable the result is.
• Do not extrapolate short periods: 3% in three months is not 12.6% a year. For periods under one year, returns are usually not annualised at all.
• Survivors: a backtest with funds that still exist today underestimates how many weak funds were closed (see backtest overfitting).

How Portfolio Lab calculates it

Portfolio Lab multiplies all period returns of the backtest (daily or monthly, depending on the setting) into a total factor and takes the root over the years covered. The years are the days between the first and last date divided by 365.25, plus one period; otherwise the first month would be missing with monthly data. Calculations are in the chosen base currency, using price series with distributions reinvested; the real CAGR additionally deducts the chosen inflation rate. Alongside the CAGR, the Backtest shows rolling returns over 1 to 10 years. Details are in the metrics methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.