CAGR formula: how to calculate annual return from a backtest

The two numbers, defined

Total return is the simplest thing you can compute: final equity divided by initial equity, minus one. Start with 10,000 and finish with 16,570 and the total return is 65.7%. Nothing else is involved, which is exactly the problem — the number is identical whether that took eighteen months or eight years.

CAGR, the compound annual growth rate, is the constant yearly rate that would take you from the start to the end over the same period: (1 + total)^(1 / years) − 1. It does not describe what happened in any particular year. It describes the smooth rate that produces the observed endpoint.

As a worked example, take a strategy we published on gold: 65.7% total return over 17,520 half-hour bars, which is about one and a half years. CAGR is (1.657)^(1/1.5) − 1, or about 40% a year. The identical 65.7% over six and a half years would be about 8.1% a year — below what a savings account has paid in some periods, and certainly not worth a gold strategy's drawdown.

Why the annualisation matters more than it looks

Compounding is not linear, so the conversion is not a division. Going from a one-year result to a three-year result multiplies, it does not add. A 30% annual return sustained for three years is a 119.7% total return, not 90%.

Run it backwards and the effect is starker. A 30% total return is 30% a year if it took a year, about 69% annualised if it took six months, and about 9.1% annualised if it took three years. The same number describes a great half-year and a poor three-year stretch.

This is the single most common way a strategy's performance gets overstated, and it is rarely deliberate. Short backtests produce impressive total returns because the period was short, and the annualised figure that would expose this is the one most often left out of the report.

The bar count is the window, and it is usually missing

Even the annualised figure is unusable without knowing the window it came from. A backtest report will often show a start date and an end date, which is enough — but the bar count is the more reliable guide, because it tells you how much data the result was actually computed from rather than how much calendar the dates span.

For our own published results we record 17,520 bars for a two-year hourly window and 17,520 bars for a one-year half-hourly window. Those are the same number of bars and wildly different amounts of time, which is precisely why the timeframe has to be stated alongside the count.

A practical rule: never compare two strategies' returns without checking that both were measured over a comparable number of bars on a comparable timeframe. If one ran for 6,570 four-hour bars (about three years) and the other for 730 daily bars (about two years), you are comparing different amounts of evidence, not just different performance.

What annualising hides

CAGR is a fiction of smoothness. It is the rate that would produce the endpoint if growth had been perfectly steady, and no strategy grows steadily. A strategy that returned 40% a year by gaining 5% a month for twelve months and a strategy that lost 30% and then gained 130% have different CAGRs and completely different risk.

It also ignores the path in the way that matters most to a real account: whether you would still have been holding it. A strategy with a 40% CAGR and a 60% maximum drawdown is a different object from one with a 40% CAGR and a 12% drawdown, and CAGR alone cannot tell them apart.

And it says nothing about how the return was achieved. High CAGR from a strategy with 2,000 trades is a different claim from high CAGR from a strategy with 40 trades, because the second may be entirely sampling noise.

A checklist for reading any return figure

First, find the window. If the report gives dates, convert to years. If it gives bars and a timeframe, convert to years from those instead — bars multiplied by the timeframe, divided by 8,760 for the annual figure.

Second, convert to CAGR. If you only have total return and no window, the number cannot be interpreted and should not influence any decision. This is not pedantry; it is the difference between a 40% and a 9% result.

Third, put the drawdown next to it. Return without drawdown is half a sentence. The question you are actually answering is not 'how much did it make' but 'how much did it make per unit of the worst thing it did to me'.

Fourth, check the trade count, and be sceptical of any annualised figure computed from a short sample. Annualising amplifies whatever the sample contained, including its luck. A three-month sample annualised is a projection, not a measurement.

What CAGR does not tell you

It does not tell you the future rate. It is a description of a past window, and the next window is not required to resemble it — this is the same non-stationarity that affects every backward-looking statistic.

It does not adjust for risk. Two strategies with the same CAGR are not equivalent if one achieved it with leverage and the other without. A useful question to add is what the return is above the risk-free rate: a 5% annual return when cash pays 4% is a 1% excess, not a 5% achievement.

And it does not tell you whether the result is distinguishable from chance. For that you need the trade count and a sense of how much of the return came from the best few trades. CAGR is a description of an endpoint. It is never the whole diagnosis.