The Principle and Traps of Annualizing Returns

Annualization is the task of unifying returns from different periods onto a "one-year basis" so they can be compared. To judge whether a 3-month investment or a 5-year investment did better by placing them side by side, you need the same yardstick.

The form most used in long-term investing is CAGR (compound annual growth rate). The formula looks like this.

CAGR = (ending value ÷ starting value) ^ (1 ÷ number of years held) − 1

For example, if about $7,400 becomes about $14,800 after 5 years, taking the fifth root of ($14,800 ÷ $7,400) and subtracting 1 gives about 14.87%. It means not "it doubled (100%) over 5 years, so 20% each year," but that it grew at about 14.9% each year through compounding.

The most common misuse of annualization is extending a short period's gain straight to one year.

Suppose you made 2% in a month. Annualizing it gives (1.02) to the 12th power − 1 = about 26.8%. At 5% a month, (1.05) to the 12th power − 1 = it soars to about 79.6%.

The problem is that this return stands on the assumption that "you will keep earning that much every month going forward." Stretching one or two lucky months out to a year amplifies even the noise 12-fold. That is why, in practice, annualizing requires at least 3–5 years of data to be meaningful. A short-period annualized figure is closer to an "illusion" than a "track record."

The second trap hides inside the words "average return."

Suppose an asset was +10% in year 1 and -10% in year 2. Simply adding and dividing (arithmetic mean) gives 0%, which looks like break-even. But in reality, 1.10 × 0.90 = 0.99, that is, a -1% loss.

More extremely, experiencing +50% and -50% gives an arithmetic mean of 0%, but the actual result (geometric mean) is about -13.4%. This is because a loss weighs more heavily than a gain, which is called "volatility drag."

What represents the speed at which your money actually grew is not the arithmetic mean but the geometric mean (CAGR). As a rough relationship, "geometric mean ≈ arithmetic mean − 0.5 × variance" is known. That is, the greater the volatility, the lower the annualized return you actually pocket compared with the average.

The long-term annualized return of the S&P 500 is known to be roughly around 10% per year on a dividend-reinvested basis. Depending on the starting year and calculation basis, it is generally reported in the 10.2%–10.6% range (on a post-1926–1928 basis).

Yet it is a big misunderstanding to think you receive this "average 10%" stably every year. According to one analysis, in about 97 years of history, actual annual returns landed in the 8–12% band in only 5 years. The rest of the years diverged greatly from the average, surging +30% or plunging -30%.

The annualized return is only a summary of "over the long run it grew at this pace"—it is not a promise that "it gives you this much stably every year." Failing to understand this difference makes it easy to waver, asking "why is it different from the average?" when you hit a down market.

Annualization is an excellent tool for comparison, but remembering just three things lets you avoid the traps.

First, check the period. See whether it is data of 3–5 years or more, or a number produced by stretching a short period.

Second, check which average it is. If it is an arithmetic mean, it may be inflated above the actual compounding.

Third, check the volatility behind the average. The same annual 10% is an entirely different experience whether it came calmly at 10% each year or was made by swinging between -30% and +40%. You have to look at the maximum drawdown and drawdown period together to judge whether that number is something you can endure.

At 'Returns of Almost Everything,' when we calculate the annualized return of lump-sum and recurring investments, we show the maximum drawdown and recovery period alongside. See directly what kind of volatility hides behind a good-looking return.