The Confusion Between Cumulative Return and Annualization
An ad saying 'made 300% in 10 years' looks impressive. But converting this to an annual basis, what percentage is it? The answer is not 30%.
Cumulative return vs. annualized return
Cumulative return shows how much the principal grew in total over the entire period. If ₩1 million became ₩4 million, that's a cumulative return of 300%.
Annualized return (CAGR) converts that result into 'what percentage would it be if it grew at the same rate each year.' Simply dividing 300% by 10 years to get 30% is wrong, because it must be calculated with compounding.
Why isn't 300% ÷ 10 years = 30%
To have the principal become 4x (cumulative 300%) over 10 years, what percentage must it grow each year with compounding? Calculating gives 4^(1/10) − 1 ≈ 14.9%. In other words, about 15% per year makes it 4x after 10 years.
Compounding 30% per year for 10 years gives 1.3^10 ≈ 13.8x, which is more than 13 times the principal. That's a completely different result from 300% (4x). Compounding goes badly wrong when you calculate it with 'division' like this.
The larger the cumulative return and the longer the period, the bigger the error of the 'division illusion.'
The habit when looking at ads and testimonials
When you see an expression like 'a return of X%,' first check two things. First, is this cumulative or annualized? Second, over how many years is this number?
Even the same 'annual 15%' becomes about 1.5x the principal over 3 years and about 16x over 20 years—completely different results. A return number that leaves out the period is half of the information.
よくある質問
Q. Are annualized return and CAGR the same?
Yes, they're the same concept. Compounding the cumulative return (or the final multiple) over the period gives the compound annual growth rate (CAGR), which is also called the 'annualized return.'
Q. Is annualization always the more honest number?
For comparison purposes, yes. That said, annualization assumes 'it rose evenly each year,' so in reality there may have been a large drawdown in between. You need to look at the maximum drawdown (MDD) alongside the annualized return to understand the real experience.
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