I think most investors know this intuitively, but many ignore it when talking about stocks.
It's common to see people say the S&P 500 returns 8% or 10% or X% annually. In many conversations it's meant to be a rough estimate, which is fine, but many newer investors just pencil it in.
The problem is there are multiple ways to calculate an average.
The numbers thrown around when calculating the average return of the index are often the simple average. This is the wrong average for investing.
A simple annual average takes all the returns for each year in a period and divides by the number of years in the period. But this is meaningless.
If you bought a stock that returned 100% in the first year and then lost 50% in the second year, then your simple average return in two years is 25%. In reality, you're return is 0% (it doubled, then halved, and now you're back where you started). It's easy to see this with such a “simple” example, but the same is true over longer periods of time with less perfect numbers.
For investors, the arithmetic average is what's important. This is what compound annual growth rates (CAGR) reflect.
For example, in the last 25 years (1998 to 2022) the S&P 500 has a simple average annual return of 9.2% and an arithmetic average annual return of 6.9%. That's a meaningful difference when planning for retirement many years away.
And if you account for inflation, then the real arithmetic average annual return is “only” 3.8% in that span (still likely your best option among investments).
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