Compound Annual Growth Rate (Annualized Return)
A problem with talking about average investment returns is that there is real ambiguity about what people mean by "average".
For example, if you had an investment that went up 100% one year and then came down 50% the next,
you certainly wouldn't say that you had an average return of 25% = (100% - 50%)/2, because your principal is back where it started: your real annualized gain is zero.
In this example, the 25% is the simple average, or "arithmetic mean".
The zero percent that you really got is the "geometric mean", also called the "annualized return", or the "CAGR" for Compound Annual Growth Rate.
Volatile investments are frequently stated in terms of the simple average, rather than the CAGR that you actually get.
(Bad news: the CAGR is smaller.)
CAGR of the Stock Market
This calculator lets you find the annualized growth rate of the S&P 500 over the date range you specify;
you'll find that the CAGR is usually about a percent less than the simple average.
(These returns are just capital gains, not dividends; if you owned an S&P 500 index fund with low fees you would have made more money than this.)
Note that 2000-2002 really was as bad as it felt, destroying about as much wealth as 1973-1974: in both of those periods one dollar "grew" to about sixty cents.
On the other hand, the ten year period from January 1993 through December 2002 still delivered an annualized return of 7.29 percent, far more than inflation.
So maybe the new economy isn't really dead, and we just have to learn to pace ourselves a little...
CAGR Approximation
There is a formula that lets you estimate the CAGR if you already know the simple average and the standard deviation:
(1 + rave)2 - StdDev2 = (1 + CAGR)2
In the example at the top of the page, the simple average is 25% and the standard deviation is 75% (since the data points of +100 and -50 lie at a distance of 75 away from the simple average);
in this case the estimate gives the exact answer of zero for the CAGR:
In the case of stock market returns, if you plug in the results of the first calculator you'll find that the approximation isn't exact, but it's still pretty good.
More CAGRs
These two calculators give annualized returns (i.e. CAGRs) of different indexes over a much longer time period.
| 
