Average annual total returns (AATR) are calculated using the CAGR formula Trent mentions. The calculation and display of these returns is mandated by FINRA (regulatory body for the industry). I would be surprised to see firms promoting “simple average” returns that covered multiple years as that would be just begging for a costly audit, if not a lawsuit.

Using the formula in the link, I get 0.13% CAGR for 2000-2007, -5.8% CAGR for 2000-2008, and 7.7% CAGR for 1980 – 2008.

To Brandon above, it’s quite possible that the 2008 data has not been officially released yet. It’s only the 19th of January. :)

https://personal.vanguard.com/us/FundsSnapshot?FundId=0040&FundIntExt=INT#hist::tab=0

If we take the starting price at the beginning of 2000 (1455.22) and the ending price at the end of 2007 (1468.36), we get a CAGR of: 0.128%. If we use the ending price of 2008 (903.25), then we get a CAGR of: -5.79%. If we use 114.16 for Jan 1980 all the way through 2008, then the CAGR is a respectable 7.67%.

Plug this formula into excel and it makes this really easy to calculate.

That being said, in this post I see why it was excluded. You wanted a positive initial result leading to a negative end result to make your point.

Nice post.

(Also, it’s amazing just how bad the markets have been the past eight years or so (and this is before adding the depressing results from last year).)

I like stock investing, but most people have not ridden the S&P 500 exactly for the past 20 years with their investments. And in another 5-10 years, how will the 20-year average be? It might actually be a losing 20yrs overall and there will be experts saying “No, don’t invest! Look at the 20-yr avg!!”

It’s silly! Invest if you want to, and if you are aware of the risks. Also invest if you are investing pre-tax dollars and/or get a match from your employer. If you get 100% match from your employer, even if it’s a down year then you might still be in the positive.

Kudos for the detailed explanation.

Another reaon why you better know what you are doing if you invest in the market.

Let’s start with a value of 1.0 for the S&P at the beginning of 2000, so a $100 investment will be buy you 100 shares. If you continue to invest $100 at the beginning of each year (up to beginning of 2007), you will invest $800 and get a total of of 981.61 shares. These are worth $976.77 at the end of 2007. Now applying the internal rate of return calculation for 8 investments of $100 and a final value of $976.77 gives you an annualized return of 4.42%.

Also one nitpick: In your calculation for 2006 you applied the 12.8% gain to the $82.49, but you should have applied it to the $84.97. After taking this into account your final value would be $99.51 instead of $96.60.

The geometric mean is calculated like this

(1-0.1014)*(1-0.1304)*…..

Then take the n-th root of that for however many years you compute and convert it into a percentage (subtract 1, multiply by 100).

The geometric mean is always less that arithmetic mean. The difference becomes particularly large if the volatility is high. Just adding up numbers historically would be naive. For future numbers, it matters less. If they are all the same, geometric=arithmetic.

Another thing that should have been learned in school is that a 50% drop in the stock market can not be regained by a 50% gain. You need a 100% gain!

Finally dollar cost averaging buys the harmonic mean of the stock prices. We also have harmonic<=geometric<=arithmetic. Hence DCA is the cheapest way to buy a stock if you make regular investments without considering the value of what you are buying.

For Excel users, you can use the AVERAGE and GEOMEAN functions to compute these stats. If your dataset includes negative numbers (like above), you’ll have problems with Excel’s GEOMEAN function. To get around that, add one to each value, compute the geometric mean, then subtract the one at the end. In the example above, I got -2.20% for the geometric mean.

A tidbit from my investments textbook: Conventionally, historical returns are represented by geometric means and forecasted returns are represented as arithmetic means. Anyone using the arithmetic mean for historical returns are inflating their numbers (as Geometric <= Arithmetic).