A Multitude Of Stock Market Averages

When you hear something like “the average annual return of the stock market since 1926, which is very near 12 percent annually when adjusted for inflation,” just what does that mean?  You may think an average is an average, but when it comes to investments, it’s not that simple.  Let’s take a look at a wildly volatile hypothetical investment.  Here’s a chart of its performance over ten months:

Performance Chart of a Hypothetical Investment

FIGURE 1 – Dates and Returns for Hypothetical Investment
Date Value
1/1/2010 $1000.00
2/1/2010 $1500.00
3/1/2010 $1250.00
4/1/2010 $950.00
5/1/2010 $900.00
6/1/2010 $1100.00
7/1/2010 $1300.00
8/1/2010 $1650.00
9/1/2010 $1550.00
10/1/2010 $1700.00

Well, that’s a scary ride.  Now, let’s say I want to calculate the average return for this period.  Well, how would I do that?  The instinctive (and wrong) thing to do is to figure up the percent change for each period and then take the average.  Let’s see how that works out for us.

So, we take out table and do some calculations.  First we find the average for each period, thusly:

FIGURE 2 – Dates and Returns for Hypothetical Investment with Averages
Date Value Return for the Previous Period
1/1/2010 $1000.00
2/1/2010 $1500.00 50.00%
3/1/2010 $1250.00 -16.67%
4/1/2010 $950.00 -24.00%
5/1/2010 $900.00 -5.26%
6/1/2010 $1100.00 22.22%
7/1/2010 $1300.00 18.18%
8/1/2010 $1650.00 26.92%
9/1/2010 $1550.00 -6.06%
10/1/2010 $1700.00 9.68%

Now, we just take the average of the column of returns and we get 8.33% per month return.*  Let’s plug that into our chart and see what we get:

Hypothetical Investment with "Average"Do you see anything wrong?  How about the fact that the two lines don’t meet at the end?  Here’s the thing, when you’re calculating averages, you can’t just take the average of a bunch of rates.  A simple example would be an investment that starts at $1000, goes to $2000, and then back down to $1000.  That a 100% increase followed by a -50% decrease divided over two years.  That averages out to be a 25% “return,” but I think you can see that there’s actually a 0% return (since we stopped at the same value we started from.)  So, how do we make sure we’re not making this kind of mistake?

Say hello to my little friend: Compound Annual Growth Rate, or CAGR to his friends.  Here’s the formula:

=(End Value/Beginning Value)^(1/Number of Periods)-1

So, if we plug in the numbers, we get (1700/1000)^1/9 – 1.  If we chart it, it looks like this:

Hypothetical Investment with CAGRNow, this looks nice.  We have a smooth compound interest curve that represents how this investment would’ve performed if it had compounded monthly instead of jumping and diving all over the place.  So, what was the rate?  6.07%.  That’s over 2 percent difference in return.  If you Compound to Crazy Land, it will have an immense effect on your investment’s end value.

So, what has the CAGR of the stock market been from 1926 to 2004 (78 years)?  According to the data over at moneychimp.com, without adjusting for inflation, the “Average” return of the stock market over that period was 12.47%.  Of course, we just saw how that isn’t very helpful and we should use the Compound Annual Growth Rate instead.  Whats the CAGR over the same time period? 10.46%  What happens if we adjust for inflation?  The CAGR drops to 7.21%.

Don’t get me wrong, I’m not knocking the stock market.  What I am knocking is that certain people who should know better are telling people who don’t know any better that they can expect returns from the market that there is no reason to expect.**

And don’t forget, we didn’t discuss that if you change the length of a period or the beginning or end date of a period, you also significantly change the CAGR.  Now that you know how CAGR works, you can be a more knowledgeable and sagacious investor.  happy average return calculations!

*  In this post, were using months as the period instead of years.  It’s not a big deal for our purposes, but don’t get confused.

**  I will now accept the award for “Most Passive-Aggressive Blog Post.”  Thank you.

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One Response to A Multitude Of Stock Market Averages

  1. stock tips says:

    I read your post . it was amazing.Your thought process is wonderful.The way you tell about things is awesome. They are inspiring and helpful.Thanks for sharing your information and views.

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