Workshop Portfolio

Compounding Makes a Difference

by Jim Stevens (JimStevens@aol.com)

Burlington, VT (November 12, 1998) -- It's been two plus years since I first darkened the front gate and entered Fooldom. Back then I noticed what I thought were some topsy-turvy ways to look at investment performance. The consistent use of the compound annual growth rate (CAGR) of a specific investment over time is one subtle example of this Motley folly.

Pick up any financial magazine or go to any mutual fund website and the method you'll find most commonly used to advertise the historical performance of a fund is not the CAGR but the average annual return. Why do fund companies choose this method over the Foolishly preferred CAGR method? Because it makes for a bigger number before the percent sign, every time. What impresses mutual fund investors the most? Apparently, a big number before the percent sign in an advertisement. And I mean big in amount, big in type size... just as noticeable and large as all get out!

Hey, it's no crime to publish the average annual growth rate. It's a perfectly legitimate calculation that can be used to compare one investment to another. Just don't go plugging that annual growth rate into your handy Quicken, MS Money, or other program's "just how filthy rich will I be" savings calculator.

Even if the fund does exactly as well in the future as it did the period over which the average was calculated, the results will overestimate the growth of your money. How can that be? Just to illustrate the point, let's compare the average annual returns and the CAGR of the Keystone 5 approach over its backtested history and the Standard & Poor's 500 Index (without 1998 partial year returns):

 
 Year      Key5      S&P 
 1986     22.00%   18.50% 
 1987      8.10%    5.20% 
 1988      8.50%   16.80% 
 1989     59.20%   31.50% 
 1990     -0.30%   -3.20% 
 1991     71.80%   30.60% 
 1992     12.40%    7.80% 
 1993     36.30%   10.10% 
 1994      9.00%    1.60% 
 1995     43.80%   37.50% 
 1996     38.20%   23.30% 
 1997     56.60%   33.20% 
  
 Annual 
 Average  30.47%   17.74% 
 CAGR     28.50%   17.02%

The average annual return is simply the arithmetic average of the yearly returns. Add up the returns and divide by the number of years. The CAGR is the geometric average, or the nth root of the product of all the years returns where n is the number of years. Though the difference may appear small, the difference in the amount accrued becomes huge over long time horizons.

If the Key5 actually did have a 30.47% CAGR over the last 12 years, it would have turned $10,000 into $243,000. But alas, it's the actual CAGR of 28.5% that (when used in a growth calculator) would reveal the REAL amount that $10,000 would have grown to over the backtested period: $202,000. The real amount is still not too shabby -- and we Fools do like to keep it real!

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