One of the problems that many investors have (and that I used to have) is how to interpret and practically apply investment return data published by the mutual fund companies. I frequently read statements made by uninformed investors about historical annual rates of return that cause them to be over-confident in their retirement planning. So I thought I would try to bring a little clarity to the issue.

### Arithmetic Average Rate of Investment Return

First, the 12% number is no longer valid. Second, the argument is based on a flawed understanding of what an “average annual return” is and how it should be applied in financial planning.

This reminds me of a brief parable: A man puts his left hand on a hot stove and the right hand on a block of dry ice. A statistician carefully observes and analyzes the temperature data. He then proclaims that on average, the man must be quite comfortable.

Do you see where I am going with this?

The average annual rate of return is an arithmetic average calculated by summing the annual returns ( or growth rate) of an investment (such as a mutual fund) over a period of years (3 years for example), then dividing the total by the number of years. Thus, if a mutual fund has annual returns of 20%, -10%, and 10% over a three year period, the annual average return will be 6.67% ((20-10+10)/3.)

This is the number that many people rely on in their retirement planning. It shouldn’t be.

### The Order of Returns is Important to Your Retirement Nest Egg

The arithmetic average rate of return ignores the order in which the returns are experienced by an investor.

Let’s take the example of someone who invested $100,000 in a large cap stock mutual fund 25 years ago. That investment would have grown to exceed $2 million by 2002. That is a 13% average annual return.

But what if the order of the actual annual returns were reversed?

The average annual return in 2002 is still 13% even with the order of returns being reversed. But for a retirement investor who needed to withdraw money from their nest egg portfolio, the ending numbers are dramatically different.

Assuming a 5% withdrawal rate, using actual returns for 1978-2002, and including a 4% withdrawal increase each year for inflation, that retiree would have $1,115,000 at the end of 2002. If you reverse the order of returns, that same retiree would end up with only $373,000 at the end of 2002. Ouch.

### Use the Geometric Compound Annual Growth Rate

The problem is that an arithmetic average is an appropriate statistical measure only if the contribution of each data point to the performance outcome is independent of the other data points. In the case of investment return performance, using the arithmetic average produces a biased outcome.

The correct performance measurement for an investment is the “compound annual growth rate” (CAGR) based on a geometric average. A geometric average is an exponential calculation so I don’t suggest you try to do it in your head. In the example I started with above, the CAGR is calculated as follows:

[(1 + .2) * (1 – .1) * (1 +.1^ 1/3 -1 = 5.91%

In the world of investment performance over a three year period, the difference between 6.67% and 5.91% is significant.

Let’s look at another example over a longer period for a mutual fund with significant variability in its annual returns. If the returns from the fund each year for five years were 90%, 10%, 20%, 30% and -90%, the arithmetic average return would be 12%.

Now calculate the geometric mean return as follows: [(1.9 x 1.1 x 1.2 x 1.3 x 0.1) ^ 1/5] – 1. This provides a geometric average annual return of -20.08%. This is quite a bit different but it is the correct number to use.

### Final Thoughts on Understanding Investment Returns

I hope that I have persuaded you to be more critical in your consideration of published investment returns. Mutual fund companies prefer to publish average return data. The CAGR data is available for most mutual funds. You just need to dig a little deeper to find it. I hope you will do that digging as part of your retirement planning.

Image credit: Misterbisson

Rendell @ Brandlessblog says

Many times, people focused too much on the investment return rate that they forget to understand the risk involved and what is inside the underlying investment. Nevertheless, it is still quite important to understand the technical aspect of their portfolio.

Jon says

You have cherry picked your example so the “investment” lost most of its value in the first year, causing substantially lower returns. 2002 was notoriously bad. Now granted someone could have plopped down $100 k in 2002 and lost a bunch of money but the more likely scenario is that they built up that $100 k in the preceeding years and had very high returns which they largely gave back. The geometric mean may be the more correct return to look at but that doesn’t excuse cherry picking dates to show lousy returns. Taking the DJIA and using the geometric average over the long haul (any given 20 year period) will show better than your 6.56 % example. And it certainly blows 4% out of the water.

If the argument is for a short period close to retirement when you are going to be withdrawling money then there is a certain sense. But not for anyone younger than 40 who expects to let their money set for 20 + years.

Having said that I defend no mutal fund with their notoriously bad performances and speak only of index funds.