Money Is Not Math…

And Math Is Not Money

Everyone wants you to believe that you can use math to predict the behavior of money.  It does not work.  Money is a commodity.  The simpliest example I can give you is, you have two oranges sitting on the counter.  You bring two more home and set them on the counter.  Math tells you that you now have four oranges (2+2=4).  Now you let the oranges sit there for 20 years.  How many oranges do you have now?  Math would say you still have 4 but you don’t.  The oranges have rotted and eroded over those 20 years.  Whatever would be left, hopefully nothing, would barely if at all resemble an orange.

The Experiment

Now I’m going to prove it to you in the investment world with the simple use of the internet and an excel spreadsheet.  So here’s the experiment and I didn’t know how this would turn out but I think it proves my point.  I can’t wait to hear your thoughts.  So what I did was go to wikipedia and look up the annual performance of the S&P 500.  I then took the last 20 years (1989-2008) and put them into an excel spreadsheet and ran three scenarios.  Scenario A: lump sum $10,000 invested in the beginning of 1989 for 20 years.  Scenario B: start with $0 and investing $5,000 at the beginning of each year for 20 years.  Scenario C: start with $100,000 and withdraw $5,000 at the beginning of each year for 20 years.  The main thing you need to know for this is that I am comparing the actual yearly performance of the S&P 500 with the average annual rate of return of the S&P 500.  Most financial planners/ advisors/ calculators/ software use average annual performance to predict or show future values.  My hypothesis is that they all fail.  In this case the average annual rate of return over the 20 years is 10.29% which is pretty good.

Scenario A:

Using the financial analysis method if you invested $10,000 on January 1st, 1989 and used a 10.29% annual rate of return over the next 20 years you would end up with $70,912.49.  That would be your expectation of what you would have.  In reality, you would have ended up with $49,238.00.  This is a shortage of $21,674.49 or 30.57%.  That’s a pretty big shortage.

Scenario B:

Using the financial analysis method of starting with $0 and investing $5,000 on January 1st of each year (from 1989 to 2008) for 20 years using a 10.29% annual rate of return you would end up with $326,435.30.  In reality, you would have ended up with $177,639.20.  This would be a shortage of $148,796.10 or 45.58%.  That’s an even bigger shortage.

Scenario C:

Using the financial analysis method of starting with $100,000 and withdrawing $5,000 on January 1st of each year for 20 years with a 10.29% annual rate of return you would end up with $382,689.60.  In reality you would have ended up with $314,740.80.  This is a shortage of $67,948.80 or 17.76%.  The best so far.  Now just for fun let’s reverse the order of the actual performance of the S&P 500.  This way we are saying that the return in 2008 instead occured in 1989, 2007 in 1990, 2006 in 1991, etc.  The average annual rate of return would stay the same because the numbers are the same we are just reversing the order.  Under this scenario you would end up with $48,383.10.  This would be a shortage of $334,306.50 or 87.36%.  That sounds like a problem.

Conclusion:

Under each scenario, even if the person doing the analysis guessed perfectly on the average annual rate of return for the next 20 years they would have grossly underestimated the actually amount of money you would have ended up with.  Math cannot predict the behavior of money.  It is the sequence of the returns that has the biggest affect on the end result.  You have an industry that advertises and uses average annual rate of return and here I’ve showed you that it fails as an indicator of your financial future.  It’s almost as though you are being set up to fail.

I understand that this isn’t a perfect experiment.  I used the assumption that you buy and hold the S&P 500 index for 20 years and most people wouldn’t do that.  However, I also didn’t account for other major eroding factors such as: inflation, taxes, technological change, plan obsolescence, financial expenses, lost-opportunity costs, interest rate declines, loans and interest charges and lawsuits.  I hope you see that adding in the other factors will probably only make things worse.

Related posts:

1. When Returns Lie
2. Destroying Your Compound Interest
3. Your Mortgage: When 30 beats 15
4. When Returns Lie Part II
5. Max Out Your 401k Math

Tagged as: average annual rate of return, Eroding Factors, Experiment, money, performance, S&P 500