The Flaw of Averages

By Sam Savage

 

Now a book from John Wiley & Sons, published June 2009

This site contains animations and downloads for Sam's original Oct. 8, 2000 article in The San Jose Mercury News

Click here for article


 

Sam's Home Page

 


Simply stated, the Flaw of Averages implies that:

Plans based on average conditions are wrong on average


An Annuity Example

You want your $200,000 retirement fund to last 20 years. How much can you withdraw per year?

Suppose the inevestment is expected to grow at an average of 14%. Assuming 14% growth, a standard annuity spreadsheet will show that if you withdraw $32,000 per year the fund will last 20 years as shown on the right.

Even if the return fluctuates in the future, as long as it averages 14% per year, the fund should last 20 years, right?

 


WRONG

Given typical levels of stock market volatility there are only slim odds that the fund will survive the full time.

 

The AVERAGE behavior of the fund is worse than the behavior associated with AVERAGE growth

Two Excel files, available for download can provide insight into this situation. NOTE: these models have not been rigorously tested and should not be used for making investment decisions. Annuity.xls simulates uncertain growth. Annuity2.xls is based on actual growth of the S&P 500.



Investment in a Microchip Fab

In this model we assume that Averge demand is 100k with a 95% confidence interval of 50k units. The cost of capacity is $300 per 1 unit, so $30 Million has been invested to achive capacity equal to the average demand of 100k. Revenue is $400 per unit,so average profit should be:

$40 Million minus $30 Million = $10 Million

right?

WRONG

Lower than average demand clearly leads to profit of less than $10 million. That's the downside. But greater demand exceeds the capacity of the plant, leading to a maximum of $10 million. There is no upside to balance the downside.

The AVERAGE profit is less than the profit associated with AVERAGE demand

Fab.xls is an Excel worksheet set up to demonstrate the Flaw of Averages with the aid of Monte Carlo simulation.

It contains two tutorials for Simulating Profit and Investing for Maximum Profit using Monte Carlo simulation.

First, download Sim.exe, which contains a trial version of the Monte Carlo simulation for Excel from Dr. Savage's book and software: INSIGHT.xla, then run the file to extract files. Readme.txt explains installation. Mac Users download Sim.hqx.

Second, download Fab.xls and save it to your hard disk. Follow the tutorial steps on the two tabs preceeding the Model.

 


A Sobering Example of the Flaw of Averages taken from Dr. Savage's INSIGHT.xla.

Consider the state of a drunk, wandering around on a busy highway. His average position is the centerline, so........

For more information on simulation, decision trees and other analytical tools for Microsoft Excel, see Dr. Savage's INSIGHT.xla, described as "A must read" by Harry Markowitz, Nobel Laureate in Economics