Lessons from Vegas: The Illusion of Average Returns

Gamblers can easily lose money by confusing actual outcomes with average outcomes. It's also a common mistake with investors and financial advisors. For example, short-term averages vary dramatically from long-term averages.

A few weeks ago I took my family to our annual vacation spot — Las Vegas.

It’s a place that defies the law of averages. Normal people stay awake 16 hours a day; in Vegas, it’s 20-plus hours a day. At home one bowl of cereal and a banana completes my breakfast; in Vegas my stomach’s capacity expands to fit five plates at the wall-to-wall buffets, and my bladder holds a gallon.

One of the lessons I learned this time is that many gamblers mistake their actual wins and losses with what should have happened based on averages.

For example, take my favorite casino game to play — craps. In this game you roll two dice and win or lose depending on what number you bet on and what number shows up on the dice.

There’s a symmetrical distribution of possible number combinations of the dice. The number 7 is statistically supposed to show up the most number of times (1 out of every 6 rolls); 2 and 12 the least number of times (1 out of every 36 rolls); and the other numbers are in between.

But when I play the game, I’ll get sequences like the following:

7 4 2 7 7 2

In that six-number sequence the number 7 showed up triple its average and the number 2 showed up 12 times its average. All the gamblers betting against the 7 empty their wallets in a hurry. They’ve made the mistake of confusing actual outcomes with average outcomes.

It’s also a common mistake I see individual investors and financial advisors make.

Let’s discuss three examples as they relate to your investment portfolio:

Short-term averages vary dramatically from long-term averages

The U.S. stock market as represented by the S&P 500 Index from 1926 to 2011 (a period of 86 years) had an average annual return of about 9.8% per year. This is how the media and financial advisors make you believe that you should expect about a 10% annual rate of return. The reality is that this is time dependent. Take a look at the average annual return by decade:

For more than half of the last eight decades your average annual rate of return was less than the long-term average, with two decades generating a slight negative return over 10 years (the Great Depression in the 1930s and the so-called “lost decade” of the 2000s).

An investor in the 1930s who threw in the towel missed out on the high returns over the next 20 years. Conversely, an investor in the 1980s and 1990s who mistakenly thought that the “new normal” was annual 20% returns was sorely disappointed in the 2000s with the financial collapse.

What makes averages even more deceptive is the fact that stock market returns don’t follow a bell shaped curve, so you’ll have extreme negative and positive events that are not explained by simple mathematical models. For example, the highest 12-month return has been +54% and the lowest return was -43% in one year.

Next time we’ll take a look at two more examples of how average returns can be illusions.

Read more Lessons from Vegas:

Don’t Be Fooled by Randomness

Are You Flipping Coins or Investing?