I was chatting with a friend recently about the sniper attacks that took place in the greater Washington, D.C., area back in 2002. I was living there at the time, and I remember how on edge we locals were. Many people walked in a zigzag line going to and from their car. They looked out for a white van that might harbor the killer.

I couldn't help worrying along with everyone else, but I was also aware of some strange things happening. We were, in general, reacting rather irrationally. (Here were my thoughts at the time.) After all, our odds of being hit by a sniper were more remote than one in a million, while our odds of being in a car accident were far greater. And yet we were taking lots of precautions to prevent becoming a sniper victim, while many continued to speed on the roads, drink and drive, and so on.

Here, check out some more odds, via a Benjamin Friedman article from Foreign Policy: The odds that you will die in a terrorist attack are, according to the U.S. Centers for Disease Control and Prevention, about 1 in 88,000. Meanwhile, "The odds of dying from falling off a ladder are 1 in 10,010. Even in 2001, automobile crashes killed 15 times more Americans than terrorism."

Why we do it
So in the course of discussing these irrationalities, my friend offered an explanation she found in a Wired article by Bruce Schneier. He said:

Our brains are much better at processing the simple risks we've had to deal with throughout most of our species' existence, and much poorer at evaluating the complex risks society forces us to face today. Novelty plus dread equals overreaction ... People tend to base risk analysis more on personal story than on data, despite the old joke that "the plural of anecdote is not data." If a friend gets mugged in a foreign country, that story is more likely to affect how safe you feel traveling to that country than abstract crime statistics. We generally give stories more weight than statistics. We give storytellers we have a relationship with more credibility than strangers, and stories that are close to us more weight than stories from foreign lands.

Regarding your wallet ...
So what financial wrong moves might you be making? Well, consider these possibilities:

  • Many people have stayed away from the stock market entirely, due to having witnessed or experienced a market crash. Crashes have happened (and they will happen again), but despite them, the overall trend of the stock market's value has been upward. If you've got a long time horizon, you'll likely profit from investing in stocks.

  • Some people stick to real estate investing (or playing the lottery, or investing solely in CDs, or what have you) instead of stocks, figuring it's safer. But real estate can crash, too. Values on farmland fell 27% between 1982 and 1987, for example. And the average annual historic return of real estate over the past 40 years or so has been 6.3% -- vs. 10% for the stock market. A simple investment in an S&P 500 index fund gets you the diversification you need without a ton of money.  

  • Some people who stick their toe into the stock market and see their first investment sink over a period of a few months, sell and never return. Often, the best thing to do with a falling stock, as long as the company is healthy and retains its competitive advantages and promise, is to hold on.

  • Meanwhile, many of us don't secure enough insurance on our homes, assuming that burglaries, house fires, major water damage, and other disasters are so rare that they won't happen to us. Wrong.

A key lesson here is to focus on the data, not anecdotal stories, though they can impart useful lessons. Similarly, when studying a company, focus on its numbers at least as much as on its compelling story. You want to see rising revenues, growing earnings per share, thickening profit margins, inventories and accounts receivable under control, and so on.

Profit from irrationality
Another angle to consider is how you might profit from other people's irrationality. It's macabre, perhaps, but lots of investors have made good money investing in companies that address terrorism. One example I didn't act on is InVision Technologies. You may have seen its luggage-scanning equipment in many airports. I wrote about it way back in 1998, but never bought it. General Electric (NYSE:GE) bought the whole company in 2004.

So when you sense yourself reacting to a fear of a nasty outcome (or ignoring a risk that shouldn't be ignored), take time to assess the situation rationally.

Longtime Fool contributor Selena Maranjian owns shares of General Electric. She recently learned about the welwitschia plant, which can live for 1,000 years and has only two leaves. For more about Selena, view her bio and her profile. Try any one of our investing services free for 30 days. The Motley Fool is  Fools writing for Fools.