Investing isn't just a coin toss

Mark Twain once said that it's not what you know that gets you in trouble, it's what you think you know for sure that ain't so. In my experience, when it comes to investing, Mark Twain was absolutely right. I've spent a lot of time trying to unlearn things I was sure of that just ain't so.

An article I recently ran across repeated a story that concludes you cannot tell anything about an investor's (or investment manager's) future performance from his track record. I first heard this story more than 20 years ago, and to tell the truth, I was once so convinced by it that for a good part of my youth, I kept my core equity portfolio almost entirely in index funds.

The author of the article asked readers to imagine a stadium full of people ready to flip a coin. After each coin toss, those who throw tails are asked to leave. At the end of 10 coin tosses, there is one person left who has the exceptional track record of throwing heads 10 times in a row.

Now, the author asks, would you bet on this person to do better than average in the next 10 coin tosses? Of course not. Even though the champion coin-tosser has a perfect track record, his chances of doing better than average in the next 10 tosses are the same as everyone else's.

Now, if you believe that an investor's returns are entirely due to luck, you can draw the same conclusion -- that it makes just as little sense to bet on the fund manager with the best track record as it does to bet on the champion coin-tosser. And that's the storyteller's point; he usually wants to encourage you to use index funds for the core of your portfolio.

Being lucky isn't the key

The story sounds persuasive until you realize that once you assume that everyone is tossing a fair coin, no one has an edge, since no one can be skilled at tossing a fair coin. But what if that assumption is wrong?

Hersh Shefrin, a professor at Santa Clara University, uses a similar thought experiment in his book, "Beyond Greed and Fear," to reach a very different conclusion. Let me try to explain.

Let's suppose that we have a group of 42,000 people who each receive one of three types of coins -- gold, silver or bronze. The gold coins are weighted so they have a 60% chance of coming up heads. The silver coins are weighted evenly to give a 50% chance of tossing heads. The bronze coins are weighted to come up heads only 40% of the time.

If everyone tossed their coin 10 times, the group would average five heads. If we want to bet on someone to beat the average of five heads out of the next 10 tosses, it would be smart to bet on someone holding a gold coin because each of these people can be expected to throw six heads.

But add one more twist: all the coins are painted green so you can't tell what kind of coin anyone has. Now, let's see if a track record has any value.

Winning again and again

At the start, 14,000 people have a gold coin, 14,000 have a silver coin and 14,000 have a bronze coin. If you had to choose someone to bet on now, your chances of selecting someone with a gold coin are 33%. But if you wait until after the first coin toss, the odds improve to 40%. Here's why.

Of the 14,000 people holding gold coins, 60% will throw heads; after the first toss, 8,400 of these people will still be in the stadium. Of the 14,000 holding a silver coin, 50% will throw heads, so 7,000 of them will remain. Of the bronze coin holders, 40% will throw heads; just 5,600 of these will get to stay.

After the first toss, there will be 21,000 people in the stadium, but 8,400 of them, 40%, will be holding gold coins.

With each successive toss, the odds of selecting a gold coin holder from the people who remain improve. After the 10th coin toss, there will be 100 people in the stadium. But 85 of them will have gold coins, 14 will have silver coins and one will have a bronze coin. If you select randomly from among the people who threw 10 heads in a row, your chances of picking someone holding a gold coin are now 85%.

Restricting your choices to those with a track record of throwing 10 heads in a row greatly increases your odds of selecting a gold coin holder, who can then be expected to throw six heads in the next 10 tosses and thus beat the average of all 42,000, which would be five.

Follow those with an edge

Since many who hold gold coins will throw fewer than six heads in the next 10 tosses, there is a good argument to choose all 100 of the people who threw 10 heads in a row instead of just one. The expected performance of the entire group of 100 in the next 10 tosses is 5.84. By choosing all 100, the probability of the group averaging more than five is higher than if you choose just a single person with a gold coin. (This is one reason I use the wisdom of our m100 -- 100 top investors who use Marketocracy.com, rather than just choosing the single person with the best track record.)

I don't mean to imply that anyone should select investment managers based solely on their past performance. Investing is a lot harder than tossing coins. My point is simply that a story that is so often used to explain why a manager's track record contains no useful information for investors does not stand up to scrutiny.

I sent a version of this journal entry to the editor of the online magazine that published the article. He sent it to the author of the article who wrote a thoughtful response. Click here to see my letter and the author's response on the next page.