Probability and investing: Take that, Murphy - MoneySense

Probability and investing: Take that, Murphy

If Murphy’s Law rules your portfolio, don’t despair. A few changes in how you think about money can save your sanity—and your fortune.


On June 13, 2006, I got an email from a distraught investor I will call Michael Buchanan. A retired social studies teacher, Buchanan could not believe his bad luck. “For years, I’ve been meaning to put some of my money in an emerging markets fund,” he recalled.  “I knew they would win big, and they did. And I knew they would keep winning big, and they did.” (The average emerging markets fund gained 55.4% in 2003, 23.7% in 2004, and 31.7% in 2005.) “It got to the point where I couldn’t sit on my hands anymore, so on May 13th, I put $10,000 into an emerging markets stock fund.” But then rising interest rates and geopolitical worries hammered investments in places like Brazil, Russia, India, and China, and Buchanan lost 22% of his money in four weeks.

“Believe it or not, this wouldn’t actually bother me so much,” Buchanan continued, “if I hadn’t bought Jacob Internet Fund in January 2000. I got my guts ripped out by that fund.” (Jacob Internet lost 79.1% in 2000, another 56.4% in 2001, and 13% more in 2002.) “So I sold it at the end of 2002. As soon as I got out, the damn thing turned into a superstar.” (Jacob went up 101.3% in 2003.)

“Why does this keep happening to me?” asked Buchanan plaintively. “I know—I don’t think, I KNOW—that the second I sell my emerging markets fund, it will take off. But if I keep it, it will keep losing money! What’s wrong with me? What should I do? Is it Murphy’s Law of mutual funds?”

Buchanan emailed me because of a column I had written in 2002 called Murphy Was an Investor. In our daily lives, we all shake our heads over the apparent workings of Murphy’s Law (“Whatever can go wrong will go wrong”) and its corollary (“. . . in the worst possible way at the worst possible time”). We tend to believe that it will rain if we forget our umbrella and be sunny if we lug it along,  or that whichever checkout line we stand in will turn out to be slowest, or that whenever we change lanes on the highway the other lanes will speed up. But does the perverse logic of Murphy’s Law govern investing, too? And is the whole concept merely a cleverly expressed superstition, or does it have some basis in fact?

The maven of Murphy’s Law is an Oxford trained physicist named Robert A. J. Matthews. A few years ago, Matthews set out to investigate one of the oldest examples of Murphy’s Law: Why does bread always seem to land butter-side down when it falls on the floor? You might think it’s because the buttered side is heavier; a psychologist might say we are more apt to recall a wet landing than a dry one; a skeptic might simply insist that which way the bread lands is random. It turns out all those views are wrong.

“Like most people, I guess,” says Matthews, “I thought it’s a 50/50 chance, unless you’ve got a pound of jam on one side.” With the uniquely British gift of taking essentially silly things very seriously, in 2001 Matthews enlisted 10,000 schoolchildren across England to tip buttered toast off plates. Just over 62% of the time, the bread landed butter first—a percentage much too high, across so many trials, to be the result of chance. Matthews easily ruled out the weight of the butter as a cause: When unbuttered toast was inscribed with the letter B in magic marker, then placed face-up on a plate and tipped off the table, it landed B-side down most of the time.

So why does toast tend to go splat on the wrong side? “The universe is designed against us,” Matthews says flatly. Given the width and velocity of falling bread and the typical height of tabletops, there isn’t enough room for a tipped piece of toast to make a full rotation before it hits the floor. And tabletops are so low because humans average less than six feet in height.

That’s what engineers call a fundamental design constraint. Does investing have its own design constraints? Of course it does. From the beginning of 2003 through the end of 2005, emerging markets gained an average of 36.3% annually. But decades—in fact, centuries—of history show that economic growth of greater than 2.5% to 3.5%, after inflation, is not sustainable. In the short run, stock markets can perform better than the economies they represent and the companies that make them up. In the long run, it’s impossible. A period of unusually high returns must be followed by more normal returns. That’s why the Japanese stock market, after its record-setting returns in the 1970s and 1980s, lost roughly two-thirds of its value in the 1990s. It’s why the U.S., after the boom of the late 1990s, suffered the bust of 2000 to 2002. And it’s why emerging markets, after years of scorching gains, were not a good choice to throw money at in early 2006. At that point, the only question was not whether they would lose money, but when. (I told Michael Buchanan to sit tight and, in fact, emerging markets went on to have a good year overall in 2006. But I reached Buchanan too late; he had already sold.)

The pursuit of extreme growth carries within it the seeds of its own destruction. As Warren Buffett quips, “Nothing recedes like success.” That brings us to Murphy’s Law of Investing: sooner or later, a stock or fund return that is much higher than average almost always fades back toward average. By the same token, a badly below-average return is also liable to reverse.

This tendency for trends to flip with the passage of time is called regression to the mean. Without it, giraffes would get taller with each passing generation until their hearts and hips burst under the strain. Big oak trees would drop bigger acorns, yielding larger and larger saplings until full-grown trees collapsed of their own height and weight. Tall people would always have even taller offspring, and so would their kids, and so on, until no one could get through a nine-foot-tall doorway without ducking.

Regression to the mean is nature’s way of leveling the playing field, in almost every game, including investing. So, whenever you gamble that a very high (or low) investment return will continue, the odds are overwhelmingly against you. Michael Buchanan should have been betting on regression to the mean; instead, he bet against it. By constantly grabbing the hottest returns he could find, he virtually guaranteed that he would get scalded sooner or later.

Other aspects of Murphy’s Law apply to investing. Robert Matthews points out that a great Cambridge mathematician, G. H. Hardy, believed in Murphy’s Law of Umbrellas. “Hardy was convinced that there is a malevolent rain god,” says Matthews, “so he would send an assistant outside carrying an umbrella to trick the god and ensure that it wouldn’t rain on Hardy’s cricket match that day.” Even in soggy England, however, the odds that it will rain during any given hour of the day are only about 10%. So, even when the forecast is for a 100% chance of rain that day, the odds of rain at any particular hour are much lower. Therefore, most of the times you lug an umbrella because of a rainy forecast, you will end up never opening it. And the more often you tote an umbrella around under a sunny sky, the more likely it is to stick in your selective memory. You will be much less inclined to remember the less common cases when you brought your umbrella and it did rain. As a result, you will tend to overestimate how often you carried an umbrella in vain, and to underestimate how often you didn’t bring it when you should have.

Likewise, whenever one sector of the stock market is hot, diversifying your money across other assets will always feel like a waste of effort—an umbrella you never seem to need. As Michael Buchanan’s story shows, however, it is a mistake to think you don’t have to be diversified. No matter how many times you carry an umbrella without needing it, you will be very glad indeed to be carrying one when a downpour finally hits.

Your apparent tendency to pick the wrong checkout line holds an investing lesson, too. If three cash registers are open, the odds that you will pick the fastest line are only 33%. Two-thirds of the time (assuming the same number of people are waiting and the checkout clerks are about equally efficient), one of the other lines will move faster. With four lines open, your odds drop to one in four. So the raw math is always against you: No matter which line you pick, it will usually be the wrong choice. You may think your success rate is a function of how well you size up lines, but in fact it’s predetermined.

Now consider mutual funds. On average, over time, half the funds will do better than the market and half will do worse—before expenses like trading costs,  management fees, and taxes. After expenses, the odds of sustained outperformance go from 50/50 to about one in three. Thus, if you try picking mutual funds that will beat the market on the basis of their past returns alone, you will end up wrong about two-thirds of the time. That’s why intelligent investors don’t make that mistake.

The regret you feel from chasing a hot fund or stock becomes even more painful when you hear strangers boasting about their successes—on television, online, at the next party you go to. You screwed up, but somehow they keep making money. It’s that same uncanny feeling you get after you switch lanes on the highway: As soon as you move out of the “slow” lane into the “fast” lane, the fast lane turns into a parking lot. Whichever lane you are in is the wrong one—or so it seems. The truth is more subtle: when the other lane is slow, you can pass many vehicles in a blur, so you have only a vague sense of how many you have passed. But when your own lane is slow, one car after another passes you in a discrete whoosh. What’s more, safe driving requires you to focus more of your attention on the road ahead than on what is in your rearview mirror. So you get a much better and longer look at the cars that have passed you than at the ones that you yourself have passed.

With investing, too, your losers, and other people’s winners, can often feel more visible than your own good decisions. At a cocktail party or a barbecue, it might seem as if everyone but you has a great investing move to brag about. As you sheepishly excuse yourself to get a refill, it might not occur to you that all these folks made investing mistakes, too, and that a party is the last place they would ever discuss them. This mistaken feeling of being the only one with investing regrets can tempt you into taking risks you normally would avoid. It’s important to remember that everyone makes mistakes, and that everyone who makes mistakes has regrets.

With investing, there are two basic kinds of mistakes. The first is instantaneous and infuriating: you buy and the price tanks, or you sell and the price soars. You instantly know you did something wrong, and you immediately kick yourself.

The second kind of mistake is not obvious at first. While you’re lying on a towel at the beach, there is no single moment when you can look at your skin and see it turn from a healthy bronze glow to the neon red of a painful sunburn. A burn occurs so gradually that the transition is invisible. An investment mistake is often like a sunburn: it results from forgetfulness, carelessness, or creeping commitment to a choice that you may never have been happy about. But after the fact there’s no mistaking it, and it can burn like hell, and you’re sorry you did it.

The more an outcome appears to be the result of your own choice and the more readily you can imagine having done something different, the more painful your regret is likely to be. So, whenever possible, do as little as possible. Instead of making judgments one at a time, you should follow policies and procedures that put your investing decisions on autopilot. Think of it as cruise control for your portfolio. In 1995, I got a speeding ticket driving my in-laws’ car—and was so mortified that I swore I would never get another. Ever since, whenever I get on a highway, I check the speed limit and set my cruise control—eliminating all worries that I will get careless or emotional and end up speeding. “The more you can automate your investing,” says psychologist Thomas Gilovich of Cornell University, “the easier it should be to control your emotions.” Here are three forms of investing cruise control.

Have rules for ruling things out.

It was easy in 2006 to be angry that you didn’t put all your money into energy stocks right before oil prices blew sky-high: “I knew it!” But you are less likely to feel regrets later if, at the time, you followed rules for ruling investments out.

What are some good rules? Never buy a stock simply because it’s been going up in price. Never put more than 10% of your money into any one company. And never put your money into any stock or fund that you’re not willing to hold for at least five years.

Sticking to a few simple guidelines for why not to buy enables you to look back and say, “I didn’t put all my money into energy stocks because I would have had to break my own investing rules.  That wouldn’t have felt right. Sooner or later, it’s bound to be a mistake.” This way, you make an impulsive decision feel like a bigger departure from your normal behavior, so you are less likely, when you look back, to regret not having acted on that impulse.

Get Help pulling the trigger.

Because it can be so hard to sell a hopeless loser, you may need to get used to the idea. If you’ve re-examined your original reasons and concluded that an investment truly was a mistake—but you still can’t face getting rid of it—then you need a push. Psychologist Robin Hogarth of Pompeu Fabra University in Barcelona suggests changing the log-on password for your brokerage account to something like “dumpmylosers.” Typing that reminder every time you check on your account, puts you in the position of a musician who practices constantly. The idea of selling losers will become second nature to you; as you internalize it, you will become more comfortable with the need for action.

Writers, engineers, and graphic designers all know that the best way to spot their errors is to have someone else look over their work. A few money-management firms make it mandatory for each investment holding to be reviewed by someone other than the person who bought it; banks can reduce their losses by having bad loans re-evaluated by someone other than the executive who first authorized them. It is a lot easier to admit that investing in a stock was a mistake if you are not the person who made the mistake. Get a second opinion whenever you can.

Think about the silver lining.

It helps to think of your losing investments not as liabilities but as the tax assets they are. Taking a tax loss is one of the few attractive loopholes left for Canadians looking to reduce their tax bills. If you let your loss fester, it has no value to you. If, instead, you sell and lock in the loss, then you generate cash you can put to work elsewhere, and you can write off the loss and cut your tax bill.

Thinking about the tax benefits of selling your losers can help you stop focusing on whether the stock you sell might bounce back as soon as you sell it. As money manager Whitney Tilson of T2 Partners likes to say, “You don’t have to make it back the same way you lost it.” If a stock or fund was really a mistake, you should get rid of it and find a better use for the money. Murphy’s Law may rule our lives, but it doesn’t have to rule our portfolios.