Random Walks?

How can we find the truth behind a set of numbers?

Photo: Jade. Source: Morguefile

If you follow the wanderings of a drunk college student and the student’s puppy, they both seem to follow a random walk. The student stumbles about, while the puppy follows every new scent that crosses its nose. But there’s something interesting about them: they never get very far from one another. Periodically, the drunk calls the dog’s name, thinking, “I can’t let him get too far off.” And the pup returns. They periodically assess how far they are from each other, and move to fill that gap.

They have what might be called an error-correcting mechanism. If you know where the student is, the dog isn’t likely to be very far away. The same holds true for the puppy: find the dog and you’ll find the student. The dog isn’t on a leash, but it never wanders too far off.

Source: Wharton Business School

There’s another aspect of this illustration that’s helpful. If you see their footprints in the snow the next morning, they seem to wander all over the place. There’s no rhyme or reason. They may go one direction, then another. But there’s a funny thing about people: eventually, they always seem to get home. If you don’t know where the student or the dog are, wait a few hours. Odds are, sometime in the wee hours, they will find their room. Eventually, you’ll find them both snoring.

There’s a lesson in here for investors. When you examine any variable up close, it can look like it follows a random walk—a drunk stumbling down the avenue. Sometimes two variables are cointegrated: they never get very far from one another. But even if you know they’re moving together, you may not know where they are.

That’s just the close-up, though. When you look at the bigger picture, you know what’s happening. After a night on the town, the drunk is headed to bed. It may take a long time or a short time, but the need for rest ultimately trumps everything else. In the same way, when you take a broader perspective, the trend in the markets is clear. It may wend and wind its way along, but in the end the market advances because earnings grow because the economy expands. Any one stock or earnings report or economic variable may seem random, but the larger picture is actually pretty clear.

S&P 500. Log scale. Source: Bloomberg

So don’t get lost trying to trace the latest market gyration. We know where this market lives. Eventually, it will get there.

Douglas R. Tengdin, CFA

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