January 27, 2009
Simple Misunderstandings
Before I reveal how this kind of reasoning has led investment managers down the primrose path, let me respond to several common objections to the definition of risk as volatility.
Some financial novices think they have found a “gotcha” when they observe that volatility that produces returns greater than the average isn’t risk. But that’s not a problem. Forget the upward moves; as long as we can calculate the probability of downward moves, we’re still dealing with risk.
Although I told you that the graph on the left looks like a bell curve, you ought to have noticed that it doesn’t look exactly like one. For one thing, it is slightly asymmetrical. I can tell you that if we were looking at monthly rather than annual returns, the graph would look more like a bell curve, but the “tails” of the graph would be fatter than those of a true bell curve.5 Fat tails mean that very large and very small returns occur more frequently than the bell curve formula implies they should.
Again, this is not a serious difficulty, at least for approximations. Considerable mathematical expertise has been devoted to working out exactly what curve best describes investment returns. The familiar bell curve doesn’t fit the data as well as some other curves (that is to say, other probability distributions), but that only means that the mathematics required for the calculations is a lot harder, not impossible.
Some investment advisors who have never cottoned to modern finance object to the treatment of risk as a statistical phenomenon, as if the vagaries of the returns of a stock of a specific company or even the returns of the stock market as a whole, behaved in a random fashion, and without cause. But this is to confuse the manifestation of volatility with its causes. Prices may move for a reason (though many of us, through long and bitter experience, become sufficiently cynical to question this). But the economic and business forces that move stock prices aren’t necessarily regular and predictable; hence, price movements, and returns, appear to be random.
Deeper Misunderstandings
Not all misunderstandings of the equation of risk with volatility are the fault of those who object to the definition. Some arise among those who love the definition not wisely but too well, who are enamored of the concept from their first introduction in business school. They have conveyed this misunderstanding in watered down form to the public. It comes out in their bland assurance—I’m sure you’ve been hearing this constantly over the last few months—that stocks and other investments may go up and down, but if you hold on tight, you’ll always come out ahead in the long run. They visualize volatility as just a series of waves around a continuing upward trend. From this, some members of the public cheerfully draw the fallacious inference that their portfolios will have higher returns if they just crank up the riskiness.
But there should be no inference from the definition that the waves of volatility—if they are waves—are regular or easily predictable. They can be small or enormous. It is also a mistake to think that the short-run fluctuations of returns must cancel each other out in the long run. (Graham seems to have made this conceptual error.) They very much tend to do so, and I take comfort from this, as should you, if you can wait a long time. As long as the economy continues to grow, and the government doesn’t nationalize businesses, and businesses don’t broadly replace common stock with other forms of financing, the stock market should trend upward. But there is neither economic law nor mathematical proof that stocks (or other investments) must always do so. There is always the possibility that, over time, downward tumbles will pitch us into a slough, even with repeated efforts to climb back up, and the trend of returns will turn out to be very much worse than the expectation. In other words, the average return that we experience may turn out to be very different from the average we expected over any future span of time that we may specify. By analogy, bears have been known to stalk their victims; they don’t always appear of a sudden. Even if the long-term trend of stock values is ever upward, that is small consolation to those who need to pull out their money when valuations are in a trough.
And who has been peddling this nostrum? Well, many financial advisors and even economists who should know better—I’ve heard them—have done so. A business journalist or other public dispenser of investment wisdom may have reassured you, for example, that there has never been a twenty-year span when the U.S. stock market has not outpaced inflation, which is true. But, to repeat, the bears haven’t signed a treaty. As the great economist Paul Samuelson once quipped, we’ve observed only one long run, and “one” is not a statistical sample. (You can’t make statistical inferences from one observation, and it’s the future long-run average of returns and their dispersion, not the past long-run average and dispersion, that concern us.) Actually, we’ve observed multiple long runs, if you consider foreign stock markets. And that statistical sample, at least of stock markets in the twentieth century, provides less reassurance. There were a number of stock markets that went out of existence altogether, such as the Russian stock market after 1918. Furthermore, that’s an entire stock market. You can recall as easily as I the names of individual corporations that have shuffled off this mortal coil. Lehman Brothers was a large company; Enron was much larger.
Display article as PDF for printing.
Would you like to send this article to a friend?
Remember, if you have a question or comment, send it to .
