January 27, 2009
The Real Problem with Volatility
Did you snicker, several paragraphs back, when I said that banks and insurance companies can calculate the size of a possible loss at any specified probability? You were right to do so.
Among the causes of the current financial crisis was the failure of our financial institutions to calculate correctly the risks inherent in the portfolios of financial securities that they held. This is not so much the fault of identifying risk with volatility, as the result of the difficulty of applying this definition in practice.6 This difficulty humbles the manager of your personal portfolio no less than it does the senior executives of the largest banks.
The source of the difficulty is an excessive but unavoidable dependence on historical numbers for predicting the future. Graham, when expounding on the importance of the margin of safety, was sensitive to this problem; that’s why he emphasized the importance of a very large margin of safety. “The bond investor does not expect future average earnings to work out the same as in the past,” he wrote, “if he were sure of that, the margin demanded might be small.”
When, a short while ago, I blithely calculated that there was a 1-in-20 chance that the U.S. stock market would have a return of less than -22.2% in a single year, I was relying on the historical average and the historical volatility of returns. (I was also assuming, contrary to the evidence, that extreme returns were no more likely than the bell curve formula implies.) The number I used for volatility represented risk, my uncertainty of what returns will be. But I don’t know what the volatility and the average return will be in the future. In short, there are two levels of uncertainty about future returns: We take volatility to be the measure of our uncertainty, but we’re uncertain about the degree of our uncertainty, because we rely on history to estimate it, and we’re uncertain what exactly it is that we’re uncertain about.
And it gets worse. Recall the bell-like plot of annual returns. Most of the returns are in the big, bulky middle. But financial ruin skulks in the left-hand tail of the plot, representing very large negative returns. Recall also that I said that the tail is fat, meaning that really bad returns have occurred more often that we’d expect if the curve were a true bell curve. But, however fat the tail, we have historically observed very few really bad annual or even monthly returns on the stock market. And that, in turn, means that, even if we could be sure that the future would be just like the past—and we’re sure of the contrary—we have too few observations to have any justifiable confidence in inferences we’d draw from these historical data about the frequency and size of these confounding returns. Moreover, whatever the idealized shape that the statisticians may fit to the historical data, it is only an ideal approximation to the irregular reality of bad investment returns as they punished us in the past and as they may punish us in the future. None of us will live long enough to see the many financial disasters required to match the smooth mathematical curves postulated by the statisticians.
Can We Do Better?
Have the financial economists and risk managers been utter fools?
Of course not. I have not been suggesting that economists (at least the ones who specialize in finance) think only that risk equals the volatility of returns, and that they therefore don’t understand risk. Neither proposition is true; well, maybe the latter, but only because the subject is deep, not because economists are simple-minded. The statistical approach to risk has indeed been fruitful, but mainly when applied to short spans of time. Measures of volatility tend to be stable over these intervals. We have lots of data for short intervals (seconds, minutes, hours, days, weeks, and to some extent, months). I have, myself, made ample use of the mechanical tools that the financial engineers have built using the statistical approach. But these tools do underestimate extreme risks, and they may not be applicable when there is an abrupt regime change in the larger economy.
How, then, should we estimate investment risk and manage our wealth around it? This is a larger topic to which I cannot do justice in this short essay. If risk were not a consideration, successful investing would be easy. Those who select individual stocks and bonds, whether private investors or professional advisors, can reasonably find comfort in Graham’s margin of safety, but this isn’t applicable to the full panoply of modern investment instruments, including mutual funds and options. It can also lead to over-engineered portfolios, like a nineteenth-century stone bridge that can safely carry a far heavier load of traffic than will ever actually pass over it. We cannot turn back the leaves of the calendar to the simpler financial world of 1950, nor should we. Alternatively, we can use the high-tech tools of the financial engineers, as long as we recognize that these are not well suited to long-term decisions, and that they may underestimate the likelihood of extreme events.
For longer-term planning, I prefer to be informed by the historical variability of returns, but I know that through them, I see the future only darkly. I continue to find useful the kind of mathematical analysis that I presented earlier, but I always remember that the results underestimate the chances of very bad investment results. I think of the estimated value corresponding to, say, a 1-in-20 chance of investments turning bad as an upper limit; the probability is likely greater than 1-in-20 that things will be that bad or worse.7 I also believe that it is necessary to take into consideration other kinds of risk besides volatility, pure and simple. Because the observed volatility of investment assets is a manifestation of underlying economic factors, we ought to consider the risks associated with those factors. And because risks are not constant at all times—that’s why we have so much difficulty estimating future risks—we should take into account the prices and cash flows of our investments, as Graham did. It only stands to reason that if the prices of the investments are high when compared with expected cash flows, then the risk is greater than it would be otherwise. Mind you, this does not mean that high prices relative to cash flows portend a crash; rather, it means that the probability of a crash has increased. It also, for that matter, means that the probability of a modest decline in returns has increased. A forecast of increased risk is not the same as a forecast of lower returns.
Objectivity and Subjectivity
My purpose in this essay has been to begin to define and negotiate the concept of investment risk, not to give false assurances. I repeat, the bears haven’t signed a treaty. All the same, despite the hard times that we are facing right now, one has to remember that such times are unusual, very unusual. Even though, in the words of the Primo Levi story, we now “taste bear meat,” there are reasons for hope.8 The U.S. government will not soon be taken over by a Communist cadre, nor will all our means of production be permanently nationalized by socialists. The U.S. has one of the younger populations among the developed countries, which means that it will continue to be highly productive. It is not time to hoard canned goods, buy guns, and move to a bunker in Idaho or Arkansas. If investment prices depend upon the outlook for the economy, we can at least say that the worst possible outcomes are not in sight.
So, having not given you false assurances, I’ve given you real assurances. That’s because I don’t know how, having considered what I just told you, you now perceive investment risk, and I don’t want this essay to alarm you unduly. It’s one thing to calculate or estimate the size of risk. It’s another to judge whether it is terrifyingly large or comfortingly small, and that judgment depends on both your circumstances (that is, your wealth and your expected income and expenses), and your emotional composure. For example, if you are already enormously wealthy, with no great commitments for your money (such as to a charitable foundation), and of sanguine temperament, then you may easily weather a halving of your wealth.
The elegance of the definition of risk as volatility lies both in its making risk a matter of statistical calculation and in its separation of risk from the concept of risk tolerance. In modern financial theory, we first treat risk as an autochthonous idea, then we define risk tolerance as the psychology of risk. And to understand risk tolerance, we need first to explore the relationship between risk and return.
Conclusion
Investment risk should be viewed as a matter of probabilities, something that may be quantifiable, and that some amount of risk, even risk of extreme outcomes, is ever present. But I have also made three other points, namely, that it is useful to identify investment risk with the volatility of returns, second, that some common inferences from this identification are incorrect, and third, that a little statistical learning can lead to dangerous underestimation of investment risk.
Even when risk isn’t quantifiable because of the vast unknowability of the future, we can nonetheless reason about it as if it were. Because risk is ever present for any investment, you should never trust anyone who implies that he or she can select investments that have no risk whatsoever. (Besides, the law forbids us advisers to make an explicit statement to that effect.) But not all investments have the same risks, and for any single investment, different outcomes have different likelihoods. For some investments, the chances of especially bad outcomes may be imponderably tiny.
I have played fast and loose with the kinds of investments I used to make my points: bonds, stocks, and markets. These all exhibit volatility of returns, but to different degrees, with different distribution curves and tails, and for different reasons. In particular, there is an important distinction to be made between the risk of individual investment securities and the risk of amalgams or aggregations of securities, which is what mutual funds and markets are. To understand this distinction, we need to explore the concept of diversification.
Adam Jared Apt, CFA, is a financial advisor and the owner of Peabody River Asset Management, based in Cambridge, MA.
7 Rebonato proposes a much more sophisticated way of addressing this issue.
8 Primo Levi, "Bear Meat,” translated by Alessandra Bastagli, The New Yorker, January 8, 2007.
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