Against the Gods: The Remarkable Story of Risk

by Peter L. Bernstein

  Nevertheless, volatility, or variance, has an intuitive appeal as a proxy for risk. Statistical analysis confirms what intuition suggests: most of the time, an increase in volatility is associated with a decline in the price of the asset.10 Moreover, our gut tells us that uncertainty should be associated with something whose value jumps around a lot over a wide range. Most assets whose value is given to springing up violently tend to collapse with equal violence. If you were asked to rank the riskiness of shares of the Brazil Fund, shares of General Electric, a U.S. Treasury bond due in thirty years, and a U.S. Treasury bill due in ninety days, the ranking would be obvious. So would the relative volatility of these four securities. The overwhelming importance of volatility is evident in the role it plays in fashioning the risk-hedging instruments known as derivatives: options, swaps, and other instruments tailored to specific investor requirements.

  Morningstar, the Chicago-based service that analyzes the performance of mutual funds, has provided an interesting example of how well volatility serves as a proxy for risk." In May 1995, Morningstar reported that mutual funds that invest in bonds and that charge fees (known as 12b-1 fees) to cover their promotional expenses-fees that come out of the shareholders' pockets-had standard deviations that averaged about 10% higher than bond funds that do not charge such fees. Morningstar came to this conclusion: "The true cost of 12b-1 fees, then, at least for bond funds, is not a slightly lower return, but a higher risk investment.... [I]t is the logical consequence of moving marketing costs into the investment equation."

  Yet there is no strong agreement on what causes volatility to fluctuate or even on what causes it in the first place. We can say that volatility sets in when the unexpected happens. But that is of no help, because, by definition, nobody knows how to predict the unexpected.

  On the other hand, not everyone worries about volatility. Even though risk means that more things can happen than will happen-a definition that captures the idea of volatility-that statement specifies no time dimension. Once we introduce the element of time, the linkage between risk and volatility begins to diminish. Time changes risk in many ways, not just in its relation to volatility.

  My wife's late aunt, a jolly lady, used to boast that she was my only in-law who never asked me what I thought the market was going to do. The reason, she explained, was this: "I didn't buy in order to sell." If you are not going to sell a stock, what happens to its price is a matter of indifference. For true long-term investors-that small group of people like Warren Buffett who can shut their eyes to short-term fluctuations and who have no doubt that what goes down will come back up-volatility represents opportunity rather than risk, at least to the extent that volatile securities tend to provide higher returns than more placid securities.

  Robert Jeffrey, a former manufacturing executive who now manages a substantial family trust, has expressed the same idea in a more formal manner: Volatility fails as a proxy for risk because "volatility per se, be it related to weather, portfolio returns, or the timing of one's morning newspaper delivery, is simply a benign statistical probability factor that tells us nothing about risk until coupled with a consequence."12 The consequence of volatility to my wife's aunt was nil; the consequence of volatility to an investor who will need to invade capital tomorrow is paramount. Jeffrey sums the matter up in these words: "[T]he real risk in holding a portfolio is that it might not provide its owner, either during the interim or at some terminal date or both, with the cash he requires to make essential outlays." (The italics are mine.)

  Jeffrey recognized that the risk inherent in different assets has meaning only when it is related to the investor's liabilities. This definition of risk reappears in many different guises, all of them useful. The central idea is that variability should be studied in reference to some benchmark or some minimum rate of return that the investor has to exceed.

  In the simplest version of this approach, risk is just the chance of losing money. In that view, a zero nominal return becomes the benchmark as investors try to build portfolios that minimize the probability of negative returns over some time period.

  That view is a long way from Markowitz's, as we can see from the following illustration. Consider two investors. One of them invested 100% in the S&P 500 at the beginning of 1955 and held on for forty years. The other invested in a 30-year Treasury bond. In order to maintain the 30-year maturity, this investor sells his original bond (now a 29-year bond) at the end of each year and buys a new 30-year bond.

  According to the Markowitz method of measuring risk, the second investor's bond, with an annual standard deviation of 10.4%, was a lot less risky than the first investor's stock portfolio, whose standard deviation worked out to 15.3%. On the other hand, the total return on the stock portfolio (capital appreciation plus income) was much higher than the bond's total return-an annual average of 12.2% as against only 6.1%. The stock portfolio's high return more than compensated for its greater volatility. The probability of a year with a zero return on the stock portfolio was 22%; the bondholder faced a 28% probability of a down year. The stock portfolio returned more than the bond's average return in two-thirds of the years in the time period. Which investor took the greater risk?

  Or consider those 13 emerging markets I mentioned earlier. From the end of 1989 to February 1994, they were three times as volatile as the S&P 500, but an investor in the package of emerging markets had fewer losing months, was consistently wealthier, and, even after the sharp drop at the end of 1994, ended up three times richer than the investor in the S&P 500. Which was riskier, the S&P 500 or the emerging markets index?

  The degree to which a volatile portfolio is risky, in other words, depends on what we are comparing it with. Some investors, and many portfolio managers, do not consider a volatile portfolio risky if its returns have little probability of ending up below a specified benchmark.* That benchmark need not be zero. It can be a moving target, such as the minimum required return for a corporation to keep its pension fund solvent, or the rate of return on some index or model portfolio (like the S&P 500), or the 5% of assets that charitable foundations are mandated to spend each year. Morningstar ranks mutual funds by riskiness in terms of how frequently their returns fall below the return on 90-day Treasury bills.

  Yet measuring risk as the probability of falling short of a benchmark in no way invalidates Markowitz's prescription for portfolio manage ment. Return is still desirable and risk is still undesirable; expected return is to be maximized at the same time that risk is to be minimized; volatility still suggests the probability of falling short. Optimization under these conditions differs little from what Markowitz had in mind. The process holds up even when risk is seen as a multi-dimensional concept that incorporates an asset's sensitivity to unexpected changes in such major economic variables as business activity, inflation, and interest rates, as well as its sensitivity to fluctuations in the market in which it trades.

  Risk can be measured in yet another probability-based fashion, this one based exclusively on past experience. Suppose an investor acts as a market-timer, trying to buy before prices rise and sell before prices fall. How much margin of error can a market-timer sustain and still come out ahead of a simple buy-and-hold strategy?

  One of the risks of market timing is being out of the market when it has a big upward move. Consider the period from May 26, 1970, to April 29, 1994. Suppose our market-timer was in cash instead of stocks for only the five best days in the market out of that 14-year period of 3,500 trading days. He might feel pretty good at having just about doubled his opening investment (before taxes), until he reckoned how he would have done if he had merely bought in at the beginning and held on without trying anything tricky. Buy-and-hold would have tripled his investment. Market timing is a risky strategy!

  Risk measurement becomes even more complicated when the parameters are fluid rather than stationary. Volatility itself does not stand still over time. The annual standard deviation of monthly returns on the S&P 500 amounted to 17.7% fr
om the end of 1984 to the end of 1990; over the next four years the standard deviation was only 10.6% a year. Similar abrupt changes have occurred in bond-market volatility. If such variation can develop in broadly diversified indexes, the likelihood is much greater that it will appear in the case of individual stocks and bonds.

  The problem does not end there. Few people feel the same about risk every day of their lives. As we grow older, wiser, richer, or poorer, our perception of what risk is and our aversion to taking risk will shift, sometimes in one direction, sometimes in the other. Investors as a group also alter their views about risk, causing significant changes in how they value the future streams of earnings that they expect stocks and long-term bonds to provide.

  An ingenious approach to this possibility was developed by Markowitz's student, associate, and fellow Nobel Laureate, William Sharpe. In 1990, Sharpe published a paper that analyzed the relationship between changes in wealth and the willingness of investors to own risky assets." Although, in accordance with the view of Bernoulli and of Jevons, wealthy people are probably more risk-averse than other people, Sharpe hypothesized that changes in wealth also influence an investor's aversion to risk. Increases in wealth give people a thicker cushion to absorb losses; losses make the cushion thinner. The consequence is that increases in wealth tend to strengthen the appetite for risk while losses tend to weaken it. Sharpe suggests that these variations in risk aversion explain why bull markets or bear markets tend to run to extremes, but ultimately regression to the mean takes over as contrary investors recognize the overreaction that has occurred and correct the valuation errors that have accumulated.

  Despite the criticisms of Markowitz's theory of portfolio selection, his contribution has been immense. It has provided the foundation for the primary theoretical work accomplished since 1952 and has given rise to practical applications that dominate the field of investing. Indeed, diversification has become a veritable religion among investors. Even the attacks on Markowitz have triggered new concepts and new applications that might never have come about without his innovative contributions.

  Yet much of what one makes of Markowitz's achievement, and the structure whose foundations he laid, depends on how one feels about the controversial issue of investor rationality. Just as Wall Street was beginning to apply the new theories of investment, the sound of different drummers was heard. The critically important work on rational behavior, most of which dates from the tumultuous early 1970s, provoked a dramatic break with the optimistic views of rationality that had characterized the innovations of the 1950s and 1960s. The stage was set to take up cudgels against the models of Daniel Bernoulli, Jevons, and von Neumann, to say nothing of the central assumptions of traditional economic theory.

  The response to this rough assault on hallowed principles of behavior was tentative at first, in part because academics do not always express themselves with clarity, and in part because of the enormous vested interests that had accumulated around the established theories of decision-making and choice. But the gloomy environment of the 1970s provided the impulse that unleashed the power, ingenuity, and common sense that marked the new ideas and ultimately brought them into the forefront of academic research and to the attention of practitioners. Today the journals are full of attacks on concepts of rational behavior and risk aversion.

  Daniel Bernoulli had admitted in his paper that there were "exceedingly rare exceptions" to his propositions. He underestimated how frequently human beings stray from the strait and narrow path he laid out for them. Recent research reveals that many of the deviations from established norms of rational behavior are systematic.

  There is another possibility. Perhaps people are not nonrational, but the traditional model of rationality may specify a pattern of behavior that captures only in part the way that rational human beings make their decisions. If that is the case, the problem is with the model of rationality rather than with us human beings. If the choices people make are both logical and predictable, even with varying rather than constant preferences, or with preferences that do not suit the strict prescriptions of rationality, behavior can still be modeled by mathematical techniques. Logic can follow a variety of paths in addition to the paths specified in the traditional model.*

  A growing volume of research reveals that people yield to inconsistencies, myopia, and other forms of distortion throughout the process of decision-making. That may not matter much when the issue is whether one hits the jackpot on the slot machine or picks a lottery number that makes dreams come true. But the evidence indicates that these flaws are even more apparent in areas where the consequences are more serious.

  The word "irrational" may be too strong to apply to such behavior, because irrationality conveys craziness and most people are (perhaps by definition?) not crazy. Richard Thaler, a University of Chicago economist, has observed that people are neither "blithering idiots" nor "hyperrational automatons."14 Nevertheless, Thaler's pioneering studies of how people make choices in real life reveal significant deviations from what Bernoulli or Markowitz believed.

  This is a fascinating area, a course in self-discovery. The more we learn about it, the more we realize that each of us fails the traditional tests of rationality in ways that we may never have thought about. Von Neumann, despite the brilliance of his insight, omitted important parts of the story.

  ll of us think of ourselves as rational beings even in times of crisis, applying the laws of probability in cool and calculated fashion .to the choices that confront us. We like to believe we are aboveaverage in skills, intelligence, farsightedness, experience, refinement, and leadership. Who admits to being an incompetent driver, a feckless debater, a stupid investor, or a person with an inferior taste in clothes?

  Yet how realistic are such images? Not everyone can be above average. Furthermore, the most important decisions we make usually occur under complex, confusing, indistinct, or frightening conditions. Not much time to consult the laws of probability. Life is not a game of balla. It often comes trailing Kenneth Arrow's clouds of vagueness.

  And yet most humans are not utterly irrational beings who take risks without forethought or who hide in a closet when anxiety strikes. As we shall see, the evidence suggests that we reach decisions in accord with an underlying structure that enables us to function predictably and, in most instances, systematically. The issue, rather, is the degree to which the reality in which we make our decisions deviates from the rational decision models of the Bernoullis, Jevons, and von Neumann. Psychologists have spawned a cottage industry to explore the nature and causes of these deviations.

  The classical models of rationality-the model on which game theory and most of Markowitz's concepts are based-specifies how people should make decisions in the face of risk and what the world would be like if people did in fact behave as specified. Extensive research and experimentation, however, reveal that departures from that model occur more frequently than most of us admit. You will discover yourself in many of the examples that follow.

  The most influential research into how people manage risk and uncertainty has been conducted by two Israeli psychologists, Daniel Kahneman and Amos Tversky. Although they now live in the United States-one at Princeton and the other at Stanford-both served in the Israeli armed forces during the 1950s. Kahneman developed a psychological screening system for evaluating Israeli army recruits that is still in use. Tversky served as a paratroop captain and earned a citation for bravery. The two have been collaborating for nearly thirty years and now command an enthusiastic following among both scholars and practitioners in the field of finance and investing, where uncertainty influences every decision.'

  Kahneman and Tversky call their concept Prospect Theory. After reading about Prospect Theory and discussing it in person with both Kahneman and Tversky, I began to wonder why its name bore no resemblance to its subject matter. I asked Kahneman where the name had come from. "We just wanted a name that people would notice and remember," he said.

  Their
association began in the mid-1960s when both were junior professors at Hebrew University in Jerusalem. At one of their first meetings, Kahneman told Tversky about an experience he had had while instructing flight instructors on the psychology of training. Referring to studies of pigeon behavior, he was trying to make the point that reward is a more effective teaching tool than punishment. Suddenly one of his students shouted, "With respect, Sir, what you're saying is literally for the birds.... My experience contradicts it."2 The student explained that the trainees he praised for excellent performance almost always did worse on their next flight, while the ones he criticized for poor performance almost always improved.

  Kahneman realized that this pattern was exactly what Francis Galton would have predicted. Just as large sweetpeas give birth to smaller sweetpeas, and vice versa, performance in any area is unlikely to go on improving or growing worse indefinitely. We swing back and forth in everything we do, continuously regressing toward what will turn out to be our average performance. The chances are that the quality of a student's next landing will have nothing to do with whether or not someone has told him that his last landing was good or bad.

  "Once you become sensitized to it, you see regression everywhere," Kahneman pointed out to Tversky.3 Whether your children do what they are told to do, whether a basketball player has a hot hand in tonight's game, or whether an investment manager's performance slips during this calendar quarter, their future performance is most likely to reflect regression to the mean regardless of whether they will be punished or rewarded for past performance.

  Soon the two men were speculating on the possibility that ignoring regression to the mean was not the only way that people err in forecasting future performance from the facts of the past. A fruitful collaboration developed between them as they proceeded to conduct a series of clever experiments designed to reveal how people make choices when faced with uncertain outcomes.