Against the Gods: The Remarkable Story of Risk

by Peter L. Bernstein

  The destruction of wealth in the bear markets of 1973-1974 was awesome, even for investors who had thought they had been investing conservatively. After adjustment for inflation, the loss in equity values from peak to trough amounted to 50%, the worst performance in history other than the decline from 1929 to 1931. Worse, while bondholders in the 1930s actually gained in wealth, long-term Treasury bonds lost 28% in price from 1972 to the bottom in 1974 while inflation. was running at 11% a year.

  The lessons learned from this debacle persuaded investors that "performance" is a chimera. The capital markets are not accommodating machines that crank out wealth for everyone on demand. Except in limited cases like holding a zero-coupon debt obligation or a fixed-rate certificate of deposit, investors in stocks and bonds have no power over the return they will earn. Even the rate on savings accounts is set at the whim of the bank, which responds to the changing interest rates in the markets themselves. Each investor's return depends on what other investors will pay for assets at some point in the uncertain future, and the behavior of countless other investors is something that no one can control, or even reliably predict.

  On the other hand, investors can manage the risks that they take. Higher risk should in time produce more wealth, but only for investors who can stand the heat. As these simple truths grew increasingly obvi ous over the course of the 1970s, Markowitz became a household name among professional investors and their clients.

  Markowitz's objective in "Portfolio Selection" was to use the notion of risk to construct portfolios for investors who "consider expected return a desirable thing and variance of return an undesirable thing. "7 The italicized "and" that links return and variance is the fulcrum on which Markowitz builds his case.

  Markowitz makes no mention of the word "risk" in describing his investment strategy. He simply identifies variance of return as the "undesirable thing" that investors try to minimize. Risk and variance have become synonymous. Von Neumann and Morgenstern had put a number on utility; Markowitz put a number on investment risk.

  Variance is a statistical measurement of how widely the returns on an asset swing around their average. The concept is mathematically linked to the standard deviation; in fact, the two are essentially interchangeable. The greater the variance or the standard deviation around the average, the less the average return will signify about what the outcome is likely to be. A high-variance situation lands you back in the head-in-the-oven-feet-in-the-refrigerator syndrome.

  Markowitz rejects Williams' premise that investing is a single-minded process in which the investor bets the ranch on what appears to be "the best at the price." Investors diversify their investments, because diversification is their best weapon against variance of return. "Diversification," Markowitz declares, "is both observed and sensible; a rule of behavior which does not imply the superiority of diversification must be rejected both as a hypothesis and as a maxim."

  The strategic role of diversification is Markowitz's key insight. As Poincare had pointed out, the behavior of a system that consists of only a few parts that interact strongly will be unpredictable. With such a system you can make a fortune or lose your shirt with one big bet. In a diversified portfolio, by contrast, some assets will be rising in price even when other assets are falling in price; at the very least, the rates of return among the assets will differ. The use of diversification to reduce volatility appeals to everyone's natural risk-averse preference for certain rather than uncertain outcomes. Most investors choose the lower expected return on a diversified portfolio instead of betting the ranch, even when the riskier bet might have a chance of generating a larger payoff-if it pans out.

  Although Markowitz never mentions game theory, there is a close resemblance between diversification and von Neumann's games of strategy. In this case, one player is the investor and the other player is the stock market-a powerful opponent indeed and secretive about its intentions. Playing to win against such an opponent is likely to be a sure recipe for losing. By making the best of a bad bargain-by diversifying instead of striving to make a killing-the investor at least maximizes the probability of survival.

  The mathematics of diversification helps to explain its attraction. While the return on a diversified portfolio will be equal to the average of the rates of return on its individual holdings, its volatility will be less than the average volatility of its individual holdings. This means that diversification is a kind of free lunch at which you can combine a group of risky securities with high expected returns into a relatively low-risk portfolio, so long as you minimize the covariances, or correlations, among the returns of the individual securities.

  Until the 1990s, for example, most Americans regarded foreign securities as too speculative and too difficult to manage to be appropriate investments. So they invested just about all their money at home. That parochial view was costly, as the following calculations demonstrate.

  From 1970 to 1993, the Standard & Poor's Index of 500 stocks brought its investors a total of capital appreciation plus income that averaged 11.7% a year. The volatility of the Index's return, as measured by its standard deviation, averaged 15.6% a year; this meant that about two-thirds of the annual returns fell between 11.7% + 15.6%, or 27.3% on the high side, and 11.7% - 15.6%, or -3.9% on the low side.

  The major markets outside the United States are usually tracked by an index published by Morgan Stanley & Company that covers Europe, Australia, and the Far East. This index is known as EAFE for short; the regulars in these markets pronounce it "Eee-fuh." EAFE's average annual return for a dollar-based investor from 1970 to 1993 was 14.3% versus S&P's 11.7%, but EAFE was also more volatile. Largely because of Japan, and because foreign market returns are translated back into a dollar that fluctuates in value in the foreign exchange markets, EAFE's standard deviation of 17.5% was over two full percentage points above the volatility of the S&P 500.

  EAFE and the U.S. markets do not usually move up and down together, which is why international diversification makes good sense. If an investor's portfolio had held 25% of its assets in EAFE and 75% in the S&P since 1970, its standard deviation of 14.3% would have been lower than either the S&P or EAFE, even while it was producing an average return that bettered the S&P 500 alone by an average of 0.6% a year.

  An even more dramatic illustration of the power of diversification appears in the accompanying chart, which shows the track record of 13 so-called emerging stock markets in Europe, Latin America, and Asia from January 1992 through June 1994. The average monthly return of each market is plotted on the vertical axis; each market's monthly standard deviation of return is plotted on the horizontal axis. The chart also shows an equally weighted index of the 13 markets as well as the performance of the S&P 500 over the same time period.

  The blessings of diversification. The track records of 13 emerging stock markets compared to the index (average of 13) and the S&P 500 from January 1992 through June 1994. The data are in percentages per month.

  Although many investors think of emerging markets as a homogeneous group, the graph shows that these 13 markets tend to be largely independent of one another. Malaysia, Thailand, and the Philippines had returns of 3% a month or better, but Portugal, Argentina, and Greece were barely in the black. Volatilities ranged from about 6% all the way out to nearly 20% a month. There is plenty of heat in this oven.

  The lack of correlation, or low covariance, among the markets caused the index to have the lowest standard deviation of any of its 13 components. A simple average of the monthly standard deviations of the twelve markets works out to 10.0%; the actual standard deviation of the diversified portfolio was only 4.7%. Diversification works.

  Note that the emerging markets were much riskier than the U.S. stock market over this 18-month period. They were also a lot more profitable, which explains why investors were so enthusiastic about these markets at the time.

  The riskiness of these markets came to light just eight months after the end of the time period covered here. Had the
analysis been extended to February 1995, it would have included the Mexican debacle at the end of 1994; the Mexican market fell by 60% between June 1994 and February 1995. From January 1992 to February 1995, the average return of the 13 markets was only a little over 1% a month, down from nearly 2% during the time span shown on the chart, while the standard deviation of the index jumped from under 5% to 6% a month; an investor in Mexico and Argentina would have ended up losing money.* The Philipines, the best-performing market, dropped from 4% a month to only 3% a month. Meanwhile, the performance of the S&P 500 showed virtually no change at all.

  By substituting a statistical stand-in for crude intuitions about uncertainty, Markowitz transformed traditional stock-picking into a procedure for selecting what he termed "efficient" portfolios. Efficiency, a term adopted from engineering by economists and statisticians, means maximizing output relative to input, or minimizing input relative to output. Efficient portfolios minimize that "undesirable thing" called variance while simultaneously maximizing that "desirable thing" called getting rich. This process is what prompted Tschampion 30 years later to describe the managers of the General Motors pension fund as "engineers."

  Investors will always want to own securities that represent "the best at the price." The expected return of a portfolio made up of such securities will be the mean, or average, of the expectations for each of the individual holdings. But holdings that appear to offer the best returns frequently disappoint while others exceed the investor's fondest hopes. Markowitz assumed that the probabilities of actual portfolio returns above and below the mean expectation will distribute themselves into a nice, symmetrically balanced Gaussian normal curve.

  The spread of that curve around the mean, from loss to gain, reflects the variance of the portfolio-with the range of possible outcomes reflecting the likelihood that the portfolio's actual rate of return will differ from its expected rate of return. This is what Markowitz meant when he introduced the concept of variance to measure risk, or the uncertainty of return; the combined approach to risk and return is commonly referred to by professionals and academics as mean/variance optimization. Common stocks have a much wider range of possible results than an obligation of the U.S. Treasury that will come due and pay off in 90 days; the return on the Treasury obligation has almost no uncertainty, because buyers will see their money again so soon.

  Markowitz reserved the term "efficient" for portfolios that combine the best holdings at the price with the least of the variance"optimization" is the technical word. The approach combines two cliches that investors learn early in the game: nothing ventured, nothing gained, but don't put all your eggs in one basket.

  It is important to recognize that there is no one efficient portfolio that is more efficient than all others. Thanks to linear programing, Markowitz's method produces a menu of efficient portfolios. Like any menu, this one has two sides: what you want is on one side and the cost of what you want is on the other. The higher the expected return, the greater the risks involved. But each efficient portfolio on the menu will have the highest expected return for any given level of risk or the lowest level of risk for any expected return.

  Rational investors will select the portfolio that best suits their taste for either aggressive objectives or defensive objectives. In the tradition of von Neumann and Morgenstern, the system provides a method to maximize each investor's utility. This is the only point in the Markowitz system in which gut matters. All else is measurement.

  "Portfolio Selection" revolutionized the profession of investment management by elevating risk to equal importance with expected return. That paper, together with the book by the same name that Markowitz wrote in 1959, provided the groundwork for just about all of the theoretical work in finance that followed. It has also supported a variety of applications over time, ranging from techniques of stock selection and the allocation of portfolios between stocks and bonds to the valuation and management of options and more complex derivative securities.

  Despite its importance, critics of "Portfolio Selection" have turned Markowitz's work into a punching bag, attacking from every side the entire set of assumptions that support it. Some of the problems they have raised are more mechanical and technical than substantive and have been overcome. Other problems continue to stir controversy.

  The first is whether investors are rational enough in their decisionmaking to follow the prescription that Markowitz set out for them. If intuition triumphs over measurement in investing, the whole exercise could turn out to be a waste of time and a flawed explanation of why markets behave as they do.

  Another criticism questions whether variance is the proper proxy for risk. Here the consequences are less clear. If investors perceive risk as something different from variance, some other measure might serve equally well and still preserve Markowitz's optimizing approach to risk and return. And perhaps not.

  Finally, what would happen if Markowitz's assumption that there is a positive relationship between risk and return fails to survive empirical tests? If high returns are systematically available on low-risk securities, or if you land in the soup with securities you thought were low-risk, a retreat to the drawing board will be necessary.

  We shall deal here briefly with the technical problems and then at greater length with the question of how well variance serves as a proxy for risk. Investor rationality is so important a matter that we devote Chapters 16 and 17 to it; investors, after all, are just people, although engaged in a particular activity, which means that the whole question of human rationality is involved.

  The technical problems arise from Markowitz's assumption that investors will have no difficulty estimating the inputs to his modelexpected returns, variances, and the covariances among all the individual holdings. But, as Keynes emphasized in A Treatise on Probability and later as well, the use of data from the past is dangerous. And degrees of belief do not always lend themselves to precise measurement, particularly with the precision that the Markowitz approach requires. As a practical matter, most applications of the approach combine past experience with forecasts, though investors recognize that a significant margin of error surrounds the results of such calculations. In addition, the sensitivity of the process to small differences in estimates of the inputs makes the results even more tentative.

  The most difficult step is in amassing the calculations required to measure how each individual stock or bond might vary in relation to each other stock or bond. William Baumol, the author of the paper demonstrating how long-term trends in productivity regress to the mean, calculated as late as 1966-fourteen years after the appearance of "Portfolio Selection"-that a single run to select efficient portfolios on the computers of that time would cost from $150 to $350, even assuming that the estimates of the necessary inputs were accurate. A more elaborate search would have run into thousands of dollars.'

  Markowitz himself was concerned about obstacles to the practical use of his ideas. In cooperation with William Sharpe-a graduate student who later shared the Nobel Prize with him-Markowitz made it possible to skip over the whole problem of calculating covariances among the individual securities. His solution was to estimate how each security varies in relation to the market as a whole, a far simpler matter. This technique subsequently led to Sharpe's development of what has come to be known as the Capital Asset Pricing Model, which analyzes how financial assets would be valued if all investors religiously fol lowed Markowitz's recommendations for building portfolios. CAPM, as it is known, uses the term "beta" to describe the average volatility of individual stocks or other assets relative to the market as a whole over some specific period of time. The AIM Constellation Fund that we looked at in Chapter 12, for example, had a beta of 1.36 during the years 1983 to 1995, which means that AIM tended to move up or down 1.36% every time the S&P 500 moved up or down 1%; it tended to fall 13.6% every time the market dropped 10%, and so on. The more stodgy American Mutual Fund had a beta of only 0.80%, indicating that it was significantly less volatile than th
e S&P 500.

  Another mathematical problem stems from the idea that a portfolio, or the security markets themselves, can be described with only two numbers: expected return and variance. Dependence on just those two numbers is appropriate if, and only if, security returns are normally distributed on a bell curve like Gauss's. No outliers are permitted, and the array of results on either side of the mean must be symmetrically distributed.

  When the data are not normally distributed, the variance may fail to reflect 100% of the uncertainties in the portfolio. Nothing is perfect in the real world, so this is indeed a problem. But it is more of a problem to some investors than to others. For many, the data fit the normal distribution closely enough to be a useful guide to portfolio decisions and calculations of risk. For others, such imperfections have become a source of developing new kinds of strategies that will be described later on.

  The matter of defining risk in terms of a number is crucial. How can investors decide how much risk to take unless they can ascribe some order of magnitude to the risks they face?

  The portfolio managers at BZW Global Investors (formerly Wells Fargo-Nikko Investment Advisors) once built this dilemma into an interesting story. A group of hikers in the wilderness came upon a bridge that would greatly shorten their return to their home base. Noting that the bridge was high, narrow, and rickety, they fitted themselves out with ropes, harnesses, and other safeguards before starting across. When they reached the other side, they found a hungry mountain lion patiently awaiting their arrival.'

  I have a hunch that Markowitz, with his focus on volatility, would have been taken by surprise by that mountain lion. Kenneth Arrow, a man who thinks about risks in many different dimensions and who understands the difference between the quantifiable and the messy, would be more likely to worry that the mountain lion, or some other peril, might be waiting at the other side of the bridge.