This outcome is known as a Nash Equilibrium, named after John Nash, another Princetonian and one of the 1994 winners of the Nobel Prize for his contributions to game theory.18 Under the Nash Equilibrium the outcome, though stable, is less than optimal. Both sides would obviously prefer almost anything to this one. Yet they cannot reach a better bargain unless they drop their adversarial positions and work together on a common policy that would give each a supportive, or at least a neutral, role that would keep them from getting into each other's way. An example of that radically different state of affairs arose in 1994, when Fed policy was contractionary and the politicians were uncharacteristically willing to stand by without interfering.
Blinder's game reveals a keen insight into the way contesting powers in Washington behave toward one another. But it can be generalized into many other situations: Drop the bomb, do nothing, or sue for peace. Cut prices, do nothing, or raise prices. Bet your poker hand on the basis of the probabilities, fold, or bluff.
In Blinder's example, the players know each other's intentions, which is seldom the case. It also fails to include the preferences of consumers, employees, and business managers, all of whom are very much involved in the outcome. When we change the rules by expanding the number of players or by restricting the information available to the players, we have no choice but to resort to higher mathematics. As von Neumann and Morgenstern remarked, ". . . what a complexity of theoretical forms must be expected in social theory."
In August 1993, the Federal Communications Commission decided to auction off wireless communications rights. Two licenses would be issued for each of 51 zones around the country; no bidder could acquire more than one license in any zone. The usual procedure in such auctions is to call for sealed bids and to award the contract to the highest bidders. This time, acting on the advice of Paul Milgrom, a Stanford University professor, the FCC chose to conduct the auction according to game theory, calling it a "Spectrum Auction."
First, all bids would be open, so that each contestant would always know what all the others were doing. Second, there would be successive rounds of bidding until no contestant wanted to raise its bid any higher. Third, between rounds, contestants could switch their bid from one zone to another or could bid simultaneously for licenses in adjoining zones; since there is an economic advantage in having licenses in adjoining zones, a particular license might be worth more to one party than it would be to another. In short, each decision would be based on the known decisions of the other players.
The contestants found that making decisions was no easy matter. Each of them had to guess about the intentions of the others, studying their reputation for aggressiveness, their financial capacity, and their existing licensing structures. On occasion, a properly placed bid by one contestant would clearly signal its intentions to the others, thereby avoiding a cycle of competitive bidding for some particular license. Pacific Telesis, which hired Milgrom as their consultant in the auction, went so far as to take out full-page ads in cities where potential competitors were located to make clear their determination to win no matter what. Some contestants joined together to prevent costly bidding for the same license.
The auction went on for 112 rounds over three months and brought the government $7.7 billion. Although some argued that the government could have raised more money if the FCC had prohibited the alliances, the allocation of licenses in the end probably turned out to be more efficient in terms of the economies of building franchises than it would have been under the traditional procedure.
The motivation to avoid destructive bidding competitions is understandable. The highest bidder in an auction of this kind often suffers what is known as the Winner's Curse-overpaying out of a determination to win. The Winner's Curse does not need a fancy auction-the same curse may be visited on an investor in a hurry to buy a stock on which someone has provided a hot tip. To avoid the curse, trading sometimes takes place on computer screens in a manner that closely resembles the spectrum auction. The players-usually large financial institutions like pension funds or mutual funds-are anonymous, but all bids and offers are displayed on the screen together with reservation prices above which the investor will not buy and below which the seller will not sell.
In January 1995, the publication Pensions and Investments reported on another application of game theory in making investments. ANB Investment Management & Trust in Chicago had introduced a strategy explicitly designed to avoid the Winner's Curse. The chief investment officer, Neil Wright, saying he had based the strategy on the Nash Equilibrium, claimed that the Winner's Curse is usually associated with stocks that have abnormally wide price ranges, which "means there is a lot of uncertainty about how the company will do." A wide price range also indicates limited liquidity, which means that a relatively small volume of buying or selling will have a significant impact on the price of the stock. Wright accordingly planned to select his portfolio from stocks with narrow trading ranges, an indication that they are priced around consensus views, with sellers and buyers more or less evenly matched. The assumption is that such stocks can be bought for little more than their consensus valuation.
Von Neumann and Morgenstern based The Theory of Games and Economic Behavior on one essential element of behavior: the winnings that will accrue to an individual who maximizes his utility-makes the best of the available tradeoffs within the constraints set by the game theory-will depend upon how much he "can get if he behaves 'rationally.' This `can get' [the winnings he can expect] is, of course, presumed to be a minimum; he may get more if others make mistakes (behave irrationall y)."19
This stipulation has posed a major problem for critics, including distinguished behavioral psychologists like Daniel Ellsberg and Richard Thaler, whom we will meet later. In a highly critical paper published in 1991, the historian Philip Mirowski asserted, "All is not well in the House of Game Theory-in every dreamhouse a heartache-and signs of pathology can no longer be ignored."20 He cites criticisms by Nobel Prize winners Henry Simon, Kenneth Arrow, and Paul Samuelson. He claims that game theory would never have amounted to anything had von Neumann not sold it to the military; he even goes so far as to speculate, "Some laid the blame for the escalation of nuclear weaponry directly at the door of game theory."21 Indeed, Mirowski claims that Morgenstern was a "godsend" to von Neumann because he proposed economists as an audience for game theory when no one else was interested. Mirowski is scathing about the naivete and oversimplification of their definitions of "that sadly abused word," rationality, which he describes as "a strange potage."22
Yet, game theory's assumption of rational behavior, and von Neumann and Morgenstern's dream that such behavior can be measured and expressed in numbers, has unleashed a flood of exciting theories and practical applications. As the examples I have offered make clear, its influence has reached far beyond the military.
During the 1950s and 1960s efforts were renewed to broaden the study of rationality, particularly in economics and finance. Some of the ideas advanced then seem lacking in substance today; in Chapters 16 and 17 we will subject those ideas to critical analysis. But we must understand that, up to about 1970, much of the enthusiasm for rationality, for measurement, and for the use of mathematics in forecasting emerged from the optimism that accompanied the great victories of the Second World War.
The return of peacetime was heralded as an opportunity to apply the lessons learned so painfully during the long years of depression and war. Perhaps the dreams of the Enlightenment and the Victorian age might at last come true for all members of the human race. Keynesian economics was enlisted as a means of controlling the business cycle and promoting full employment. The aim of the Bretton Woods Agreements was to recapture the stability of the nineteenth-century gold standard. The International Monetary Fund and the World Bank were set up to nourish economic progress among disadvantaged people around the world. Meanwhile, the United Nations would keep peace among nations.
In this environment, the Victorian concept of ra
tional behavior regained its former popularity. Measurement always dominates intuition: rational people make choices on the basis of information rather than on the basis of whim, emotion, or habit. Once they have analyzed all the available information, they make decisions in accord with well-defined preferences. They prefer more wealth to less and strive to maximize utility. But they are also risk-averse in the Bernoullian sense that the utility of additional wealth is inversely related to the amount already possessed.
With the concept of rationality so well defined and so broadly accepted in intellectual circles, its transformation into rules for governing risk and maximizing utility was bound to influence the world of investing and managing wealth. The setting was perfect.
The achievements that followed brought Nobel prizes to gifted scholars, and the definitions of risk and the practical applications that emerged from those achievements revolutionized investment management, the structure of markets, the instruments used by investors, and the behavior of the millions of people who keep the system working.
,his chapter deals specifically with how to measure risk when we invest in securities. Impossible as that may sound, quantification of investment risk is a process that is alive, well, and regularly practiced by professionals in today's world of globalized investing. Charles Tschampion, a managing director of the $50 billion General Motors pension fund, recently remarked, "Investment management is not art, not science, it's engineering.... We are in the business of managing and engineering financial investment risk." The challenge for GM, according to Tschampion, "is to first not take more risk than we need to generate the return that is offered."' A high degree of philosophical and mathematical sophistication lies behind Tschampion's words.
Throughout most of the history of stock markets-about 200 years in the United States and even longer in some European countries-it never occurred to anyone to define risk with a number. Stocks were risky and some were riskier than others, and people let it go at that. Risk was in the gut, not in the numbers. For aggressive investors, the goal was simply to maximize return; the faint-hearted were content with savings accounts and high-grade long-term bonds.
The most authoritative statement on the subject of risk had been issued in 1830 and had been purposefully vague.' It appeared in the judge's decision in a lawsuit over the administration of the estate of John McLean of Boston. McLean had died on October 23, 1823, leaving $50,000 in trust for his wife to receive the "profits and income thereof' during her lifetime; on her death, the trustees were to distribute half the remainder to Harvard College and the other half, or "moiety," to Massachusetts General Hospital. When Mrs. McLean died in 1828, the estate was valued at only $29,450. Harvard and the hospital promptly joined in bringing suit against the trustees.
In rendering his decision in the case, justice Samuel Putnam concluded that the trustees had conducted themselves "honestly and discreetly and carefully, according to the existing circumstances, in the discharge of their trusts." He declared that trustees cannot be held accountable for a loss of capital that was not "owing to their wilful default.... If that were otherwise, who would undertake such hazardous responsibility?" He continued with what came to be immortalized as the Prudent Man Rule:
Do what you will, the capital is at hazard.... All that can be required of a trustee to invest, is, that he shall conduct himself faithfully and exercise a sound discretion. He is to observe how men of prudence, discretion, and intelligence manage their own affairs, not in regard to speculation, but in regard to the permanent disposition of their funds, considering the probable income, as well as the probable safety of the capital to be invested.
There the matter rested for 122 years.
In June 1952, the Journal of Finance, the leading academic journal in finance published a fourteen-page article titled "Portfolio Selection. "3 Its author was Harry Markowitz, an unknown 25-year-old graduate student at the University of Chicago. That paper was innovative on so many levels, and ultimately so influential both theoretically and in terms of practicality, that it earned Markowitz a Nobel Prize in Economic Science in 1990.
In choosing equity investing as his topic, Markowitz was dealing with a subject that serious journals up to that time had considered too dicey and speculative for sober academic analysis. Even more daring, Markowitz was dealing with the management of the investor's total wealth, the portfolio.* His main theme was that a portfolio of securities is entirely different from holdings considered individually.
He had no interest in the foolishness that characterized most stockmarket literature, such as lessons from a ballet dancer on how to become a millionaire without really trying, or how to be recognized as a guru among market forecasters.4 Nor did he make any effort to present his ideas in the simple-minded language typical of most articles about the stock market. At a time when any kind of mathematical treatment was rare in economics, particularly in and von Neumann had cut a lot less ice up to that point than they had hoped-ten of the fourteen pages that make up Markowitz's article carry equations or complicated graphs.
Markowitz is parsimonious in providing footnotes and bibliography: he makes only three references to other writers in a setting where many academics measured accomplishment by the number of footnotes an author could manage to compile. This failure to credit his intellectual forebears is curious: Markowitz's methodology is a synthesis of the ideas of Pascal, de Moivre, Bayes, Laplace, Gauss, Galton, Daniel Bernoulli, Jevons, and von Neumann and Morgenstern. It draws on probability theory, on sampling, on the bell curve and dispersion around the mean, on regression to the mean, and on utility theory. Markowitz has told me that he knew all these ideas but was not familiar with their authors, though he had invested a good deal of time studying von Neumann and Morgenstern's book on economic behavior and utility.
Markowitz placed himself solidly in the company of those who see human beings as rational decision-makers. His approach reflects the spirit of the early years after the Second World War, when many social scientists set about reviving the Victorian faith in measurement and the belief that the world's problems could be solved.
Strangely, Markowitz had no interest in equity investment when he first turned his attention to the ideas dealt with in "Portfolio Selection." He knew nothing about the stock market. A self-styled "nerd" as a student, he was working in what was then the relatively young field of linear programming. Linear programming, which happened to be an innovation to which John von Neumann had made significant contributions, is a means of developing mathematical models for minimizing costs while holding outputs constant, or for maximizing outputs while holding costs constant. The technique is essential for dealing with problems like those faced by an airline that aims to keep a limited number of aircraft as busy as possible while flying to as many destinations as possible.
One day, while waiting to see his professor to discuss a topic for his doctoral dissertation, Markowitz struck up a conversation with a stock broker sharing the waiting room who urged him to apply linear programming to the problems investors face in the stock market. Markowitz's professor seconded the broker's suggestion, enthusiastically, though he himself knew so little about the stock market that he could not advise Markowitz on how or where to begin the project. He referred Markowitz to the dean of the business school, who, he hoped, might know something about the subject.
The dean told Markowitz to read John Burr Williams' The Theory of Investment Value, an influential book on finance and business management. Williams was a scrappy, impatient man who had launched a successful career as a stock broker in the 1920s but had returned to Harvard as a graduate student in 1932, at the age of thirty, hoping to find out what had caused the Great Depression (he didn't). The Theory of Investment Value, published in 1938, was his Ph.D. thesis.
Markowitz dutifully went to the library and sat down to read. The book's very first sentence did the trick for him: "No buyer considers all securities equally attractive at their present market prices ... on the contrary, he seeks `the
best at the price."'S Many years later, when Markowitz was telling me about his reaction, he recalled, "I was struck with the notion that you should be interested in risk as well as return."
That "notion" seems unremarkable enough in the 1990s, but it attracted little interest in 1952, or, for that matter, for more than two decades after Markowitz's article was published. In those days, judgments about the performance of a security were expressed in terms of how much money the investor made or lost. Risk had nothing to do with it. Then, in the late 1960s, the aggressive, performance-oriented managers of mutual fund portfolios began to be regarded as folk heroes, people like Gerry Tsai of the Manhattan Fund ("What is the Chinaman doing?" was a popular question along Wall Street) and John Hartwell of the Hartwell & Campbell Growth Fund (" [Performance means] seeking to get better than average results over a fairly long period of time-consistently") .6
It took the crash of 1973-1974 to convince investors that these miracle-workers were just high rollers in a bull market and that they too should be interested in risk as well as return. While the Standard & Poor's 500 fell by 43% from December 1972 to September 1974, the Manhattan Fund lost 60% and the Hartwell & Cambell Fund fell by 55%.
This was a dark time, one marked by a series of ominous events: Watergate, skyrocketing oil prices, the emergence of persistent inflationary forces, the breakdown of the Bretton Woods Agreements, and an assault on the dollar so fierce that its foreign exchange value fell by 50%.
Against the Gods: The Remarkable Story of Risk Page 26