Fortune's Formula (27 page)

L
IKE A LONG-SIMMERING
family dispute, the Kelly criterion feud often sidetracked onto what each side thought the other insinuated. Nils Hakansson’s 1971 article (“Capital Growth and the Mean-Variance Approach to Portfolio Selection”) recast Kelly’s and Latané’s ideas within the framework of utility theory and mean-variance analysis. He was speaking the language practically all economists spoke.

The article contained a mistake in the math. In a responding article, Merton and Samuelson jumped all over the error, rightly enough. Concluded the MIT authors: “Again the geometric mean strategy proves to be fallacious.”

Except that it wasn’t actually the geometric mean strategy they had refuted. It was an error in an article about it.

Jimmie Savage died in 1971. His death did not end the squabbling over what he said or didn’t say in that footnote. “Given the qualifications,” wrote Latané in 1978, it was “very difficult to refute” Savage’s original statement, no matter what he might have said to Samuelson later.

Samuelson fired back that Latané should “spare the dead” and “free [Savage’s] shade of all guilt”—the guilt of having once endorsed the geometric mean criterion.

“It is surprising to note,” wrote Hebrew University’s Tsvi Ophir (1978), “how some erroneous propositions may persist long after they have been thoroughly disproven. Such is the case with regard to the geometric mean rule for long-run portfolio selection—and this despite the fact that no less an authority than Paul Samuelson had debunked it.”

“As far as I know,” countered Latané (1978), by then an elderly economist at the University of North Carolina,

Did anyone actually believe the “false corollary”? Well, no one was going around saying they thought the false corollary was true. (“We heartily agree that the corollary is false,” Thorp wrote in a 1971 response to Samuelson.) What some of the pro-Kelly people were saying is that utility can be
irrelevant
. John Kelly, for instance, wrote that his racetrack gambler’s system “has nothing to do with the value function which he attached to his money.”

“My position as to the usefulness of
G
in no sense depends on utility,” said Henry Latané. “I have never considered
G
a utility measure.” “We are not interested in utility theory in this paper,” wrote Stanford’s Robert Bell and Thomas Cover. “We wish to emphasize the objective aspects of portfolio selection.”

There were two prongs to this post-utility argument. One was the positivist position that utility is an unnecessary concept that ought to be discarded (the economists’ phlogiston). Forget utility. Think of something you can see and touch, like dollars, euros, yen, casino chips, or matchsticks. The growth of dollars, euros, etc., under various money management schemes may be compared objectively, like the growth of bacteria in petri dishes. The dollars subjected to the Kelly system survive and grow faster than those subjected to any other system. The experiment can be repeated as many times as it takes to convince the skeptic.
Then
ask: Which system would you prefer for your money?

Henry Latané’s years on Wall Street gave him a more pragmatic approach than many other economists. He apparently felt that outside of the ivory tower, no one cares about utility functions. Return on investment is the portfolio manager’s scorecard. Investors flock to a manager, or abandon him or her, because of that number. Is that not itself a reason for being interested in the system that maximizes compound return?

Latané pointed out that “it is difficult to identify the underlying utilities and to tell exactly when the utilities are being maximized” in the case of a mutual fund or pension fund. The fund manager is cooking for an army. It’s impractical to gauge everyone’s taste for salt—or risk.

Thorp was managing money not only for wealthy individuals but for corporate pensions and Harvard University’s endowment. For most of these investors, Princeton-Newport was just one of many investments. The investors could do their own asset allocation. It was Thorp’s job to provide an attractive financial product. Undoubtedly, investors judged the fund largely by its risk-adjusted return.

In articles published in 1972 and 1976, Harry Markowitz made this point most forcefully. The utility function of a long-term investor should be denominated in compound return, not terminal wealth, Markowitz suggested. Imagine you’re choosing between two mutual funds. As a long-term investor, you probably have no clear idea of how long you’ll stay invested or what you’ll do with future gains. You would surely pick the fund that you believe to have the higher compound return rate. There is not much point in figuring that you’ll have X dollars in so many years with one fund and Y dollars with the other. There is even less point in deciding what you’d buy with that money and how much you prefer X dollars to Y dollars. Compound return is the only reasonable criterion for preferring one long-term investment to another.

“What about the argument,” asked Merton and Samuelson (1974), “that expected average compound return deserves analysis because such analysis may be relevant to those decision makers…who just happen to be interested in average-compound-return? After some reflection, we think an appropriate reaction would go as follows: It’s a free country. Anybody can set up whatever criteria he wishes. However, the analyst who understands the implications of various criteria has the useful duty to help people clarify goals they will, on reflection, really want…In our experience, once understanding of the issues is realized, few decision makers retain their interest in average compound return.”

It’s a
duty
to talk people out of caring about average compound return? Comments like that mystified the pro-Kelly people almost as much as Merton and Samuelson’s claim that they
succeeded
in doing so. Thorp reported that when he explained the Kelly criterion to investors, “most people I talk to say ‘Yeah, sounds great to me, I want that.’”

Thorp was in a better position to cite “real world” results than anyone. His article “Portfolio Choice and the Kelly Criterion” lists the performance record of “a private institutional investor that decided to commit all its resources to convertible hedging and to use the Kelly criterion to allocate its assets.” This investor, Thorp now confirms, was his fund Convertible Hedge Associates. From November 1969 through December 1973, the fund’s cumulative gain was 102.9 percent, versus a loss (-0.5 percent) for the Dow Jones average in the same period. “Proponents of efficient market theory, please explain,” Thorp wrote. “We consider almost surely having more wealth than if an ‘essentially different’ strategy were followed as the desirable objective for most institutional portfolio managers.”

A
T THE END
of the cul-de-sac stand two near-identical houses. Inside are two near-identical families with near-identical incomes. The Joneses are obsessed with material things. They have a list of ambitious goals, like putting in a new swimming pool by next summer, buying a big SUV when their current lease runs out, and sending their four-year-old to Harvard. The Joneses have figured out precisely what their goals will cost and precisely when they will need the money. They use these goals to design the best investment plan for themselves. Under this plan they have the best chance of having the money they’ll need when they need it.

Their neighbors, the Kellys, pay no attention to financial goals. They invest to make money, specifically to achieve the highest possible compound return on their investments. At cocktail parties, neighbors know better than to get the Kellys started on compound return. It’s all they care about!

As time goes on (we may have to wait a
very
long time) it is all but certain that the Kellys will be richer than the Joneses. As the years pass, the wealth gap between the Kellys and the Joneses will grow wider and wider.

The Joneses can’t help feeling a twinge of envy as they gaze across the picket fence. They do, after all, prefer having more money than less. The Joneses have reason to be philosophical about the growing disparity of wealth, however. “The Kellys have money,” the Joneses tell themselves; “we have something more important.” What the Joneses have is
utility
. They have tailored their investments to meet the goals that really matter to them.

The Kellys think the Joneses are crazy. Who can see this “utility” the Joneses talk about? Goals can be flexible, the Kellys say. The important thing is to make as much money as possible, as quickly as possible—and then to worry about how you’ll spend it.

Who is acting more reasonably: the utility-obsessed Joneses or the compound-return-crazy Kellys?

The Joneses have a clear-cut utility function based on wealth. Never do they wonder whether money will bring happiness. They know
exactly
how much happiness X dollars will bring. They optimize their portfolio to match these preferences. That is the hallmark of rationality as most economists see it.

There is no mystery why the Kellys end up richer.
Their
portfolio is optimized for capital growth. No other, more personal constraints are allowed to slow the Kellys’ wealth-building. The only thing that’s perhaps unexpected is the Joneses’ envy of the Kellys. Even by the Joneses’ own standards, the Kellys’ greater wealth is preferable to their own.

This is the nub of the Kelly criterion debate. To an economist, it is as natural as breathing to assume that people have mathematically precise utility functions (of wealth). They assume this without a moment’s hesitation because they need a utility function to do math. Due in no small part to Samuelson, math is what economics is all about.

The reality is that people’s feelings about wealth are often fluid, inconsistent, and hard to identify with any neat mathematical function (including logarithmic ones). Preferences are often generated on demand. You do not know what you want until you go to a certain amount of trouble to find out. This is hardly news to the organizers of opinion polls and focus groups. People have deep-seated opinions on some issues only. With other issues, you have to press them to decide—and a lot depends on how exactly you phrase the question.

About the only rock-solid preference most people have about money is that they want as much of it as possible, as fast as possible. Ask an investor how much risk he’s comfortable with, and the answer is often along the lines, “Gee, I dunno…How much risk should I be comfortable with?”

This does not mean that the investor is a dope. It means the investor has an open mind. He is above all interested in convincing himself that he is taking a reasonable position on risk and return.

The suggestion that utility might not be a concept of great practical value is one that most economists resist. Hebrew University’s Tsvi Ophir ended one article with the telling riposte that “a person accepting Latané’s [line of reasoning] has to forgo not only expected utility but the concept of utility itself.” Ophir evidently felt that was a little like forgoing sanity itself.

Behavioral finance studies suggest that people are motivated not only by absolute gains and losses but by envy. We compare our investment returns to our neighbors’ and to market indexes. A “good” return is one that compares favorably. Of all money management strategies, only Kelly’s has the virtue of being unbeatable in the long run.

There is a catch. Life is short, and the stock market is a slow game. In blackjack, it’s double or nothing every forty seconds. In the stock market, it generally takes years to double your money—or to lose practically everything. No buy-and-hold stock investor lives long enough to have a high degree of confidence that the Kelly system will pull ahead of all others. That is why the Kelly system has more relevance to an in-and-out trader than a typical small investor.

Economists are not primarily in the business of studying gambling systems. Nor did the exotic doings of arbitrageurs attract much attention from the theorists of Samuelson’s generation. The main issue of academic interest on which the Kelly system appeared to have something new to say was the asset allocation problem of the typical investor. How much of your money should you put in risky, high-return stocks, and how much in low-risk, low-return investments like bonds or savings accounts?

The Kelly answer is to put
all
of your money in stocks. In fact, several authors have concluded that the index fund investor is justified in using a modest degree of leverage. (Though the stock market is subject to crashes, and though many an individual stock has become worthless, none of the U.S. stock indexes has ever hit zero.)

Economists’ reaction to this sort of talk is: Get real. Buy-and-hold stock investing is a case where utility matters. Few investors are comfortable with an all-equity portfolio (much less with buying on margin). A not-so-unlikely market crash could cut life savings drastically, and even middle-aged people might never recover the lost ground. The “long run” is not as important to stock investors as the short and medium runs. The Kelly system may avoid utter ruin, but that is an inadequate guarantee of safety.