Ended: Nov. 1, 2012
Shannon’s most radical insight was that meaning is irrelevant. To paraphrase Laplace, meaning was a hypothesis Shannon had no need of. Shannon’s concept of information is instead tied to chance. This is not just because noise randomly scrambles messages. Information exists only when the sender is saying something that the recipient doesn’t already know and can’t predict. Because true information is unpredictable, it is essentially a series of random events like spins of a roulette wheel or rolls of dice. If meaning is excluded from Shannon’s theory, what is the incompressible substance that exists in every message? Shannon concluded that this substance can be described in statistical terms. It has only to do with how unpredictable the stream of symbols composing the message is.
Assuming you wanted your spouse to bring home Shamu, you wouldn’t just say, “Pick up Shamu!” You would need a good explanation. The more improbable the message, the less “compressible” it is, and the more bandwidth it requires. This is Shannon’s point: the essence of a message is its improbability. Shannon was not the first to define information approximately the way he did. His two most important predecessors were both Bell Labs scientists working in the 1920s: Harry Nyquist and Ralph Hartley. Shannon read Hartley’s paper in college and credited it as “an important influence on my life.” As he developed these ideas, Shannon needed a name for the incompressible stuff of messages. Nyquist had used intelligence, and Hartley had used information. In his earliest writings, Shannon favored Nyquist’s term. The military connotation of “intelligence” was fitting for the cryptographic work. “Intelligence” also implies meaning, however, which Shannon’s theory is pointedly not about. John von Neumann of Princeton’s Institute for Advanced Study advised Shannon to use the word entropy. Entropy is a physics term loosely described as a measure of randomness, disorder, or uncertainty. The concept of entropy grew out of the study of steam engines. It was learned that it is impossible to convert all the random energy of heat into useful work. A steam engine requires a temperature difference to run (hot steam pushing a piston against cooler air). With time, temperature differences tend to even out, and the steam engine grinds to a halt. Physicists describe this as an increase in entropy. The famous second law of thermodynamics says that the entropy of the universe is always increasing. Things run down, fall apart, get used up.
Shannon’s theorem of the noisy channel describes a quantity aptly called equivocation. It is a measure of ambiguity. In the case of an unreliable source (assuming you choose to consider that source as part of the communications channel), equivocation can be due to words that sound alike, typos, intentionally vague statements, mistakes, evasions, or lies. Equivocation describes the chance that a received message is wrong. Shannon showed that you must deduct equivocation from the channel capacity to get the information rate.
Kelly describes an alternate and more useful version of the same basic system. I will give a slightly different formula from the one in Kelly’s 1956 article. It is easier to remember and can be used in many types of gambling situations. It is what gamblers now call the “Kelly formula.” The Kelly formula says that you should wager this fraction of your bankroll on a favorable bet: edge/odds The edge is how much you expect to win, on the average, assuming you could make this wager over and over with the same probabilities. It is a fraction because the profit is always in proportion to how much you wager. Odds means the public or tote-board odds. It measures the profit if you win. The odds will be something like 8 to 1, meaning that a winning wager receives 8 times the amount wagered plus return of the wager itself. In the Kelly formula, odds is not necessarily a good measure of probability. Odds are set by market forces, by everyone else’s beliefs about the chance of winning. These beliefs may be wrong. In fact, they have to be wrong for the Kelly gambler to have an edge. The odds do not factor in the Kelly gambler’s inside tips. Example: The tote-board odds for Secretariat are 5 to 1. Odds are a fraction—5 to 1 means 5/1 or 5. The 5 is all you need. The wire service’s tips convince you that Secretariat actually has a 1-in-3 chance of winning. Then by betting $100 on Secretariat you stand a 1/3 chance of ending up with $600. On the average, that is worth $200, a net profit of $100. The edge is the $100 profit divided by the $100 wager, or simply 1. The Kelly formula, edge/odds, is 1/5. This means that you should bet one-fifth of your bankroll on Secretariat. A couple of observations will help to make sense of this. First: Edge is zero or negative when you have no private wire. When you don’t have any “inside information,” you know nothing that anyone else doesn’t. Your edge will be zero (or really, negative with the track take). When edge is zero, the Kelly wager, edge/odds, is zero. Don’t bet. Edge equals odds in a fixed horse race. The most informative thing you can learn from a private wire is that the race has been fixed and that such and such a horse is certain to win. How much you can make on a fixed race depends on the odds. It’s better for the sure-to-win horse to have long odds. At odds of 30 to 1, a $100 wager will get you $3,000 profit. When a horse has to win, your edge and the public odds are the same thing (30 in this case). The Kelly formula is 30/30 or 100 percent. You stake everything you’ve got. You do unless you suspect that people who fix horse races are not always trustworthy. “Equivocation” will reduce your estimated edge and should reduce your wager.
IN ITS BROADEST MATHEMATICAL FORM, Kelly’s betting system is called the “Kelly criterion.” It may be used to achieve the maximum return from any type of favorable wager. In practice, the biggest problem is finding those rare situations in which the gambler has an advantage. Kelly was aware that there is one type of favorable bet available to everyone: the stock market. People who are willing to “gamble” on stocks make a higher return, on the average, than people choosing safer investments like bonds and savings accounts. Elwyn Berlekamp, who worked for Kelly at Bell Labs, remembers Kelly saying that gambling and investment differ only by a minus sign. Favorable bets are called “investments.” Unfavorable bets constitute “gambling.” Kelly hints at an application to investing in his 1956 paper. Although the model adopted here is drawn from the real-life situation of gambling it is possible that it could apply to certain other economic situations. The essential requirements for the validity of the theory are the possibility of reinvestment of profits and the ability to control or vary the amount of money invested or bet in different categories. The “channel” of the theory might correspond to a real communications channel or simply to the totality of inside information available to the investor. “Totality of inside information available to the investor” may suggest insider trading. Shannon was once asked what kind of “information” applied to the stock market. His slightly alarming answer was “inside information.” The informational advantage need not be an illegal one. An investor who uses research or computer models to estimate the values of securities more accurately than the rest of the market may use the Kelly system. Yet it may be worth acknowledging that a certain ethical ambiguity has always been attached to Kelly’s system. In describing his system, Kelly resorted to louche examples (rigged horse races, a con game involving quiz shows…). The subtext is that people do not knowingly offer the favorable opportunities that the Kelly system exploits. The system’s user must keep quiet about what he or she is doing. Just as a steam engine cannot move when all temperature differences are eliminated, the Kelly gambler must stop when his private information becomes public knowledge.
Shannon invoked the law of large numbers throughout information theory. In a noisy communications channel where every bit is uncertain, the one certain thing is playing the percentages. Kelly used an analogous approach to make money from positive-expectation bets. The Kelly system manages money so that the bettor stays in the game long enough for the law of large numbers to work.
Active investing is therefore a zero-sum game. The only way for one active investor to do better than average is for another active investor to do worse than average. You can’t squirm out of this conclusion by imagining that the active investors’ profits come at the expense of those wimpy passive investors who settle for average return. The average return of the passive investors is exactly the same as that of the active investors, for the reason just outlined. Now factor in expenses. The passive investors have little or no brokerage fees, management fees, or capital gains taxes (they rarely have to sell). The expenses of the active traders vary. We’re using that term for everyone from day traders and hedge fund partners to people who buy and hold a few shares of stock. For the most part, active investors will be paying a percent or two in fees and more in commissions and taxes. (Hedge fund investors pay much more in fees when the fund does well.) This is something like 2 percent of capital, per year, and must be deducted from the return.
Bernoulli showed that a relatively poor merchant may improve his geometric mean by buying insurance (even when that insurance is “overpriced”) while at the same time a much wealthier insurance company is also improving its geometric mean by selling that insurance. Bernoulli maintained that reasonable people are always maximizing the geometric mean of outcomes, even though they don’t know it: “Since all of our propositions harmonize perfectly with experience it would be wrong to neglect them as abstractions resting upon precarious hypotheses.”
There is a deep connection between Bernoulli’s dictum and John Kelly’s 1956 publication. It turns out that Kelly’s prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric mean of outcomes. This rule, of broader application than the edge/odds Kelly formula for bet size, is the Kelly criterion.
When the possible outcomes are not all equally likely, you need to weight them according to their probability. One way to do that is to maximize the expected logarithm of wealth. Anyone who follows this rule is acting as if he had logarithmic utility.
Markowitz was the founder of the dominant school of portfolio theory, known as mean-variance analysis. Markowitz used statistics to show how diversification—buying a number of different stocks, and not having too much in any one—can cut risk. This idea is so widely accepted that it is easy to forget that sensible people ever thought otherwise. In 1942 John Maynard Keynes wrote, “To suppose that safety-first consists in having a small gamble in a large number of different [companies] where I have no information to reach a good judgment, as compared with a substantial stake in a company where one’s information is adequate, strikes me as a travesty of investment policy.” Keynes was afflicted with the belief that he could pick stocks better than other people could. Now that Samuelson’s crowd had tossed that notion in the dustbin of medieval superstition, Markowitz’s findings had special relevance. You may not be able to beat the market, but at least you can minimize risk, and that’s something. Markowitz used statistics to show, for instance, that by buying twenty to thirty stocks in different industries, an investor can cut the overall portfolio’s risk by about half. Markowitz saw that even a perfectly efficient market cannot grind away all differences between stocks. Some stocks are intrinsically riskier than others. Since people don’t like risk, the market adjusts for that by setting a lower price. This means that the average return on investment of risky stocks is higher. As the name indicates, mean-variance analysis focuses on two statistics computed from historical stock price data. The mean is the average annual return. It is a regular, arithmetic average. The variance measures how much this return jumps around the mean from year to year. No equity investment is going to have the same return every year. A stock may gain 12 percent one year, lose 22 percent the next, gain 6 percent the next. The more volatile the stock’s returns, the higher its variance. Variance is thus a loose measure of risk. For the first time, Markowitz concisely laid out the trade-off between risk and return. His theory pointedly refuses to take sides, though. Risk and return are apples and oranges. Is higher return more important than lower risk? That is a matter of personal taste in Markowitz’s theory. Consequently, mean-variance analysis does not tell you which portfolio to buy. Instead, it offers this criterion for choosing: One portfolio is better than another one when it offers higher mean return for a given level of volatility—or a lower volatility for a given level of return.
Latané’s 1957 doctoral dissertation treats the problem of choosing a stock portfolio. This is something that Bernoulli did not do, and that Kelly alluded to only vaguely, in the midst of a lot of talk about horse races and entropy. With Savage’s encouragement, Latané published this work in 1959, three years after Kelly’s article, as “Criteria for Choice Among Risky Ventures.” It appeared in the Journal of Political Economy. It’s unlikely that any of the article’s readers had heard of John Kelly. Latané himself had not heard of Kelly at the time of the Cowles seminar. Latané called his approach to portfolio design the geometric mean criterion. He demonstrated that it is a myopic strategy. A “near-sighted” strategy sounds like a bad thing, but as economists use it, it’s good. It means that you don’t have to have a crystal ball on what the market is going to do in the future in order to make good decisions now. This is important because the market is always changing. The “myopia” of the geometric mean (or Kelly) criterion is all-important in blackjack. You decide how much to bet now based on the composition of the deck now. The deck will change in the future, but that doesn’t matter. Even if you did know the future history of the deck’s composition, it wouldn’t bear on what to do now. So it is with portfolios. The best you can do right now is to choose a portfolio with the highest geometric mean of the probability distribution of outcomes, as computed from current means, variances, and other statistics. The returns and volatility of your investments will change with time. When they do, you should adjust your portfolio accordingly, again with the sole objective of attaining the highest geometric mean.
The geometric mean criterion can also resolve the Hamlet-like indecision of mean-variance analysis. It singles out one portfolio as “best.” Markowitz noted that the geometric mean can be estimated from the standard (arithmetic) mean and variance. The geometric mean is approximately the arithmetic mean minus one-half the variance. This estimate may be made more precise by incorporating further statistical measures.
The Kelly criterion is meaningful only when gambling profits are reinvested. Take a gambler who starts with a single dollar and rein-vests his winnings once a week. (He does not add any more money, nor take any out.)
In 1974 Paul Samuelson wrote that a high-PQ trader “is in effect possessed of a ‘Maxwell’s Demon’ who tells him how to make capital gains from his effective peek into tomorrow’s financial page reports.” Like Maxwell’s demon, Shannon’s stock system turns randomness into profit. Shannon’s “demon” partitions his wealth into two assets. As the asset allocation crosses the 50 percent line from either direction, the demon makes a trade, securing an atom-sized profit or making an atom-sized purchase—and it all adds up in the long run. The “trick” behind this is simple. The arithmetic mean return is always higher than the geometric mean. Therefore, a volatile stock with zero geometric mean return (as assumed here) must have a positive arithmetic mean return. Who can make money off an arithmetic mean? One answer: Kelly’s dollar-a-week gambler. One week he buys $1 worth of penny stock. If he’s lucky, the stock doubles. He sells, locking in a dollar profit. (It promptly goes into his wife’s hat fund.) The next week he gets a brand-new dollar and buys more penny stock. This time, he’s unlucky. The stock loses half its value. He sells, having lost 50 cents. Mr. Dollar-a-Week has gained a dollar and lost 50 cents in this typical scenario. He has averaged a 25 percent weekly profit while the stock’s price has gone nowhere. The problem with Mr. Dollar-a-Week is that he doesn’t think big. Because he bets the same amount each week, his expectation of profit remains the same. Someone serious about making money should follow the (regular) Kelly gambler, who always maximizes the geometric mean. When the Kelly gambler is allowed to split his bankroll between the cash account and the random-walk stock in any proportion, he will choose a 50–50 split, for this has the highest geometric mean. Shannon’s scheme is a special case of Kelly gambling. Kelly’s gambler does not coin money. He only redistributes it. Here the parallel breaks down. Maxwell’s demon will disappoint anyone looking for an environmentally friendly energy source. The redistributive nature of Kelly gambling rarely bothers people. Racetracks and stock markets are full of people who are only too glad to redistribute money into their own pockets.
There was a question-and-answer period after Shannon’s talk. The very first question posed to Shannon was, did he use this system for his own investments? “Naw,” said Shannon. “The commissions would kill you.” Shannon’s stock scheme harvests volatility. If you could find a stock that doubles or halves every day, you’d be in business. As described above, $1 can be run into a million in about 240 trades. The commissions would be thousands of dollars. So what? You’d end up with a million for every dollar invested… No stock is anywhere near that volatile. With realistic volatility, gains would come much slower and would be less than commissions. There
Shannon’s system is an example of what is now known as a constant-proportion rebalanced portfolio. It is an important idea that has been studied by such economists as Mark Rubinstein and Eugene Fama (who were apparently unaware of Shannon’s unpublished work). Rubinstein demonstrated that given certain assumptions, the optimal portfolio is always a constant-proportion rebalanced portfolio. This is one reason why it makes sense for ordinary investors to periodically rebalance their holdings in stocks, bonds, and cash. You get a slightly higher risk-adjusted return than you would otherwise. Commissions and capital gains taxes cut into this benefit, though.
Samuelson’s favored word for describing the Kelly criterion was “fallacy.” From that, you might think he had spotted a subtle though fatal error in the reasoning. Not exactly. In a 1971 article, Samuelson conceded as valid this Theorem. Acting to maximize the geometric mean at every step will, if the period is “sufficiently long,” “almost certainly” result in higher terminal wealth and terminal utility than from any other decision rule…. From this indisputable fact it is apparently tempting to believe in the truth of the following false corollary: False Corollary. If maximizing the geometric mean almost certainly leads to a better outcome, then the expected value utility of its outcomes exceeds that of any other rule [in the long run].
The Kelly criterion is greedy. It perpetually takes risks in order to achieve ever-higher peaks of wealth. This results in that sexy feature, maximum rate of return. But capital growth isn’t everything. To performance car nuts, 0-to-60 acceleration time may be the only number that matters. If that were the only criterion for preferring one car to another, we’d all be driving Lamborghinis. In the real world, other things matter. Most people grow up and buy sensible Toyotas. The Kelly system may also be too conservative for some people. It makes a shibboleth of long-term performance and zero risk of ruin. These go together. The Kelly gambler shuns the tiniest risk of losing everything, for unlikely contingencies must come to pass in the long run. The Kelly criterion has, in Nils Hakansson’s words, an “automatically built in…air-tight survival motive.” That attractive feature too comes at a cost. In the short term, the Kelly system settles for a lower return than would be possible by relaxing this requirement. A true gambler who lives in the moment—who cares nothing about risk or the long term—might well choose to maximize simple (arithmetic) expectation. This gambler can expect to achieve a higher-than-Kelly return, albeit with risk, on a single spin of fortune’s wheel. Another automotive analogy (due to money manager Jarrod Wilcox) is in the way we deny the risks of driving a car. You might say that driving is a favorable “wager.” You bet your very life that you won’t get killed in a traffic accident in order to get where you want to go with more comfort and convenience than with other means of transportation. The death toll on American streets and highways corresponds to one fatal auto accident per 6,000 years of driving. A Kelly-like philosophy would find that unacceptable. You would have to forgo the benefits of driving because driving is incompatible with living forever. Hardly anyone thinks this way. As Keynes said, in the long run we are all dead. We are willing to take risks that are unlikely to hurt us in our lifetime. In short, the Kelly criterion may risk money you need for gains you may find superfluous; it may sacrifice welcome gains for a degree of security you find unnecessary. It is not a good fit with people’s feelings about the extremes of gain and loss.
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.
John Maddux, longtime editor of Nature, proposed a facetious law that might in some measure apply to either side of the Kelly dispute: “Reviewers who are best placed to understand an author’s work are the least likely to draw attention to its achievements, but are prolific sources of minor criticism, especially the identification of typos.”
“My experience has been that most cautious gamblers or investors who use Kelly find the frequency of substantial bankroll reductions to be uncomfortably large,” Thorp himself wrote. The gambling community has evolved ways to tame the Kelly system’s fearsome volatility. Thorp used similar approaches at Princeton-Newport. The importance of this is hard to overstate. It would be impossible to market a hedge fund whose asset value was as volatile as the bankroll of the serial Kelly bettor. There are two ways to smooth the ride. One is to stake a fixed fraction of the Kelly bet or position size. As before, you determine which opportunity or portfolio of opportunities maximizes the geometric mean. You then stake less than the full Kelly bet(s). A popular approach with gamblers is “half Kelly.” You consistently wager half of the Kelly bet. This is an appealing trade-off because it cuts volatility drastically while decreasing the return by only a quarter. In a gamble or investment where wealth compounds 10 percent per time unit with full-Kelly betting, it compounds 7.5 percent with half-Kelly. The gut-wrenching and teeth-gnashing is diminished much more. It can be shown that the full Kelly bettor stands a 1/3 chance of halving her bankroll before she doubles it. The half-Kelly bettor has only a 1/9 chance of losing half her money before doubling it. Ray Dillinger, writing on the Web, has described the Kelly criterion as the “bright clear line” between “aggressive investing” and “insane investing.” That is a good way of characterizing the just-short-of-fatal attraction of the Kelly system.
Bill Benter, who has made many millions using a fractional Kelly approach to racetrack wagering, says that it is easy for the best computer handicapping models to overestimate the edge by a factor of 2. This means that someone attempting to place a Kelly bet might unintentionally be placing a twice-Kelly bet—which cuts the return rate to zero. A fractional Kelly bet doesn’t sacrifice much return. In case of error, it is less likely to push the bettor into insane territory. Most of the people who successfully use the Kelly criterion in fact aim for a bet or position size less than the Kelly bet—the amount determined by the uncertainties and any preference for less volatility. In a 1997 speech in Montreal, Thorp encapsulated his position in four sentences: Those individuals or institutions who are long term compounders should consider the possibility of using the Kelly criterion to asymptotically maximize the expected compound growth rate of their wealth. Investors with less tolerance for intermediate term risk may prefer to use a lesser fraction. Long term compounders ought to avoid using a greater fraction (“overbetting”). Therefore, to the extent that future probabilities are uncertain, long term compounders should further limit their investment fraction enough to prevent a significant risk of overbetting. To its critics, the Kelly system is a mere utility function—one idiosyncratic blend of greed and recklessness. To people like Thorp and Benter, the Kelly system is more a paradigm. It is a new way of mapping the landscape of risk and return.
Unfortunately, the average stock investor can diversify only so far. She can and should diversify away some risk by buying an index fund or other well-balanced portfolio. That still leaves considerable risk of a general market crash. She can diversify a bit more by buying a global fund. This too has its limits. In our global economy, virtually all stocks and stock markets are correlated to varying degrees. A crash in Tokyo will depress stocks in New York. For this reason, the Kelly approach to regular stock investing has limited appeal. Anyone who puts all her assets in stocks is going to have to accept large dips in wealth. This fact has weighed heavily on the critics of Kelly investing. For Thorp and his hedge fund, it was largely irrelevant.
Among the small group of Kelly economists and money managers, the rhetoric is stronger yet. In several articles, portfolio manager Jarrod Wilcox offers a sweeping vision in which overbetting is behind many of the world’s financial ills—not only LTCM but Enron, debt-financed telecommunications industry overexpansion, and the 1987 failure of portfolio insurance on Black Monday. In a 2003 issue of Wilmott magazine, Thorp linked the LTCM collapse to Merton and Scholes’s intellectual critique of the Kelly system: “I could see that they didn’t understand how it controlled the danger of extreme risk and the danger of fat-tail distributions,” Thorp said. “It came back to haunt them in a grand way.”
The University of British Columbia’s William Ziemba has estimated that LTCM’s leverage was somewhere around twice the Kelly level. If correct, that would imply that the fund’s true compound growth rate was hovering near zero.
It had nothing to do with arbitrage. Shannon was a buy-and-hold fundamental investor. “In a way, this is close to some of the work I have done relating to communication and extraction of signals from ‘noise,’” Shannon told Hershberg. He said that a smart investor should understand where he has an edge and invest only in those opportunities.
Shannon emphasized “what we can extrapolate about the growth of earnings in the next few years from our evaluation of the company management and the future demand for the company’s products…Stock prices will, in the long run, follow earnings growth.” He therefore paid little attention to price momentum or volatility. “The key data is, in my view, not how much the stock price has changed in the last few days or months, but how the earnings have changed in the past few years.” Shannon plotted company earnings on logarithmic graph paper and tried to draw a trend line into the future. Of course, he also tried to surmise what factors might cause the exponential trend to continue or sputter out. The Shannons would visit start-up technology companies and talk with the people running them. Where possible, they made it a point to check out the products of companies selling to the public. When they were thinking of investing in Kentucky Fried Chicken, they bought the chicken and served it to friends to gauge their reactions. “If we try it and don’t like it,” Shannon said, “we simply won’t consider an investment in the firm.”
The Kelly cultists feel themselves surrounded by the indifferent and skeptical. Nils Hakansson estimates that no more than 10 percent of M.B.A. programs bother to mention the Kelly criterion (a situation he describes as “shameful”). “The Kelly criterion is integral to the way we manage money,” wrote chairman Bill Miller in the 2003 annual report of the Legg Mason Value Trust. But Miller says that “my guess is most portfolio managers are unaware of it, since it did not arise from the classic work of Markowitz, Sharpe, and others in the financial field.” Investment manager Jarrod Wilcox told me the subject is still “fringe.” The idea pops up in the strangest places. It has gained currency in the cryonics subculture, those people who plan to have their bodies frozen at death for potential reanimation by the medical nano-technology of a remote future. (Thorp has arranged to have his body frozen.) The unlikely connection is the need to set up a trust fund to pay for ongoing refrigeration. Art Quaife, director of the International Cryonics Foundation and chairman of its Suspension Funds Investment Committee, argued that a Kelly investment policy “should handily beat the published investment policies of other cryonics organizations.”