Capital Markets and Oracles

Introduction

The idea of self-negating prophecies has been examined since academic interest was first drawn to the Biblical story of the prophet Jonah’s harrowing experience on his way to Nineveh. In that story, after spending time in the belly of a fish, Jonah finally followed instructions and predicted the destruction of the great but wicked city of Nineveh. This prediction was self-negated, much to Jonah’s surprise, because his prophecy caused the city’s inhabitants to repent, and the city to be saved. Decades later, the concept of self-negating predictions entered the social sciences. Recently, economist Alex Tabarrok introduced this idea as a public choice problem. Politicians deciding about precaution taking with respect to future disasters they predict can be inefficiently discouraged by the likely responses to their warnings and to expensive precaution taking. They may underspend on precautions because of the character of political rewards. The idea of self-negating predictions might now be situated in behavioral economics as much as in sociology and psychology. In any event, self-negation, like a claim of self-fulfillment, requires us to think that audiences and prophets are rational but not hyperrational, as discussed in previous work.1

Small investors might be dissuaded from taking optimal precautions simply because it is difficult to evaluate risks. A vast corporate finance literature depends on an ability to evaluate risk, but doing so normally requires a continuing history of firm behavior and outcomes. Evaluating young firms is therefore difficult. Similarly, consider the ship captain who has superior information or experience, and takes a roundabout path to avoid icebergs. Most passengers and freight owners are unable to assess the risks the captain faces. They can observe late arrivals and the very rare disasters at sea. More often than not, precautions taken by the vessel’s captain prove unnecessary, and the captain is likely to be criticized for the vessel’s late arrival at its destination. Resultingly, it is possible that the captain will take insufficient precautions in the future. Similarly, an investment manager is rewarded for producing high rates of return and is often abandoned when underperforming other professional investors. This phenomenon encourages risk-taking that may be difficult to evaluate and that would be shunned by perfectly informed clients. There is no paradox in these examples; the inefficient precaution taking is simply a product of imperfect risk-reward calculations. The discussion in Part V of this Essay considers whether this unappreciated risk-taking is less troubling than apparent. Things are different for a recognized oracle with significant influence on the market. One task in this Essay is evaluating the likelihood that predictions by this oracle can be self-negating rather than self-fulfilling.

I. The Predictor’s Dilemma Examined

A. Evaluating Predictions

The predictor’s problem comes about where there can be external responses to a warning. Icebergs do not respond to a captain’s warning, and the market rarely responds to one investment manager. In contrast, many people and organizations react to predictions in the capital market made by well-known prophets who have performed well in the past and who add to their credibility by investing their own funds consistent with their own predictions. A simple example of self-negation without such an accompanying investment is useful: A teacher—a possible experienced prophet with superior information about prospective exams and students’ abilities—warns a student that they are likely to fail an important test. The act of making that prediction can trigger the listener to study harder, leading them to pass the test. The initial prediction would then be proven inaccurate because of the student’s reaction to it. In turn, the teacher-prophet might not be believed in the future, and other students who are not warned might lose out because they do not take the precaution of additional exam preparation. This is a straightforward example of the prophet’s paradox, also known as the predictor’s dilemma. In some settings, it can be thought of as a second-order moral hazard. The prophet warns and triggers a response that then shows the prophet to be wrong—and makes future predictions less likely to be believed even though they were (prior to any response) correct. In the language of corporate law, potential investors do not know the quality of experts, however admired they may be. The first-level reasoning by common investors about failed predictions can encourage even excellent prophets to diverge from what they know to be good predictions.

Of course, the clever teacher could guard against disbelief on the part of listeners who are assumed to be something less than hyperrational by announcing: “If you study three hours a day, I predict that you will pass the exam.” The student might succeed and the prophet better trusted, but of course the teacher has not been asked to predict more precisely what will happen if the student does not study as directed. Predicting doom is more likely to trigger action. Let’s assume that politicians, like teachers, can best stimulate costly precaution taking with dire threats. Investment managers are more likely to gain from upswings, and it is plausible that they are less likely to make dire predictions in the first place. Things might be different if they were appropriately compensated and penalized for performance that was inferior to the larger market; most are rewarded for upside success as well as compensated based on the assets under their management. But optimal compensation contracts require confidence in our ability to measure risk and then risk-adjusted returns. The discussion here takes compensation patterns as given and leaves the question of optimal rewards for another day and to existing works of significance.

The teacher might stimulate more studying by not warning of failure, because too many “false” warnings get the teacher characterized as a boy who cries wolf. In many situations it is difficult to know whether self-negation is more likely than self-fulfillment. In turn, it is difficult to identify good prophets, to ignore or even discipline false prophets, and to respond efficiently to warnings. Closer to home, there are probably some people who are exceptional in their ability to outperform the market, but it is difficult to identify them in the cloud of lucky and unlucky investors, not to mention difficulties in assessing the riskiness of start-ups with no history and with operations in rapidly changing markets.

Self-fulfilling predictions are more familiar than self-negating prophecies. If the Federal Reserve Board predicts a recession, fewer factories will be built and a recession is more likely to follow, even though this outcome might not have occurred without the prediction. Indeed, the rational entrepreneur will hold back on building the marginal factory even if, or especially if, they are aware of the phenomenon of self-fulfilling prophecies. The owner need only reason that others will regard the expert as knowledgeable and likely to make correct predictions. This is the stuff of bank runs. We are familiar with government insurance and bailouts, but it is possible that law should instead reward investors who do not run. Similarly, if inflation is predicted by someone thought to have superior information, consumers might rush to hoard because they think that they can make purchases more rapidly than sellers will raise prices.2 This increase in consumer demand does in fact raise prices. Placebo effects in medical care are also examples of self-fulfilling prophecies. The doctor and patient might have equal information—because patients can be told they are or might be receiving placebos, and the experiment might be double-blinded—and yet there is often a limited and somewhat curious self-fulfilling prophecy. The sugar pill brings about the same result as the real FDA-approved capsule.

These prediction curiosities, and especially the phenomenon of self-negation, suggest that a prediction can only be truly validated, and the prophet’s skill evaluated, if it is ignored or unknown, or if the predicted event is a natural occurrence that would have happened regardless of the prediction. Even then, multiple trials with these conditions are required, and the listener needs to be certain that the prophet has not made many different predictions to separate audiences in order to have a subset of predictions prove correct. As an empirical matter, if we think there is such a thing as a good predictor or prophet, then we want the prophet to be tested by making predictions in a black box, with no announcements, so that there is no response that brings about self-fulfillment or self-negation.

B. Semi-validation of Predictions

With respect to some precautions, the quality of prediction can be evaluated with comparisons to results in comparable organizations. In the political arena, the comparison is often to neighboring jurisdictions. Imagine that a politician says that crime can be reduced by hiring more police officers. The expenditure can be assessed by comparing outcomes to those achieved in neighboring jurisdictions where policing was unchanged. The comparison is imperfect; criminal activity may have moved to the neighboring jurisdiction, and that jurisdiction may change its policing in the next round. Similarly, a corporation may invest in advertising. After one successful round, competitors are likely to imitate the strategy; as a result, costly advertising may prove to be a lose-lose strategy. Correspondingly, the investment manager that suggested buying stock in one company may look good in the first round but may (themselves and contrary predictors) look bad after the second round when competitors imitate the first mover. As with so many empirical questions, a truly good prophet may need to have predicted an upswing in round one and suggested a quick sell-off before round two. This strategy reappears in Section IV.A in the context of the rise and apparent fall of returns on investments in private equity.

Some sophisticated investors might invest in passive mutual funds because they doubt anyone’s ability to beat the semi-efficient market; others might believe in an occasional oracle, like Warren Buffett, who created an active mutual fund of sorts and over a long period of time outperformed the larger market. Finally, far from the world of mutual funds that invest in a large number of publicly traded companies, there is the world of private equity (PE). It is easy for casual investors to envy the Carlyle Group. It is known for its very active investments in companies that are not publicly traded. The PE designation here refers to investments (often with borrowed money) in companies that are not widely traded, and that are accompanied by some guidance about management and redirection of capital. Ideally, some PE firms are good prophets, able to choose among many companies seeking capital. PE firms lend money to these companies at high rates of return (and with more risk) or go along for the ride by buying shares or otherwise becoming co-owners. For a time, PE firms did very well. Smaller investors were drawn to the higher rates of return earned by Carlyle and other PE firms, and they were able to invest through intermediating companies able to satisfy the requirements imposed by law to protect investors who might be ill-informed. In recent times, these PE firms have not done well,3  a pattern examined in Part IV.B.

An objection to much of what follows is the contradiction between claims like the one just made about the declining success of PE along with the (debatable) observation that despite great advances in corporate finance, it is not easy to assess the riskiness of firms and portfolios. Most readers are familiar with the Sharpe Ratio, which compares a return to what a risk-free investment would have earned. It is the difference between the return of an investment and the risk-free return divided by the standard deviation of the investment returns. In principle, it reveals the additional amount of return per unit of increase in risk. The ex post Sharpe Ratio is commonly used because we can observe actual returns rather than expected returns. A high Sharpe Ratio is attractive to investors. Buffett’s Berkshire Hathaway firm had a remarkable Sharpe ratio of .79 over forty years,4 while the S&P 500’s ratio was about .5.

In any event, the immediate and simple point here is that PE targets do not have long histories, so the best we can do is look at the Sharpe numbers offered by investors, intermediaries, or PE firms that claim to be good at choosing among enterprises that seek investors. We might be able to evaluate Carlyle or one of the many firms that university endowments invest in, hoping to do as well as Carlyle. But most of these also do not have long histories; they change personnel over time, and they can easily change their strategies as a year proceeds.

II. Doubting the Argument About Insufficient Precautions

If an informed but strategic decision-maker does not spend on precautions or otherwise reduce risk, and the disaster does occur, he or she loses points for not taking precautions. The lack of preparedness for a disaster is likely to end a career. If the claim is simply that politicians, voters, and other investors have short time horizons—they save money (or earn more) now but risk future disasters—there is nothing added by a recognition of the predictor’s dilemma. Most politicians only serve short terms, while disasters may occur far in the future. Self-fulfillment is likely (though incorrectly) to add to the prophet’s reputation, unless a competitor warned of and drew attention to the self-fulfillment effect. Meanwhile, self-negation is likely to cast doubt on the prophet’s abilities. Perhaps this is why many politicians try to give the impression that they “follow the science” when it is inevitable that they must make predictions about the costs of disasters and precautions, in order to position themselves to blame others for an unmitigated and unpredicted disaster.

It is hard to know how much rationality to incorporate in this picture. A clever prophet can say: “You are likely to fail the test unless you study more. If you do study 50 hours, you are far more likely to pass the next exam.” Similarly, a prophetic politician might say: “If we do not build up our military, the enemy will attack. If we do start building it up, the enemy is likely to arm and perhaps to act preemptively, but the harm will be less severe than if we do not take precautions.” This prophet can be proven wrong if there is no buildup and no attack, but there is no room for self-negation, and the prophet has warned of self-fulfillment. It is hard to disprove and criticize a two-step prediction, much as it is difficult to say that a probabilistic prediction was incorrect. Self-acclaimed prophetic investment managers are in a more difficult position. If they say there is a 70% chance that following their advice will beat the market, they can overcome some of the problem by showing over several years that they did in fact beat the market 70% of the time, but it is more difficult to show sophisticated clients that they did not do this by simply taking more risk than reflected in the larger market.

Returning to the political sphere and military spending, a larger military may threaten an enemy that could, in response, build up its own military or strike preemptively, in which case the politician will look wise for having predicted the threat from abroad as well as the reaction to precautions. Overinvestments can look good. For most investment managers, there is no corresponding response by the market, and therefore no opportunity to be rewarded in the manner just described. For politicians, it is hard to say whether the expected responses to predictions are more likely to lead to over- or underinvestments in precaution taking.

The prophet’s paradox focuses on self-negating predictions, but self-fulfilling predictions may be as important. A modern example is Iran’s investment in nuclear weapons. If its claim was that it would prevent an attack from abroad, the precaution proved self-negating, as it was bombed in 2025 to prevent what Israel (and then the United States) saw as a future threat. If Iran’s claim was instead that an investment would give it power to influence and frighten other countries, then it was self-fulfilling. It is likely that its leader used both arguments depending on the audience.

Despite the first-order claims of the prophet’s paradox idea, prophets can get credit when some predictions prove wrong, because their predictions brought about precautions that are themselves valued. It is surely true that the teacher who predicts failure might look like a bad prophet when the student is frightened into studying more and then passes the exam, but it is plausible that the teacher will be thanked for encouraging this extra effort and the knowledge that comes with it. An incorrect prediction that brings about an inherently worthwhile or pleasurable precaution is acceptable. Young athletes who are encouraged to follow their dreams are rarely angry when they fail to earn the gold medal. Their costly efforts, or precautions, are valued; they gain utility and status on their way to “failure.”

False prophets can escape ridicule in other ways. An entire industry predicts that without costly preparation, applicants will do poorly on standardized exams that are useful for college applications. Yet when test takers get good scores (with little empirical evidence that prep courses meaningfully help), they do not seem to respond in a way that brings about the failure of the test preparation industry. The prep course market knows to make the more careful prediction that the course will raise scores; it is difficult for customers to know how much their scores would have increased without the expensive course. Most customers know that the prep course suppliers are in it to make money, but the customers are risk averse and aware that the providers want test takers’ scores to rise and draw in more customers.

Presumably, most politicians do not want a disaster to strike, even if that will show that precautions were worthwhile because the disaster was mitigated. But my goal here is not to insist that the prophet’s paradox regularly leads to insufficient precaution taking. For now, there are several points to bear in mind. One is the first-order claim and possibility of insufficient precaution taking. But the contrary second-order idea is hardly eliminated; self-negation can at times lead to overinvestment in precautions, depending on how predictions are framed and how audiences respond with different degrees of rationality. A hyperrational audience will consider how much the predictor considered the likely reaction of the audience, which in turn must take account of the predictor’s ability to think several steps ahead. Unsurprisingly, investors in every setting would like to know the reliability of predictions sent their way.

III. Solutions to the (Potential) Problem of Insufficient Precaution Taking

Let’s take the plausible and ingenious first-order claim of self-negation (and the politician’s reaction to it) as correct. There are many examples of insufficient precaution taking, and it is likely that some can be traced to the self-negation take on the paradox. What solutions might law (or the market) provide to offset the danger of insufficient precaution taking by politicians or based on the likelihood of self-negation leading to skepticism? The reader can see that insufficient precaution taking in the case of business investments will lead to overly or insufficiently compensated risk.

Inasmuch as the claim is strongest where the benefit from precaution taking is only experienced in the future, one solution in the world of political decision-making is to ask the apparent beneficiaries to absorb the cost of earlier precautions. The self-negation feature associated with insufficient precautions can be understood as a familiar problem of externalities, in which case a solution is one of internalization. In that case, there are two options: First, the present body politic needs to somehow internalize the costs of a future disaster, thus creating the incentive to take immediate, but only efficient, precautions. Alternatively, the future generation—the generation that was saved from disaster or experienced an efficient reduction in the probability of disaster—needs to absorb the cost of earlier and efficient precautions that they would wish to have been taken.

In the case of disasters, the beneficiaries of insufficient precautions are current citizens who do not spend on precautions. In the case of investments, there are only occasional beneficiaries. For example, people who invest in risky real estate might find themselves part of a sizeable interest group able to be bailed out in the future. On a large scale, this might be offset by taxing risky gains more heavily, but this too requires an ability to know what is risky. Moreover, as suggested in Part V of this Essay, risky investments might come with a positive externality. Other investors are likely to lose coming and going. A university that makes the wrong predictions will find its endowments compared to more fortunate universities and then be more likely to find some large donors disgruntled. These donors might reason that the wealth is better left in their own hands, so they suggest the possibility of future gifts. Moreover, they take the poor performance of an endowment as evidence that the university is not well-run and therefore a bad investment. This sequence of reasoning might explain why universities are likely to follow the advice of known supporters who, as trustees, have influence over investment strategies.5

The internalization strategy is a familiar one. Precautions can be paid for with borrowed funds, with these debts repaid by the future beneficiaries. This is much like saying that a bridge built today, and expected to last thirty years, should be funded by borrowed money and then by tolls that repay the debt over the lifetime of the bridge. Correctly done—but perhaps impossible in a world where interest groups work to gain contracts for building bridges—this practice will encourage efficient bridge building. In the case of the risk-inclined investment manager, we normally find the reverse. The manager takes a share of the upside and does not pay in the event of declines. The market has not developed the solution advanced here, nor do politicians explain that they are paying for precautions with debt. 

IV. Oracles in the Business World

The problem of assessing predictive talent is found, and only partially solved, in the world of business enterprises. Again, the discussion distinguishes large-scale investors or investment managers that might face a prediction paradox from those that simply face the usual market features of supply, demand, and diminishing marginal returns.

A. Warren Buffett’s Problem

The most interesting claim in this Section is that self-negation might defeat self-fulfillment. Consider an identified oracle like Warren Buffett, with many years of success, especially in his first fifty years as an investor. Buffett’s Berkshire Hathaway, a publicly traded firm, has outperformed the stock market in risk-adjusted terms over many years. It is a cautious enterprise; it is now a significant investor in Apple, for example, but it was late in moving into such modern industries. It buys and holds stocks for long periods. It has more than fifty fully owned subsidiaries (like GEICO and Dairy Queen) and then a similar number of publicly traded companies (like Apple and American Express) in which it is a substantial investor.

The self-fulfillment is easily observed here. Berkshire Hathaway’s investments are well-known. Buffett invests in Stock X; the fact that Buffett identifies X causes others to invest in it. The stock price rises not only because of Berkshire Hathaway’s significant purchases but also because others flock to this investment, and X’s stock price rises. Buffett’s prediction is self-fulfilling.

To be sure, Buffett could be wrong about the expected performance of X. In that case, the initial self-fulfillment will eventually be followed by a drop in X’s price as X’s actual earnings do not support the higher stock price. Self-fulfillment would then be a temporary phenomenon. This is unlike the case of the politician in country T who predicts that a hostile enemy, U, is arming itself for war. T invests in its military; this is likely to cause U to spend more on its military. Both countries are worse off by way of this self-fulfillment. A good leader would not have started the competition. In contrast, even rational investors who somehow know Buffett to be wrong with respect to X might copy Buffett and then sell shares of X after a few months, before its disappointing earnings come to light. Buffett himself would have been better off not investing in X. His reputation as the Oracle of Omaha is tarnished.

Imagine that Buffett buys Y stock at a price of $30, but his sizeable purchase increases the price by 10% to $33. There may be a “Buffett bump,” but the rational investor cannot quite imitate Buffett once the bump occurs. It is tempting to say that the rational investor ought not to buy at $33, because Buffett’s action only indicated that Y was a good investment at $30 but not necessarily at $33. This analysis is probably incorrect.

It is incorrect because Buffett probably expects more than a 10% increase in the long run. Put another way, there are many companies in which Buffett can invest, and the fact that he chose Y is a useful signal. This assessment is similar to deciding that the model car bought by Avis for its large fleet is a good car to buy. Avis thinks hard about the long-term value of the car, and the fact that it chose a given model—even at the lower price it can probably get from the manufacturer—is a useful signal to the one-time customer. Part of the reason Avis gets a good price on each vehicle is its volume purchase, but part is the fact that other buyers will flock to the car that Avis chose. Again, the fact that Avis surely gets a lower price does not mean that buyers get no information from Avis’s purchase. To the contrary, Avis could have struck a similar deal with another manufacturer. Its decision provides valuable information because Avis is unlikely to extract the full value of its signaling.

Similarly, while there is a Buffett bump, it is rational to buy Y after the bump. To be sure, an investor inclined to follow Buffett might simply decide to avoid this price increase by investing alongside Buffett in Berkshire Hathaway itself. That is not possible in the case of Avis’s purchase. On the other hand, many investors are not quite like Berkshire Hathaway and have reason to invest in only some of the firms that Buffett selects. For example, a university has different tax considerations than those faced by Buffett and his Berkshire Hathaway firm. Part of Berkshire Hathaway’s attraction to most individuals is that it does not pay taxable dividends. A university, as a 501(c)(3) entity, does not pay taxes on dividends and might therefore prefer companies that taxpaying individuals avoid. Moreover, some universities are committed to spending only the amount their investments have earned and therefore prefer investments that pay dividends or rents.6 In any event, Buffett’s actions and predictions are likely to be self-fulfilling, even if only for a limited period.

The Oracle’s signals can also be self-negating. This is easiest to see when the predictor adds capital to a venture, rather than simply buying existing shares. Imagine that Buffett announces that he avoids PE because it is risky and overvalued. We could just as easily stay closer to the discussion in Part I.B by imagining that Buffett prefers to buy bonds rather than a new issue of stock, when both are put on the market by company X. This example is equivalent to saying that he is investing in precautions by turning down the higher yields available from equity.

If Buffett abandons or avoids PE and builds up his cash reserves or invests in X’s bonds, some investors will decline to invest in PE because they follow the Oracle. This situation would simply be another example of self-fulfilling prophecies if we stop at the point at which we observe a reduction in the value of PE companies. But consider now the behavior of PE firms. They have been exploring the market for investment opportunities and using their own skills to identify targets. Presumably, they can rank these targets. With less capital now at their disposal, they invest in the highest-ranking targets. The return on these investments should soon be greater than it would have been had they had the additional capital previously at their disposal. The overall picture is that the Oracle causes a drop in PE (the parent firms of actual, on the ground, enterprises) prices and in the amount of money available to PE, followed by an increase in the real returns to PE once fewer but better investments are made. If this is jarring, it is because it is difficult to define private equity and measure its growth or decline. Some large firms are not publicly traded and therefore often counted as private equity, but the discussion here is about firms that choose among investment opportunities.

Any decline in PE is experienced by investors who want to sell their shares in firms that promise to invest in ventures that are not publicly traded, but the future increase in the rate of return is quite real. With less capital, the experts—whom we might think of as secondary oracles for their presumed ability to select among available firms (and perhaps redirect or help manage them as well)—now invest in fewer firms, but in firms that are among the best prospects they are able to identify. If their decisions are better than random, the rates of return they generate will be better than before. Buffett, the earlier and most trusted oracle, will find his prediction––that is, his distaste for PE––to be self-negating. To summarize: The Oracle predicts a decline, capital leaves the industry, the industry is left to invest in fewer targets, and the rate of return on these targets is higher than the rate of return earned on the larger portfolio in previous years. The Oracle’s prediction of a decrease leads to an increase in the rate of return; the prediction has been self-negating.

There are many moving parts here, and it is easy to see why this kind of theorizing is difficult to evaluate empirically. For starters, the success of PE in period one is likely to attract talent to the industry. As the industry prospers in period two, it grows and is populated with players who are less talented at identifying good targets.7 This pattern is true in most industries, but while the market is quickly able to evaluate and price good computers, good cars, and even good job applicants, it is more difficult to evaluate companies with little history and unknown risk. It takes more time to evaluate these assets in a risk-adjusted manner.8 If this theorizing is sensible, then it is tempting to say that the rational investor would know to expect that a sizeable and reputable oracle’s purchases would cause an increase in their prices followed by a decrease. One should therefore invest and then sell before the market. As in the familiar puzzle of initial public offerings, if it is really good to invest but then sell before the subsequent drop, the puzzle is why this strategy is not well-known, and why the initial increase occurs in the first place. It is always difficult to know when the assumption of rationality drifts into unrealistic hyperrationality. But the claim or contribution here is not to suggest an investment strategy but rather to bring the self-negation idea into play. Put more generally, most claims of self-fulfillment and self-negation require rational but not hyperrational players. Over time, even merely rational investors should observe that the Oracle brings about self-fulfillment followed by self-negation. Following a negative prediction by the Oracle, there will be a race to sell and then to buy. Presumably an equilibrium will materialize with both the Oracle and the market getting things right. With repeat play, self-negation will disappear; in contrast, the hypotheticals of the ship captain and the politician do not present enough events for equilibria to be reached.

B. Private Equity

The dramatic increase in the size and scope of PE over the last twenty-five years can be attributed to many factors; claims of self-negation are likely to be a matter of guesswork with so many other variables in play. Begin with the era in which PE was unavailable to retail investors without considerable wealth. There are several common explanations for the emergence of PE. First, PE firms can avoid the substantial cost of regulation under the Securities Acts. Second, predictors who believe in their ability to find (and assist) targets will want to capture all the gains from their skills. If they get paid for their skills by other investors, they are likely to run into the costs imposed by securities law. So long as they can use their own capital along with capital provided by a few (under two thousand) wealthy investors, they can be paid for their superior ability to find targets. These investors free ride on the predictor’s skills, but the predictors free ride, in a manner of speaking, on the outside capital which broadens the field of potential targets from which to choose. There are some scale economies, if only in the form of diversification, before the drop in expected returns emphasized here. The recent history of PE reflects this idea—as does Berkshire Hathaway and its relationship to Buffett. Third, so long as the SEC does not get in the way, intermediaries will inevitably form to allow small investors to invest in PE. This development is inevitable because if PE earned high risk-adjusted rates of return, more investors would want in on the game. Institutional investors bought in first, but even they encouraged private investors to benefit from PE returns by funneling wealth through the institutional investors. Fourth, most small investors will pay for liquidity. Many institutional investors, and certainly the predictors themselves, can afford or even relish long-term commitments. They are happy to be paid in return for committing capital. It is common to trace the higher rates of return once earned by PE to a combination of increased risk and decreased liquidity.

Of the things left out here, one is the idea (associated with the Fama-French model) that when smaller firms are added to portfolios, the risk-adjusted rate of return increases. A skeptic might wonder why larger firms do not simply buy smaller ones; perhaps it is easier to monitor smaller firms such that the surviving firms do a bit better. In any event, the size variable may provide some explanation for the success of PE. A second contributing factor left out of the previous list is that investors may be unable to assess the true riskiness of firms. I have not therefore suggested that any increase in PE comes from a preference for riskier investments. Besides, investors who want risk can simply borrow money to buy publicly traded stock, as explained long ago by economists Franco Modigliani and Merton Miller.

Whether we go with one, four, or the preceding six explanations for the remarkable rise of PE, basic economics suggests that as the supply of investment opportunities grows (because of greater demand for the product type), there will be a decline in the quality of the products that even the best predictors can find. They will start with low-hanging fruit and work their way up to less attractive opportunities. This analysis assumes that the predictors, or PE companies, are skilled in searching. It is possible that they only add value by assisting in management; perhaps their targets might as well be randomly chosen from the pool of available opportunities. This result seems unlikely, and nothing in the empirical or theoretical literature suggests it to be the case. I will assume the more likely proposition that successful PE firms can rank the available targets. They begin with the most attractive targets, and as they take on more targets, the quality is reduced. Inasmuch as they are paid for size and for upside returns,9 they have a strong incentive to keep finding targets. Eventually the rate of return should fall. Of course, the rate of return has fallen in recent times,10 but we should take this finding with a grain of salt. The rates of return need to be risk adjusted, and I have insisted that these adjustments are suspect. This is especially the case when returns are reported episodically.11

Viewed this way, it is a mistake to call the decline in PE returns (if it is truly that) an example of self-negation. It is Buffett’s predictions that bring about the mid-term increase in value after he predicts a decline. This decrease, in turn, makes Buffett’s reputation suffer. Only a hyperrational investor would do the opposite of what Buffett does in anticipation of this second-step self-negation. In the case of PE more generally, investors see above-market performance and then seek to get a piece of the action. This development brings about an increase in the size of the industry but then a decrease in the average rate of return. Something like a gold rush is underway, and the eventual decline in value is not a matter of self-negation. The first person who finds gold should keep digging for he12 has apparently found a good spot in which to dig.

Buffett, quite similarly, thinks that risky investments are paying an insufficient premium compared to that offered by a set of conventional and large firms. He profits by investing in the publicly traded stock of the subset of large firms he identifies. The investors who follow Buffett run the same risk faced by latecomers to a gold rush. If they think his key prediction was the inferiority of PE, then they slowly take capital out of that market—for they are constrained by restrictions on liquidity—and soon enough, only the best targets are left. They might not move all their capital from PE to Buffett (or a low-cost and broadly diversified mutual fund) because the stocks chosen by Buffett now sell at higher prices. Buffett’s reputation then suffers. 

In the future, investors might not invest with Buffett because they see him as a bad predictor. This is an error. If he is a true oracle, the correct strategy is to invest in Berkshire Hathaway or in the companies he identifies. One must avoid believing he is a bad oracle simply because his prediction about other companies, or PE quite generally, looks wrong. This recalibration is especially necessary if Buffett cares about his average rate of return—he seems to care because we observe Berkshire Hathaway buying back its stock, thus decreasing the amount of capital at its disposal and almost surely increasing the rate of return.

V. Externalities from Risk-Taking

Many observers, and the SEC itself, are inclined to warn unsophisticated observers away from alternative investments. There are many puzzles and inconsistencies here. Someone who goes to art school, opens a restaurant, or engages in sports with the hope of becoming a professional basketball player is making a much riskier investment, yet law stays away from these overly optimistic risk-takers except for imposing penalties on outright fraud. Should law work harder to discourage or forbid these investments by people who are not wealthy, as it does for many alternative investments like PE? By and large, there are few self-negation problems in these endeavors. Still, it is fair to ask why law focuses so much on investments in securities and not on investments in so many other riskier endeavors. One can try to become an artist or singer without reading pages of documents about the risks involved and the low chance of success. A possibility, or piece of wishful thinking, is that the artists enjoy what they do. They would like to earn a living or succeed in a winner-takes-all industry, but if they are average or unappreciated, then at least we think they enjoyed the process. In contrast, we imagine that an investor who knew that a firm would fail, or its share prices fall, would avoid making the investment. At the same time, we all benefit from the (very occasional) great artist. It is as if we count on thousands of people who enjoy painting or playing basketball so that we can get great pleasure watching the best and then talking about their great performances. We know that most will fail in economic terms, but we let them fail in order to enjoy the few successes. Along the way, we observe that they like what they are doing even if they fail. The risks they take offer a positive externality, and we encourage rather than discourage these forms of risk-taking.

And yet, even these endeavors bring a kind of self-negation. The great performer is like the Oracle of Omaha. A great basketball player that earns tens of millions of dollars a year encourages thousands of young people to shoot for the stars. The successful star brings about many disappointments. Again, we might all gain. Pop artist Taylor Swift might cause many young people to head for disappointment, but the few who succeed give pleasure to their fans. These stars raise the average (the mean as well as the highest) return to the activity, and this encourages entry. But the median performer, like 99% of all who invest, loses time and money. Similarly, the success of Thurgood Marshall might have inspired many young people to choose law as their career, but we know that many who spend money going to law school are unable to secure employment, much less bring world-changing civil rights cases. Yet we gain from the very few who succeed. Self-negation is often a private problem but a public good.

Conclusion

If there are individuals or firms that are oracles with respect to the capital markets, what are their goals? If it is to maximize earnings, then we should expect increased sales of an oracle’s advice until the marginal investment is unimpressive; at that point, the oracle has brought in as many investors as possible to raise the price of the oracle’s own investments or extract the maximum fees the oracle can demand. Eventually the rate of return offered to the public falls and is close to what the market makes available without the guidance offered by the exceptional predictor. This is probably the story of Berkshire Hathaway—which no longer does much better than the S&P 500 year after year—as well as that of PE.

If the goal is to go down in history as a great oracle, then the exceptional predictor will limit entry. The oracle gains from outside capital because there is some economy of scale, but we should expect capital accumulation to stop once the best targets have been found. This possibility is like a great athlete retiring at the top, rather than continuing to play until age makes the athlete worse than the marginal player available to the team. The athlete might want to have the best lifetime batting average, but the team benefits from performance for some years after the peak, and the industry encourages more play (and more paying fans). Lifetime achievement for most hits in baseball (Pete Rose, 4,256) becomes as important as most hits in one season (Ichiro Suzuki, 262). The same is true in capital markets, with more at stake. We want the oracle to help capital flow to its most productive uses, so it is a good thing that Warren Buffett did not retire at his peak.

A third possibility is that the oracle wants to do what is best for the economy. Increasingly, the oracle’s own wealth depends on the economy’s success. If so, the oracle will not worry about self-negation. The oracle will turn out to be “wrong” on many occasions, and their reputation will suffer, but less so than if the oracle trades against the oracle’s own predictions.

This Essay has speculated, and perhaps demonstrated, that the possibility of self-negation needs to be taken into account in our study of capital markets. Along the way, it has argued that risk assessment is critical to investments and therefore to regulation of markets. Such assessments are unlikely to be correct when it comes to firms without long histories and with changing strategies and demographics. Given the way investment managers are rewarded, it is likely they take on more risk than investors recognize. That is the argument for more regulation, but this Essay has also suggested that risk-taking might come with positive externalities. The point is not to conclude with a policy suggestion but rather to suggest a way of thinking about capital markets and the occasional presence of talented investment managers.

• See, e.g., Saul Levmore, Prediction Paradoxes and Litigation Incentives, 206 Public Choice (2026).
• I leave aside the question of why sellers do not respond even more quickly, in which case the prediction would be self-fulfilling from the other direction.
• See the ongoing work of Professor Steve Kaplan, including Robert S. Harris, Tim Jenkinson, Steven N. Kaplan & Ruediger Stucke, Has Persistence Persisted in Private Equity? Evidence from Buyout and Venture Capital Funds, 81 J. Corp. Fin. 1, 15–16 (2023); Ege Y. Ercan, Steven N. Kaplan & Ilya A. Strebulaev, Interim Valuations,Predictability, and Outcomes in Private Equity 22 (’Nat'l Bureau of Econ. Rsch., Working Paper No. 33637, 2025).
• I use forty years because the Sharpe approach has a well-known problem: Many investments look good for a short period until they collapse. How do we really know the risk? And even if we follow the advice of the corporate finance literature and use thirty-year histories, there is the problem of firms or asset managers’ attracting money with high Sharpe numbers and then altering their investment strategies to become riskier. This is a serious problem if the managers (who sell themselves as predictors who can beat the market available to all investors) expect compensation that grows with their ability to beat the market.
• Unfortunately, the board of trustees is “a ‘they,’ not an ‘it.’” Following the investment advice of one trustee is likely to put off another. Moreover, following advice gives up a form of hedging. If the potential donor’s own wealth increases, that investor will be in a position to give more to the university. The rational donor might insist that the university follow a strategy that is at odds with the one the potential donor adopts. (I have seen no evidence of this; most billionaires think they are as wise as good oracles rather than lucky, and they might be right.)
• Universities with this preference must believe that the way they spend money now is superior to what the future generation, or next set of executives, would do with that money plus its earnings.
• This line of reasoning assumes that senior PE executives can also rank those who seek employment in the industry.
• This is not the first publication to question our ability to apply the various tools measuring excess rates of return. Empirically oriented readers will want to know whether we indeed see a drop in PE assets and then a rise in average returns. I am skeptical that this can be done with so many omitted variables and the difficulty of measuring risk-free returns in an industry with so few firms with long-term histories. There is also the problem of defining PE. The claims here are therefore theoretical and suggestive.
• PE firm compensation is most commonly an annual percentage of assets under management plus a percentage of any increase in value, as with the familiar two-and-twenty arrangement.
• See supra Part IV.B.
• For interesting data on this topic—even if one can argue with the author’s conclusions—see Benjamin C. Bates, Retail Access to Private Markets: What Are the Risks? 51–53 (Feb. 18, 2026) (unpublished manuscript) (available on SSRN).
• In the early years of the California Gold Rush, men were more than 90% of the population in mining districts. Malcolm J. Rohrbough, Days of Gold: The California Gold Rush and the American Nation 295–300 (Univ. of Cal. Press 1997).