The fundamental conceit of efficient-market theory—that markets can perfectly assess and thus price, slice, and dice risk—has collapsed like Edgar Allen Poe’s House of Usher. Its terminus arguably was the admission during October 2008 by former US Federal Reserve Chairman Alan Greenspan that the modern paradigm of risk assessment and management had essentially collapsed. Because efficient-market theory predicted very low levels of risk, most models used by quantitative analysts justified extremely high leverage—leverage that, in the end, has jeopardized our entire global financial framework.

Before we can reform the global financial system, we must first understand the chief lesson from this crisis: we are fundamentally unable to properly assess financial market risk, much less optimally hedge against it. That runs counter to classical efficient-market-theory economics, which says that relevant risks can always be assessed and, indeed, optimally managed. The first signs of trouble with this paradigm surfaced a quarter of a century ago, when Yale’s Robert Shiller and others showed that efficient-market theory can only account for about one-fifth of observed market risk. Where does the rest of the risk come from?

New research by Professor Mordecai Kurz at Stanford has indentified the true source of the extra risk, which he has dubbed “endogenous risk.” This source lies in the mistakes investors make in their trading and portfolio decisions. In fact, the principal weakness of efficient-market economics is that it assumes that investors make no mistakes, thus ignoring a crucial source of volatility. More specifically, classical theory makes three fundamental assumptions:

• First, while investors do not know future news with certainty, all investors know the correct probability of all future news events. That is, everyone knows his risks perfectly.
• Second, given any news, all investors know how to price such news perfectly. Thus there is no pricing model uncertainty.
• Third, all investors can optimally hedge all of their risks, and can do so via complex derivatives-based hedging strategies that can never backfire and melt down.

If these assumptions were correct, economic life would be substantially risk free. Investors would never have to look back and say, “Oh, I was wrong. I wish I had had a different probabilistic forecast about the news and the price. And I wish I had known how to better price such news.” Not only is the amount of risk very low in this idealized world, but any downside risk can be truncated at will via the perfect hedging assumption. The key point here is that in such a hypothetical low-risk environment, the optimal level of leverage will be very high for investors with normal degrees of risk aversion.

However, all three of these assumptions involving mistakes-free economics are demonstrably, and quite obviously, false. To begin with, most of us are regularly wrong in our forecasts. Economists did not predict productivity growth between 1995 and 2003, when it tripled after two decades of stagnation. More recently, we were wrong about the magnitude of the decline in housing prices and wrong about how much default rates would grow. Kurz has shown that “correlated mistakes” of this kind are a very important source of increased risk.

Next, while there may not be any pricing-model uncertainty (PMU) in classical finance, it abounds in the real world. No one, from Joe the Investor to Lawrence Summers, had a clue about how to value the complex securities lying at the heart of the 2007 credit-market crisis. In my work, I have recently shown mathematically that the greater the degree of PMU in an environment of performance-benchmarked investors, the greater the extent of “price overshoot” (both downward and upward) and hence the greater the degree of price volatility.

Finally, it is by now well known that many risks cannot be hedged at all and that the hedges that do exist can completely melt down when investors need them most. The afternoon of 1987’s “Black Monday,” when “dynamic hedging” strategies completely imploded, offers spectacular evidence of this reality.

Kurz’s new theory of rational beliefs demonstrates that it is possible to explain all observed risk in normal times by incorporating these three previously ignored sources of risk. To explain the additional volatility that occurs during periods such as the one we are currently weathering, it is necessary to take into account the impact of excessive leverage. The crucial insight here is that increased financial leverage nonlinearly amplifies the endogenous risk that arises in a world where investors can be “wrong” in the three ways defined above. Incidentally, no assumption of investor irrationality is required by this new analysis of the nature and sources of total market risk. Mistakes amplified by leverage—not irrationality—are the culprit.

Lessons to be learned and requisite policy reforms

The first lesson to be learned from all this is that efficient-markets financial theory predicted a very low level of risk and hence justified a very high degree of leverage. Such leverage has brought the global system down. It is dangerously inconsistent with the true amount of risk that exists in the real world. Therefore, leverage must be significantly curtailed by law throughout the entire financial system, not just at banks. The web of interdependencies unearthed in the recent crisis made it clear that the distinctions between traditional and newer financial players must be removed.

The second lesson concerns the misplaced hope that “superior risk assessment” in the future will prevent a recurrence of what has happened. It will not do so, because it cannot do so. We now know that the endogenous risks described by Kurz usually cannot be “assessed” at all. This theorem is akin to Heisenberg’s uncertainty principle, which teaches us that no amount of modeling will permit an observer to determine the momentum of an electron given knowledge of its position, and vice versa. As a riveting, and quite disturbing, example of such “unknowability” in finance, consider the variable designating the value of the total write-downs of the net worth of financial institutions in the world by January 1, 2011. The probability distribution of this variable is bounded on the left by today’s accumulated losses of $650 billion. But will the final loss amount to $1 trillion, $1.5 trillion, $2 trillion, or more? This all-important distribution is unknowable.

The third lesson is that the three sources of endogenous risk cannot be exorcised. We are stuck with the reality that we are always going to be mistaken in our forecasts, insecure in our ability to price “news” (the right P/E of the Russian market, anyone?) and incapable of optimally hedging in a textbook sense. The only variable that can be controlled is leverage.

Our fundamental conclusion is thus that “it’s the leverage, stupid.” More specifically, if we wish to prevent future perfect storms, we must never again entrust the financial well-being of the public to firms with 30:1 leverage ratios, or worse. None of this is to suggest that leverage per se is bad. What matters is the determination of the optimal amount of leverage. This cannot be a fixed ratio; rather, it should vary over time with the degree of overvaluation or undervaluation in any given asset market, just as the Federal Reserve funds rate varies with economic conditions.

The new paradigm of risk introduced above is not yet understood. It is easy to blame our problems today on greed, lax oversight, conflicts of interest, and perverse incentives. All these factors do indeed play a role, but regrettably, most cannot be controlled. Leverage can be controlled, used to be controlled more than it is today, and must again be controlled. It is high time for regulators to earn their keep by recognizing this.

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