Saturday, February 28, 2009
Too Big to Fail Doesn't Mean a Fat Tail
Many observers -- including recently the editors of Scientific American -- have argued that the financial and economic crisis the world faces today was caused by "quants" who miscalculated rare events, ignored correlations and fundamentally misunderstood "fat-tailed" distributions.
Of course, mainstream econometrics and mathematical finance have addressed these issues for generations. Undergraduate statistics textbooks routinely devote several pages to sample size, covariance and kurtosis. Graduate texts go further, covering topics such as non-stationary processes, time-varying distributions and cointegration; statistical tests for normality, heteroskedasticity, leptokurtosis, serial correlation.
Such subjects were all the rage in econometrics and math finance in the mid 1980s, when ARCH and GARCH hit the scene.
Any quant in the credit field has studied a "jump-to-default" model or two. Robert Merton introduced jump-diffusions to mainstream mathematical finance in the mid 1970s, and in 1993, Stephen Heston gave the world a closed-form model for option pricing under stochastic volatility.
In short, there is a solid understanding of fat tails and black swans among quants. The foundational material has been studied in great depth by all mathematical finance doctoral students in the last 20 years. Believe me.
So what drove the recent bubble and the ensuing crisis?
The reasons for today's situation go much deeper than quants choosing the wrong distribution. It is due to something far more nefarious.
First, we must accept that the bubble, and its collapse, was endogenous -- it was created within the system itself -- as opposed to exogenous (as in an asteroid striking the Earth).
The financial system amplified its own problems in a feedback loop. Leverage begat more leverage, assets became intertwined, and the system became unstable.
Second, the financial system -- politically and structurally -- operated on the myth that no single participant could significantly influence the market, that market frictions were few, and that information was readily availabie. Economists would describe such a system as perfectly competitive.
Of course, the economic and political reality is that the system is imperfectly competitive. The global economy is oligopolistic. A small number of firms are so large that their very existence (or extinction) affects markets: e.g., Countrywide, Fannie Mae, Freddie Mac, Northern Rock, Reserve Fund, Lehman Brothers, Citigroup, AIG, General Motors... The notion is ensconced in the Federal Reserve's policy of "too big to fail." Government itself influences the marketplace, through monetary, fiscal, banking, housing and industrial policy, as monopsonist as well as monopolist. To top it off, the crisis has clearly demonstrated that markets can seize up (e.g., credit and housing) and that information can be painfully asymmetric (cf. TARP).
Along with imperfect competition comes a plethora of issues surrounding incentives and equilibrium. One truth seems to prevail: market participants -- large and small -- can be expected to act more or less in their own best interest.
That truth is the foundation of game theory. The theory has created powerful tools for studying the oligopolistic competition, principal-agency problems and asymmetric information that characterize today's financial system. In particular, game-theoretic models explicitly allow for a single participant to affect the market, as one would expect under oligopolistic competition where firms are "too big to fail."
Game theory also sheds light on the often perverse nature of economic equilibria. It doesn't take much of a stretch to argue that the world fell into a great Prisoner's Dilemma equilbrium. Everyone from Citi's Chuck Prince -- who had to keep on dancing -- to the first-time homebuyer in Las Vegas who took out a no-doc option ARM with a piggyback loan -- acted in his or her own best interest at the time, without realizing that if everyone acted in his or her own best interest, the worst possible outcome would be realized for all.
Few mathematical financial models in common use today are game theoretic. Few allow market participants to single-handedly affect the markets. Indeed, they typically assume near-perfect competition with minimal market frictions. As an example, the widely used copula CDO pricing models do not consider the effect of large positions on systemic liquidity. Of course, that is exactly the kind of analysis needed under a policy of "too big to fail".
If mathematical financial theory is to keep up with the demands of the financial industry, it needs to progress rapidly into the realm of oligopolostic competition, principal-agency issues, market frictions and asymmetric information.
This requires mathematical finance to augment its physical-science roots with traditional economic theory and game theory. Valiant researchers have established beachheads in these areas, but the practical results are few, limiting the adoption of these models by industry. Hopefully, this crisis will be a valuable lesson, and spur further research and study in these areas. --GAHjr
Of course, mainstream econometrics and mathematical finance have addressed these issues for generations. Undergraduate statistics textbooks routinely devote several pages to sample size, covariance and kurtosis. Graduate texts go further, covering topics such as non-stationary processes, time-varying distributions and cointegration; statistical tests for normality, heteroskedasticity, leptokurtosis, serial correlation.
Such subjects were all the rage in econometrics and math finance in the mid 1980s, when ARCH and GARCH hit the scene.
Any quant in the credit field has studied a "jump-to-default" model or two. Robert Merton introduced jump-diffusions to mainstream mathematical finance in the mid 1970s, and in 1993, Stephen Heston gave the world a closed-form model for option pricing under stochastic volatility.
In short, there is a solid understanding of fat tails and black swans among quants. The foundational material has been studied in great depth by all mathematical finance doctoral students in the last 20 years. Believe me.
So what drove the recent bubble and the ensuing crisis?
The reasons for today's situation go much deeper than quants choosing the wrong distribution. It is due to something far more nefarious.
First, we must accept that the bubble, and its collapse, was endogenous -- it was created within the system itself -- as opposed to exogenous (as in an asteroid striking the Earth).
The financial system amplified its own problems in a feedback loop. Leverage begat more leverage, assets became intertwined, and the system became unstable.
Second, the financial system -- politically and structurally -- operated on the myth that no single participant could significantly influence the market, that market frictions were few, and that information was readily availabie. Economists would describe such a system as perfectly competitive.
Of course, the economic and political reality is that the system is imperfectly competitive. The global economy is oligopolistic. A small number of firms are so large that their very existence (or extinction) affects markets: e.g., Countrywide, Fannie Mae, Freddie Mac, Northern Rock, Reserve Fund, Lehman Brothers, Citigroup, AIG, General Motors... The notion is ensconced in the Federal Reserve's policy of "too big to fail." Government itself influences the marketplace, through monetary, fiscal, banking, housing and industrial policy, as monopsonist as well as monopolist. To top it off, the crisis has clearly demonstrated that markets can seize up (e.g., credit and housing) and that information can be painfully asymmetric (cf. TARP).
Along with imperfect competition comes a plethora of issues surrounding incentives and equilibrium. One truth seems to prevail: market participants -- large and small -- can be expected to act more or less in their own best interest.
That truth is the foundation of game theory. The theory has created powerful tools for studying the oligopolistic competition, principal-agency problems and asymmetric information that characterize today's financial system. In particular, game-theoretic models explicitly allow for a single participant to affect the market, as one would expect under oligopolistic competition where firms are "too big to fail."
Game theory also sheds light on the often perverse nature of economic equilibria. It doesn't take much of a stretch to argue that the world fell into a great Prisoner's Dilemma equilbrium. Everyone from Citi's Chuck Prince -- who had to keep on dancing -- to the first-time homebuyer in Las Vegas who took out a no-doc option ARM with a piggyback loan -- acted in his or her own best interest at the time, without realizing that if everyone acted in his or her own best interest, the worst possible outcome would be realized for all.
Few mathematical financial models in common use today are game theoretic. Few allow market participants to single-handedly affect the markets. Indeed, they typically assume near-perfect competition with minimal market frictions. As an example, the widely used copula CDO pricing models do not consider the effect of large positions on systemic liquidity. Of course, that is exactly the kind of analysis needed under a policy of "too big to fail".
If mathematical financial theory is to keep up with the demands of the financial industry, it needs to progress rapidly into the realm of oligopolostic competition, principal-agency issues, market frictions and asymmetric information.
This requires mathematical finance to augment its physical-science roots with traditional economic theory and game theory. Valiant researchers have established beachheads in these areas, but the practical results are few, limiting the adoption of these models by industry. Hopefully, this crisis will be a valuable lesson, and spur further research and study in these areas. --GAHjr
