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New: A Generalized Higher-Moment Capital Asset Pricing Model, with Theoretical Implications and Legal Applications
(March 30, 2017)
The conventional capital asset pricing model (CAPM) has come under severe attack for its failure to reflect investor behavior. This paper describes financial decision-making under uncertainty in formal mathematical terms as a generalized higher-moment capital asset pricing model. It develops that model through the Taylor series expansion of the logarithm of expected financial returns. This mathematical expedient treats the conventional two-moment CAPM and a four-moment variant (expressed in terms of mean, variance, skewness, and kurtosis) as convenient, mentally tractable special cases of a generalized higher-moment model.
This paper then explores the theoretical implications and legal applications of higher-moment asset pricing. In prospect theory, perhaps the best known expression of behavioral economics, a “fourfold pattern” of decisionmaking under uncertainty predicts risk-seeking behavior in particular circumstances. Skewness preference arises in a wide variety of economic ...
REVISION: Legal Responses to Biodiversity Loss and Climate Change
(November 13, 2016)
The greatest vectors of biodiversity loss today are climate change, habitat destruction, invasive species, pollution, population, and overkill. Climate change, habitat destruction, and alien invasive species should figure more prominently than overkill and the marketing of products derived from endangered species. The law, however, imposes its clearest, harshest sanctions precisely where the drivers of extinction are weakest: when humans consciously capture or kill other living things. More helpfully, the Endangered Species Act has been adapted to address habitat destruction on private land and to mitigate climate change.
REVISION: The Fragile Menagerie: Biodiversity Loss, Climate Change, and the Law
(November 9, 2016)
The greatest vectors of biodiversity loss in the Anthropocene epoch are climate change, habitat destruction, invasive species, pollution, population, and overkill. Perversely enough, the legal understanding of extinction mechanisms remains frozen in time, like a cave dweller in ice. Climate change, habitat destruction, and alien invasive species should figure more prominently than overkill and the marketing of products derived from endangered species. The law, however, imposes its clearest and harshest sanctions precisely where the drivers of extinction are weakest: when humans consciously capture or kill other living things. The Endangered Species Act has been adapted to address habitat destruction on private land and to mitigate climate change. Nevertheless, the law’s lack of congruence with conservation biology impedes efforts to preserve biodiversity and mitigate climate change.
REVISION: Baryonic Beta Dynamics: Splitting the Atom of Systematic Risk
(September 19, 2016)
Despite the rise of multi-factor models emphasizing value, firm size, and momentum, beta remains the primary measure of risk in asset pricing. Designed to define systematic risk, net of idiosyncratic risk that can be neutralized through diversification, beta combines a measure of volatility with a measure of correlation.
Much of the frustration with beta stems from the failure to disaggregate beta’s discrete components. Conventional beta is often treated as if it were “atomic” in the original Greek sense: uncut and indivisible.
This article rehabilitates beta by splitting the atom of systematic risk. Particle physics provides a fruitful framework for evaluating discrete components of financial risk. Quantum chromodynamics (QCD) focuses on six flavors of quarks in three matched pairs: up/down, charm/strange, and top/bottom. Baryons are subatomic particles consisting of three quarks. They include protons and neutrons, which account for most of the mass of the visible ...
REVISION: Price-Level Regulation and Its Reform
(September 13, 2016)
Price-level, or “price-cap,” regulation offers an alluring alternative to the traditional technique of monitoring a regulated firm’s profits. Part II of this article contrasts price-level regulation with conventional cost-of-service ratemaking and with Ramsey pricing. Price-level regulation stands as a market-based, incentive-driven “third way” between traditional regulation and complete deregulation. Part III provides formal specifications of price-level regulation. Although some jurisdictions have set price caps according to operating cost and rate-of-return calculations that clearly parallel those steps in conventional ratemaking, this article will focus on price-level methodologies that combine an economy-wide measure of inflation with an x-factor reflecting total factor productivity within a regulated industry.
Part IV addresses the simpler component of price-level regulation, the choice of an inflation index. Part V devotes detailed attention to the treatment of the ...
REVISION: The Promise and the Peril of Parametric Value-at-Risk (VaR) Analysis
(August 22, 2016)
Leptokurtosis, or the risk lurking in “fat tails,” poses the deepest epistemic threat to economic forecasting. Parametric value-at-risk (VaR) models are extremely vulnerable to kurtosis in excess of the levels associated with a normal, Gaussian distribution. This article provides step-by-step guidance on the use of Student’s t-distribution to enhance the statistical robustness of VaR forecasts. For degrees of freedom greater than 4, Student’s t-distribution can emulate any level of kurtosis exceeding that of a Gaussian distribution. Because VaR is elicitable from historical data, observed levels of excess kurtosis can inform the proper use of Student’s t-distribution to measure value-at-risk. In addition, the calculation of parametric VaR according to the number of degrees of freedom implied by historical levels of excess kurtosis leads directly to the corresponding value of expected shortfall. Conducted in this fashion, parametric VaR not only exploits the elicitability of that ...
REVISION: Sinking, Fast and Slow: Bifurcating Beta in Financial and Behavioral Space
(August 19, 2016)
Modern portfolio theory accords symmetrical treatment to all deviations from expected return, positive or negative. This assumption is vulnerable on both descriptive and behavioral grounds. Many of the predictive flaws in contemporary finance stem from mathematically elegant but empirically flawed Gaussian models. In reality, returns are skewed. The presumption that returns and volatility are symmetrical also defies human behavior. Losing hurts worse than winning feels good; investors do not react equally to upside gain and downside loss. Moreover, correlation tightening during bear markets, not offset by changes in correlation during bull markets, suggest that standard diversification strategies may erode upside returns without providing adequate protection during times of stress.
This article outlines mathematical tools for calculating volatility, variance, covariance, correlation, and beta, not merely across the entire spectrum of returns, but also on either side of mean ...
REVISION: Legal Quanta: A Mathematical Romance of Many Dimensions
(August 19, 2016)
Many things can be measured and expressed numerically. Nature speaks in the language of mathematics. Mathematical analysis of law is often associated with the application of established empirical techniques to ever-growing bodies of legal data. Other distinct applications of mathematics to law include machine learning, legal networks, and analytical modeling. Mathematical analysis of law ultimately follows not only the data describing the legal world as we find it, but also the own internal logic of mathematics.
REVISION: Momentary Lapses of Reason: The Psychophysics of Law and Behavior
(August 19, 2016)
The conventional capital asset pricing model (CAPM) remains the preferred approach to risk management in a wide range of economic settings. At the same time, the neoclassical assumptions underlying the CAPM have come under severe attack by behavioral economics. In sharp contrast with the purely rational agents of neoclassical economics, real humans make decisions under the constraints imposed by their innate heuristics. The tension between conventional asset pricing theory and behavioral economics puts particular pressure on law. As an applied branch of social science, law purports to subject human conduct to rules that should optimize objective well-being as well as subjective satisfaction.
This paper proposes a mathematically expedient method of alleviating this tension. A four-moment capital asset pricing model captures the emotional impact of odd and even moments of statistical distributions. Critically, a four-moment CAPM transcends the limits of financial models that ...
REVISION: Law on the Market? Evaluating the Securities Market Impact of Supreme Court Decisions
(August 14, 2016)
Do judicial decisions affect the securities markets in discernible and perhaps predictable ways? In other words, is there “law on the market” (LOTM)? This is a question that has been raised by commentators, but answered by very few in a systematic and financially rigorous manner. Using intraday data and a multiday event window, this large scale event study seeks to determine the existence, frequency and magnitude of equity market impacts flowing from Supreme Court decisions.
We demonstrate that, while certainly not present in every case, "law on the market" events are fairly common. Across all cases decided by the Supreme Court of the United States between the 1999-2013 terms, we identify 79 cases where the share price of one or more publicly traded company moved in direct response to a Supreme Court decision. In the aggregate, over fifteen years, Supreme Court decisions were responsible for more than 140 billion dollars in absolute changes in wealth. Our analysis not only ...
REVISION: Anthropocene Agricultural Law
(June 30, 2016)
Agricultural controversies in affluent, comfortably fed countries increasingly emphasize the esthetic or expressive elements of food. Consumer advocates can indulge in litigation over foie gras, for instance, or coffee production certification. This expressive turn elevates the ornamental aspects of food at the expense of agriculture's utilitarian purposes. The modernist principles articulated in Adolf Loos's "Ornament und Verbrechung" urge the subordination of agriculture's ornamental aspects in favor of its original instrumentalist underpinnings.
Meanwhile, ecological disaster looms. Human ecological impacts are so severe that geological history has arguably entered a new epoch, the Anthropocene. Exhaustion of vital inputs (petroleum, phosphorus) and evolutionary calamity (mass extinctions, herbicide and pesticide resistance) threatens future agricultural productivity. Food security and the economic foundations of civilization hang precariously in the balance.
Human beings, ...
REVISION: Inflation-Based Adjustments in Federal Civil Monetary Penalties
(April 7, 2016)
Civil monetary penalties play a vital role in federal law. The Federal Civil Penalties Inflation Adjustment Act of 1990, Pub. L. No. 101-410, prescribes rules for the regular adjustment of federal civil monetary penalties in response to inflation. Three statutory defects have undermined the Inflation Adjustment Act. First, the Act's 10 percent cap on initial adjustments creates an "inflation gap" relative to the level that would properly reflect inflation. Second, the Act directs federal agencies to use Consumer Price Index data that are at least 7 months and as many as 18 months out of date. This creates "CPI lag" in the adjustment of civil monetary penalties. Third, the Act's rounding rules can force some agencies to wait 15 years or more between adjustments.
Originally prepared as a report for the Administrative Conference of the United States, this article examines the Inflation Adjustment Act and recommends possible legislative remedies for the Act's defects.