Economic Crises and the Integration of Law and Finance: The Impact of Volatility Spikes

The 2008 financial crisis raised puzzles important for understanding how the capital market prices common stocks and in turn, for the intersection between law and finance. During the crisis, there was a dramatic five-fold spike, across all industries, in “idio­syncratic risk”—the volatility of individual-firm share prices after adjustment for movements in the market as a whole. This phenomenon is not limited to the most recent financial crisis. This Article uses an empirical review to show that a dramatic spike in idiosyncratic risk has occurred with every major downturn from the 1920s through the recent financial crisis. It canvasses three possible explanations for this phenomenon. Thereafter, this Article explores the implications of these crisis-induced volatility spikes for certain legal issues that depend analytically on valuation methodology and hence are affected by volatility: using event studies to determine materiality and loss causation in fraud-on-the-market securities litigation, determining materiality in cases involving claims of both insider trading and misstatements or omissions in registered public offerings, and deter­mining the extent of deference given to a corporate board that rejects an acquisition offer at a premium above the pre-offer market price. This analysis shows that the conventional use of event studies during periods of economic-crisis-induced volatility spikes results in understating the number of occasions when a corporate misstatement can be shown to have had a meaningful impact on a firm’s stock price. Relatedly, the analysis suggests that during crisis times, insiders have substantially more opportunities to profit from trading on the nonpublic information that they possess and issuers conducting offerings have more opportunities to sell securities at an inflated price. Analysis shows that trying to cure this problem by lowering the standard of what is considered statistically significant is as likely to be socially harmful as socially beneficial. These conclusions counsel that the best response to the reduced effectiveness of private litigation as a deterrent to securities law violations during crisis times is to provide additional resources to SEC enforcement. Lastly, with respect to Delaware courts’ recognition of “substantive coercion” as a justification for target-corporation deploy­ment of takeover defenses—arguably a dubious justification in normal times—crisis-induced idiosyncratic-risk spikes provide an unusually plausible claim that target shareholders may indeed make a mistake in tendering into a hostile offer. Analysis of the timing of the spikes in recent cases, however, shows that the claim is tenuous even in these circumstances

Idiosyncratic Risk During Economic Downturns: Implications for the Use of Event Studies in Securities Litigation

We reported in a recent paper that during the 2008-09 financial crisis, for the average firm, idiosyncratic risk, as measured by variance, increased by five-fold. This finding is important for securities litigation because idiosyncratic risk plays a central role in event study methodology. Event studies are commonly used in securities litigation to determine materiality and loss causation. Many bits of news affect an issuer’s share price at the time of a corporate disclosure that is the subject of litigation. Because of this, even if an issuer’s market–adjusted price changes at the time of the disclosure, one cannot determine with certainty whether the disclosure itself had any effect on price. An event study is used to make a probabilistic assessment of whether in fact it did. Use of event studies generates a certain rate of Type I errors (disclosures that had no actual effect on price being identified as having had an effect) and a certain rate of Type II errors (disclosures that had an actual effect not being identified as such). This paper sets out a simple model of the tradeoff between these Type I and Type II errors. The model is used to establish three fundamental points. First, an economic crisis can radically worsen this tradeoff by making it much more difficult to catch a disclosure of a certain size without introducing more Type I errors. Second, during crisis periods a relaxation of this standard (and hence an increase in the acceptable rate of Type I errors) may actually decrease Type II errors by less than it would in normal times. We prove that whether the decrease is greater or smaller in crisis times depends on whether the disclosure’s actual impact on price is more or less negative than a definable crossover point. Third, whether relaxation of the standard in troubled times would increase or decrease social welfare is ambiguous. It depends on distribution of potentially actionable disclosures in terms of their actual impact on price and the social costs and social benefits of imposing liability for disclosures of each given level of actual negative impact on price

Sintering of screen-printed platinum thick films for electrode applications

Pt electrodes with a 6-8-μm thickness were produced on alumina substrates by a double-print Pt screen-printing process that included a sequential heat treatment at 600 °C and 1300 °C. This process improved the final sintered double-print film because the first printed layer acted as a sintering template for the second printed layer. The sintered Pt films have a 95% coverage of the alumina surface, 92% density, 0.73-μm average surface roughness, and 16.10−5 Ω cm resistivity. The sintering behavior of Pt films exhibited three stages of densification: Stage I (T °C < 700 °C), exhibiting neck growth, and Stage II (700 < T °C < 1300 °C), exhibiting grain growth, have activation energies of 64 kJ/mol and 125 kJ/mol, respectively. Stage III exhibits a decrease in shrinkage due to Pt coalescence and island formation. The transition temperature, 700 °C, between Stages I and II corresponds to an anomalous increase in surface roughness and resistivity. The thickness of Pt films was a critical parameter for achieving alumina surface coverage. Uniaxial pressing of dried Pt films increased densification and reduced the surface roughness of double-print Pt film

Materials for Biomedical Applications

This paper discusses two ceramic material systems for selective laser sintering (SLS) that are being developed for biomedical applications for use in repair of bone defects. SLS is the preferred method of fabricating ceramic implants that exhibit well defined porous microstructures. Implants fabricated in this. manner have proven effective in-vivo showing excellent biocompatibility as well as considerable osseous integration and remodeling of the imp'ant materialMechanical Engineerin

Perturbation theory for a stochastic process with Ornstein-Uhlenbeck noise

The Ornstein-Uhlenbeck process may be used to generate a noise signal with a finite correlation time. If a one-dimensional stochastic process is driven by such a noise source, it may be analysed by solving a Fokker-Planck equation in two dimensions. In the case of motion in the vicinity of an attractive fixed point, it is shown how the solution of this equation can be developed as a power series. The coefficients are determined exactly by using algebraic properties of a system of annihilation and creation operators.Comment: 7 pages, 0 figure

Proton deflectometry analysis in magnetized plasmas: magnetic field reconstruction in one dimension

Proton deflectometry is increasingly used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The algorithm is verified against analytic solutions and applied to example data. The virtue of a 1-D algorithm is that it is fast and can be incorporated into higher-level analysis routines and workflows, for example to scan parameters and conduct uncertainty analysis. Furthermore, working through the 1-D algorithm exposes the fundamental importance of boundary conditions and the initial proton fluence profile for an accurate reconstruction. From these considerations we propose a hybrid mesh-fluence reconstruction technique where fields are reconstructed from fluence data in an interior region with boundary conditions supplied by direct mesh measurements at the boundary.Comment: 10 pages, 6 figures. For code library, see: https://github.com/wrfox/PRADICAMEN