Reformulation in planning

Reformulation of a problem is intended to make the problem more amenable to efficient solution. This is equally true in the special case of reformulating a planning problem. This paper considers various ways in which reformulation can be exploited in planning

Diphenylphosphinoyl chloride as a chlorinating agent - The selective double activation of 1,2-diols

© The Royal Society of Chemistry 2006Treatment of 1,2-diols with diphenylphosphinoyl chloride in pyridine produces beta-chloroethyl phosphinates which react with complete control of stereochemistry to give epoxides and azido-alcohols, useful intermediates in cyclopropane synthesis.David J. Fox, Daniel Sejer Pedersen, Asger B. Petersen and Stuart Warre

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