Lucky CEOs

We study the relation between corporate governance and opportunistic timing of CEO option grants via backdating or otherwise. Our methodology focuses on how grant date prices rank within the price distribution of the grant month. During 1996-2005, about 12% of firms provided one or more lucky grant -- defined as grants given at the lowest price of the month -- due to opportunistic timing. Lucky grants were more likely when the board did not have a majority of independent directors and/or the CEO had longer tenure -- factors associated with increased influence of the CEO on pay-setting. We find no evidence that gains from manipulated grants served as a substitute for compensation paid through other sources; total reported compensation from such sources was higher in firms providing lucky grants. Finally, opportunistic timing has been widespread throughout the economy, with a significant presence in each of the economy's twelve (Fama-French) industries.

Lucky Directors

While prior empirical work and much public attention have focused on the opportunistic timing of executives' grants, we provide in this paper evidence that outside directors' option grants have also been favorably timed to an extent that cannot be fully explained by sheer luck. Examining events in which public firms granted options to outside directors during 1996-2005, we find that 9% were "lucky grant events" falling on days with a stock price equal to a monthly low. We estimate that about 800 lucky grant events owed their status to opportunistic timing, and that about 460 firms and 1400 outside directors were associated with grant events produced by such timing. There is evidence that the opportunistic timing of director grant events has been to a substantial extent the product of backdating and not merely spring-loading based on private information. We find that directors' luck has been correlated with executives' luck. Furthermore, grant events were more likely to be lucky when the firm had more entrenching provisions protecting insiders from the risk of removal, as well as when the board did not have a majority of independent directors.

1-Bit Matrix Completion

In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements generated according to a probability distribution determined by the real-valued entries of M. The central question we ask is whether or not it is possible to obtain an accurate estimate of M from this data. In general this would seem impossible, but we show that the maximum likelihood estimate under a suitable constraint returns an accurate estimate of M when ||M||_{\infty} <= \alpha, and rank(M) <= r. If the log-likelihood is a concave function (e.g., the logistic or probit observation models), then we can obtain this maximum likelihood estimate by optimizing a convex program. In addition, we also show that if instead of recovering M we simply wish to obtain an estimate of the distribution generating the 1-bit measurements, then we can eliminate the requirement that ||M||_{\infty} <= \alpha. For both cases, we provide lower bounds showing that these estimates are near-optimal. We conclude with a suite of experiments that both verify the implications of our theorems as well as illustrate some of the practical applications of 1-bit matrix completion. In particular, we compare our program to standard matrix completion methods on movie rating data in which users submit ratings from 1 to 5. In order to use our program, we quantize this data to a single bit, but we allow the standard matrix completion program to have access to the original ratings (from 1 to 5). Surprisingly, the approach based on binary data performs significantly better

Can We Learn to Beat the Best Stock

A novel algorithm for actively trading stocks is presented. While traditional expert advice and "universal" algorithms (as well as standard technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can "beat the market" and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning

Modulated Floquet Topological Insulators

Floquet topological insulators are topological phases of matter generated by the application of time-periodic perturbations on otherwise conventional insulators. We demonstrate that spatial variations in the time-periodic potential lead to localized quasi-stationary states in two-dimensional systems. These states include one-dimensional interface modes at the nodes of the external potential, and fractionalized excitations at vortices of the external potential. We also propose a setup by which light can induce currents in these systems. We explain these results by showing a close analogy to px+ipy superconductors