Overlapping subsampling and invariance to initial conditions

This article studies the use of the overlapping blocking scheme in unit root autoregression. When the underlying process is that of a random walk, the blocks’ initial conditions are not fixed, but are equal to the sum of all the previous observations’ error terms. When non overlapping subsamples are used, these initial conditions do not disappear asymptotically. In this article, we show that a simple way of overcoming this issue is to use overlapping blocks. By doing so, the effect of these initial conditions vanishes asymptotically. An application of these findings to jackknife estimators indicates that an estimator based on moving blocks is able to provide obvious reductions to the mean square error. Also results are shown to be robust to local-to-unity frameworks, when the autoregressive parameter is unknown.     

The Adverse Consequences of Share-Based Pay in Risky Companies

Shareholders increasingly regard it as desirable to link director pay packages to the share price, in order to align directors’ incentives with those of the shareholders. The result of such remuneration packages is that directors’ wealth will become concentrated in one stock, giving them an undiversified portfolio of shares. The resulting need to diversify will encourage directors to exercise their share options, irrespective of their expectations about future stock price performance. This benefit to diversifying will be greater the riskier the stock. Consistent with this, this paper finds that only option exercises in relatively low risk companies are informed, and precede significantly negative abnormal returns over the following 2-month period. As a result, providing directors in riskier companies with share-based pay packages might not be effective in aligning their incentives with those of the shareholders.