Dynamical models for circle covering: Brownian motion and Poisson updating

We consider two dynamical variants of Dvoretzky's classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length $\ell$ is updated at rate $\ell^{-\alpha}$ where $\alpha \ge0$ is a parameter. For the model with Brownian motions, a special case of our results is that if the length of the $n$th interval is $c/n$, then there are times at which a fixed point is not covered if and only if $c<2$ and there are times at which the circle is not fully covered if and only if $c<3$. For the Poisson updating model, we obtain analogous results with $c<\alpha$ and $c<\alpha+1$ instead. We also compute the Hausdorff dimension of the set of exceptional times for some of these questions.Comment: Published in at http://dx.doi.org/10.1214/07-AOP340 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ownership, Economic Entrenchment and Allocation of Capital

In an efficient economy, capital should be quickly (re)allocated from declining firms and sectors to more profitable investment opportunities. This process is affected by the concentration of corporate control, which in turn is affected by market institutions. We employ a panel of 12,000 firms across 44 countries to estimate the functional efficiency of capital markets. We adapt a measure for the efficiency of capital allocation using the accelerator principle. Our empirical results show weak property rights and highly concentrated ownership reduce the functional efficiency of capital markets. Findings support the economic entrenchment hypothesis but not the legal origins hypothesis.Allocation of capital; accelerator principle; ownership; functional efficiency; economic entrenchment

A Methodological Note on Measuring the Functional Efficiency of Capital Markets

We apply the accelerator principle to measure the functional efficiency of capital markets. We estimate the elasticity of capital with respect to output using a panel of firms across 44 countries, and compare the results with existing approaches. Furthermore, we correlate our measure with corporate governance institutions.Allocation of capital; accelerator principle; functional efficiency:

The Cost of Insecure Property Rights: R2 Revisited

In the conventional CAPM model only a single risk factor is considered. However, using a world market portfolio to estimate systematic risk in national portfolios little of the required rate of return is explained in developing as compared to developed countries. Adding a factor representing institutional risk the predictive power increases substantially. By stressing importance of property and investor rights in this fashion, we add to the research on international differences in R2 initiated by Morck et al. (2000). Our findings are consistent with the hypothesis that stock price synchronicy depends on the institutional quality.Asset pricing; International financial markets; Property rights; Financial economics

Promarket Reforms and Allocation of Capital in India

The government of India initiated pro-market reforms in the 1990s, after almost five decades of socialist planning. These and subsequent policy reforms are credited as the drivers of India’s radical economic transformation. Prior to reforms, private investment was strictly regulated and restricted to certain areas and sectors. There have since been numerous changes in sectors important for investment, which should lead to changes in outcomes of firm-level strategic decision making and investment behavior. By most estimates, India will continue to grow. The purpose of this paper is to investigate changes in investment behavior from the introduction of reforms to current conditions. Reforms changed several institutional frameworks for firm operations, allowing firms to pursue more competitive strategies. Given the importance of ownership in determining firm efficiency and access to capital, we examine the effect of ownership on the performance of Indian firms for the period 1991-2006. We also examine industry differences in capital allocation. We compute a measure of investment efficiency derived from the accelerator principle: Elasticity of capital with respect to output. We examine the effect of various ownership structures on investment behavior and the efficiently of capital allocation across different sectors of the economy. We find that the allocation of capital has been slow to respond to reforms, indicating similar pace of firm responses.allocation of capital; India; institutional reforms; ownership

Family Ownership and Returns on Investment – Founders, Heirs, and External Managers

This paper investigates how family ownership, control, and management affect firms’ investment performance. We use the identity of Chief Executive Officer (CEO) and Chairman of the Board (COB) to establish under what management the firm is: founder, descendant, or external management. The results show that founder management has no effect on investment performance in family firms, whereas descendant management has a negative impact on returns on investment. Having an externally hired manager significantly improves investment performance. The results also indicate that the separation of voting right from cash flow right has a negative impact on investment performance in both family and non-family firms, but the negative effect is larger in family firms.Ownership; Control; Management; Family Firms; Returns on Investments

Mutual neutralization in collisions of H+ with Cl.

The cross section and final state distribution for mutual neutralization in collisions of H+ with Cl- have been calculated using an ab initio quantum mechanical approach. It is based on potential energy curves and nonadiabatic coupling elements for the six lowest 1Σ+ states of HCl computed with the multireference configuration interaction method. The reaction is found to be driven by nonadiabatic interactions occurring at relatively small internuclear distances (R &lt; 6 a0). Effects on the mutual neutralization cross section with respect to the asymptotic form of the potential energy curves, inclusion of closed channels, as well as isotopic substitution are investigated. The effect of spin-orbit interaction is investigated using a semiempirical model and found to be small. A simple two-state Landau-Zener calculation fails to predict the cross section