Three essays in finance

Abstract

This thesis consists of three essays on asset pricing. Chapter 1 presents an equilibrium model to study the convergence trading of large hedge funds in segmented markets. The model provides an alternative explanation for the anomaly of a price gap between two fundamentally identical securities. Strategic arbitrageurs, taking into account their price impact, do not close the price gap. This gap makes investors who trade with the strategic arbitrageur less willing to invest in risky assets ex ante. Thus, the gap brings an additional source of risk, anticipation risk. The model predicts that the future price gap is wide when the current trading volume is high. Daily data for Royal Dutch and Shell provides evidence in support of the model. Chapter 2 (coauthored with Joon Chae and Andrew W. Lo) is about stock price behavior. We perform various statistical analyses on stock market returns as Fama (1965) did, using CRSP index returns from 1926-2005. We investigate stock return distributions and report return characteristics. First, stock returns do not follow a normal distribution, though many studies assume this.

(cont.) Second, autocorrelations of stock returns are not zero (as verified by many predictability studies). In addition, the level of autocorrelations varies widely across time. Third, there is little evidence for long term memory and cyclic behavior. Finally, several stock market anomalies, including January effect, weekday effect, turn-of-the-month effect and turn-of-the-quarter effect, are still significant after many years of their discoveries. Chapter 3 studies the statistics of Sharpe ratio differences. We derive the statistical distributions of the Sharpe ratio differences using standard asymptotic theory under three sets of assumptions for the return-generating process - independently and identically distributed returns, stationary returns, and with time aggregation. We compare the hedge fund Sharpe ratios and find that the Sharpe ratio differences are not statistically different from zero.