Three Essays on Market Efficiency and Limits to Arbitrage

This dissertation consists of three essays. The first essay focuses on idiosyncratic volatility as a primary arbitrage cost for short sellers. Previous studies document (i) negative abnormal returns for high relative short interest (RSI) stocks, and (ii) positive abnormal returns for low RSI stocks. We examine whether these market inefficiencies can be explained by arbitrage limitations, especially firms' idiosyncratic risk. Consistent with limits to arbitrage hypothesis, we document an abnormal return of -1.74% per month for high RSI stocks (>=95th percentile) with high idiosyncratic volatility. However, for similar level of high RSI, abnormal returns are economically and statistically insignificant for stocks with low idiosyncratic volatility. For stocks with low RSI, the returns are positively related to idiosyncratic volatility. These results imply that idiosyncratic risk is a potential reason for the inability of arbitrageurs to extract returns from high and low RSI portfolios.

The second essay investigates market efficiency in the absence of limits to arbitrage on short selling. Theoretical predictions and empirical results are ambiguous about the effect of short sale constraints on security prices. Since these constraints cannot be eliminated in equity markets, we use trades from futures markets where there is no distinction between short and long positions. With no external constraints on short positions, we document a weekend effect in futures markets which is a result of asymmetric risk between long and short positions around weekends. The premium is higher in periods of high volatility when short sellers are unwilling to accept higher levels of risk. On the other hand, riskiness of long positions does not seem to have a similar impact on prices.

The third essay studies investor behaviors that generate mispricing by examining relationship between stock price and future returns. Based on traditional finance theory, valuation should not depend on nominal stock prices. However, recent literature documents that preference of retail investors for low price stocks results in their overvaluation. Motivated by this preference, we re-examine the relationship between stock price and expected return for the entire U.S. stock market. We find that stock price and expected returns are positively related if price is not confounded with size. Results in this paper show that, controlled for size, high price stocks significantly outperform low price stocks by an abnormal 0.40% per month. This return premium is attributed to individual investors' preference for low price stocks. Consistent with costly arbitrage, the return differential between high and low price stocks is highest for the stocks which are difficulty to arbitrage. The results are robust to price cut-off of $5, and in different sub-periods.