The Limits of Arbitrage and Stock Mispricing: Evidence from Decomposing Market to Book Ratio

The purpose of this paper is to investigate the effect of the "limits of arbitrage" on securities mispricing. Specifically, I investigate the effect of the availability of substitutes and financial constraints on stock mispricing. In addition, this study investigates the difference in the limits of arbitrage, in the sense that it will lead to lower mispricing for these stocks, relative to non-S&P 500 stocks. I also examine if the lower mispricing can be attributed to their lower limits of arbitrage. Modern finance theory and efficient market hypothesis suggest that security prices, at equilibrium, should reflect their fundamental value. If the market price deviates from the intrinsic value, then a risk-free profit opportunity has emerged and arbitrageurs will eliminate mispricing and equilibrium is restored. This arbitrage process is characterized by large number of arbitrageurs which have infinite access to capital. However, a better description of reality is that there are few numbers of arbitrageurs to the extent that they are highly specialized; and they have limited access to capital. Under these condition arbitrage is no more a risk-free activity and can be limited by several factors such as arbitrage risk and transaction costs. Other factors that are discussed in the literature are availability of substitutes and financial constraints. The former arises as a result of the specialization of arbitrageurs in the market in which they operate, while the latter arises as a result of the separation between arbitrageurs and capital. In this dissertation, I develop a measure of the availability of substitutes that is based on the propensity scores obtained from propensity score matching technique. In addition, I use the absolute value of skewness of returns as a proxy of financial constraints. Previous studies used the limits of arbitrage framework to explain pricing puzzles such as the closed-end fund discounts. However, closed-end fund discounts are highly affected by uncertainty of managerial ability and agency problems. This study overcomes this problem by studying the effect of limits of arbitrage on publicly traded securities. The results show that there is a significant relationship between proxies of limits of arbitrage and firm specific mispricing. More importantly, empirical results indicate that stocks that have no close substitutes have higher mispricing. In addition, stocks that have high skewness show higher mispricing. Subsequent studies show that the S&P 500 stocks have different levels of liquidity, analysts’ coverage and volatility. These characteristics affect the ability of arbitrageurs to eliminate mispricing. Preliminary univariate tests show that S&P 500 stocks have, on average, lower mispricing and limits of arbitrage relative to non-S&P 500 stocks. In addition, the multivariate test shows that S&P 500 members have, on average, lower mispricing relative to non-S&P 500 stocks