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Research on the Limits of Arbitrage J.C. Lin Collette Endowed Chair of Financial Services and Professor Louisiana State University Prepared for Presentation at University of Vaasa, Finland October 2004 Limited Arbitrage and Short Sales Restrictions: Evidence from the Option Markets by Ofek, Richardson, and Whitelaw, 2002, JFE Law of one price: Two assets with the same payoffs should have the same price. If this restriction is violated, then at least two conditions must be met. 1. there must be some limits to arbitrage. 2. there must be a reason why these assets have diverging prices in the first place. The goal of this paper is to analyze the impact of these two conditions under put-call parity. Put-Call Parity For European options on non-dividend paying stocks, S=PV(K) +C-P. For American options, the put will be more valuable because at every point in time there is positive probability of early exercise, implying S>=PV(K)+C- P. With an early exercise premium, EEP, it can be rewritten as S=PV(K)+C-P+EEP. Research Design Investigate violations of the modified put-call parity, S=PV(K)+C-P+EEP, and relate them to the following conditions: (i) limited arbitrage via either short sales restrictions or transaction costs, and (ii) potential periods of mispricing. expected maturity effects, potential structural shifts in mispricing, forecastability of future returns. Short Sales Restrictions Two reasons why short sales restrictions exist: Investors are either unwilling to sell stock short or find it too difficult to do so. Because of the Investment Company Act of 1940, mutual fund managers are unwilling to short stock (Chen, Hong, and Stein (2002, JFE). Almazan, Brown, Carlson, and Chapman (2002) show only a small fraction of mutual funds short stocks; and greater mispricing occurs when mutual funds are absent from the market. Short Sales Restrictions (continued) It is difficult to short stocks on a large scale. To short a stock, the investor must be able to borrow it. Not many shares available. There is no guarantee that the short position will not get called through either the lender demanding the stock be returned or a margin call. no guarantee that the investor will be able to re-short the stock. Short Sales Restrictions (continued) When an investor shorts a stock, she places a cash deposit equal to the proceeds of the shorted stock. That deposit carries an interest rate referred to as the rebate rate. One way to measure the difficulty in short selling is to compare the rebate rate on a stock against the median rebate rate. The rebate rate spread can be used as the actual cost of borrowing a stock. It can also be used as a signal of the difficulty of shorting. Findings Violations of the put-call parity are asymmetric in the direction of short sales restrictions. For example, after shorting costs, 13.63% of stock prices still exceed the upper bound implied by the option market, while only 4.36% are below the lower bound. The mean difference between the option-implied stock price and the actual stock price for these violations is 2.71%. Findings (continued) Both the probability and magnitude of the violations can be linked directly to the magnitude of the rebate rate. A one standard deviation decrease in the rebate rate spread implies a 0.67% increase in the deviation between the prices in the stock and options markets. Possible Explanations The results suggest that the relative prices of similar assets with identical payoffs can deviate from each other when arbitrage is not possible. What possible explanations exist? If markets are segmented such that the marginal investors across these markets are different, it is possible that prices can differ. In the absence of some friction that prevents trading in both markets, this segmentation will not be rational. Behavioral finance argues that prices can deviate from fundamental values because a significant part of the investor class is irrational. Behavioral Finance Irrational investors look to market sentiment or are driven by psychological (rather than financial) motivations. In the presence of limited arbitrage, there is no immediate mechanism for correcting the resulting mispricings. If the equity and options markets are segmented, i.e., have different investors, then mispricing in the equity market do not necessarily carry through to the options market. In other words, irrational investors do not use the options market. A Framework Consider a framework in which the stock and options markets are segmented and the equity markets are “less rational” than the options markets. This framework allows us to interpret the price differences as mispricing in the equity markets. The framework also generates predictions about the relation between put-call parity violations, short sales constraints, and future returns. Stock returns are expected to fall over the life of the options conditional on a put-call parity violation and/or a negative rebate rate spread. Forecasting Returns Conditional on a rebate rate spread of less than -0.5%, the mean excess return over the life of the option is -9.96%, versus 0.70% for zero rebate rate stocks. Conditioning on put-call parity violations of greater than 1.0%, the mean excess returns over the life of the option is -4.49% versus 0.13% for violations of less than zero. Combining these signals produces an average excess returns of -12.57%, which illustrates that the rebate rate and the violation contain independent information about future stock price movements. Implications Put-call parity violations pose considerable problems for rational asset pricing models. The results support the foundations of behavioral finance, i.e., there are enough irrational investors to matter for pricing assets. The forces of arbitrage do appear to limit the relative mispricing of assets, i.e., there is clear relation between arbitrage constraints (e.g., transaction costs and rebate rates) and the level of mispricing. It is a puzzle why any investor would ever wish to purchase poorly performing stocks. Future research?? Limited Arbitrage in Equity Markets by Mitchell, Pulvino, and Stafford, 2002,JF Consider the situation where a firm’s market value is less than the value of its ownership stake in a publicly traded subsidiary. Commonly referred to as “negative stub value.” It can arise following equity carve out of subsidiaries or from partial acquisition of a public traded firm. Research Design and Findings Examine 82 situations with negative stub values. The link between parent and subsidiary firms disappears without convergence of the arbitrage spread 30 percent of the time. This happens when a corporate event permanently alters the relative mispricing in a manner that is detrimental to the arbitrageur’s profits. For example, going bankrupt. • Negative stub values are not risk-free arbitrage opportunities. Uncertainty There is substantial variability in the time to termination. The average time between the initial mispricing and a termination event is 236 days, the median is 92 days, the minimum is 1 day, and the maximum is 2,796 days. As a result of this uncertainty, even if convergence is eventually achieved, the negative-stub-value investment often underperforms the risk-free rate. Discouraging investments by arbitrageurs who are uncertain of the time to convergence. Implication There are costs that limit arbitrage in equity market. Uncertainty about the distribution of returns and characteristics of risks limits arbitrage. Future research?? The Limits of Arbitrage by Shleifer and Vishny, 1997, JF Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky. The absolute and relative values of different securities are hard to calculate. Professional Arbitrageurs Using other people’s capital. Facing the problems of possible interim liquidations before mispricing disappears. Uncertain the horizon over which mispricing is eliminated. Risk averse. Avoiding extremely volatile markets. High volatility could make arbitrage less attractive if expected alpha does not increase in proportion to volatility. They may prefer bond markets over equity markets. Implication Anomalies in financial markets are likely to appear, and why arbitrage fails to eliminate them. Future research??
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