+ Limited Arbitrage in Equity Markets Author: MARK MITCHELL, TODD PULVINO, and ERIK STAFFOR Presenter: Laura Huiqi Ma

+ Outline Objective Data & Measurement Fundamental & Financial Risk Arbitrage in Imperfect Capital Markets Conclusion & Comments

+ Objective Impediments to Arbitrage in Equity Markets Negative Stub Values A firm‘s market value is less than the value of its ownership stake in a publicly traded subsidiary Sample Size: 82 situations between 1985 and 2000

+ Data Description Sample Selection Criteria Stub Assets V Stub = MV Equity – MV Stake – [MV Other Assets – MV Liabilities ] Rule 1 Rule 2 

+ Data Description Sample Construction Find the parent – IPO pairs Search the Securities Data Corporation (SDC) database from 1985 through 2000 for all initial public offerings (IPO) where another publicly traded firm owned the IPO shares prior to the offering Calculate the stub value Use stock price data from CRSP (pre-2000) and Datastream (during 2000) to calculate the ratios specified by Rule 1 and Rule 2 from the time of the IPO through December 2000 Search for extreme relative value situations

+ Data Description Sample Construction Resulting Sample Covering the period from 1985 through December 2000 Rule 1: 70 parent/subsidiary pairs Rule 2: 82 parent/subsidiary pairs

+ Data Description Shares Outstanding, Returns, and Short Rebates Shares Outstanding Quarterly company filings of financial reports Financial press for relevant news Short Rebates The rate paid to investors on the proceeds obtained from short selling a stock Obtained from Ameritrade Holding Corporation December 1998 through October to 50 basis points less than the federal funds rate

+ Measuring Investment Returns Investment Criteria and Thresholds R Rule 2

+ Measuring Investment Returns Investment Capital and Financial Leverage Investment Capital Long- and short-stock positions Additional precautionary capital Financial Leverage “Textbook” Leverage "Regulation T" leverage “Conservative" leverage

+ Measuring Investment Returns “Textbook” Leverage Assumption 1 Regulation T initial margin requirements Initial invested capital is equal to 50 percent of the long market value and 50 percent of the short market value Assumption 2 No maintenance margin requirements

+ Measuring Investment Returns "Regulation T" leverage Regulation T initial margin requirements Stock exchanges (e.g.,NYSE) and self-regulatory organizations (e.g., NASD) maintenance margin rules after initial transaction “Conservative" leverage Preclude all margin calls ex post

+ Measuring Investment Returns Assessing Investment Performance Isolation Investment Performance Mean annualized return in excess of the risk-free rate Frequency of negative returns Frequency of margin calls

+ Measuring Investment Returns Portfolio Analysis Monthly Investment Returns Regulation T Leverage Compounding daily portfolio returns Diversification Constraint No more than 20 percent of the portfolio's equity to be initially invested in any one negative-stub-value transaction Rebalance Crossed the buy or sell threshold Close positions Satisfy a maintenance margin call Direct transaction costs $0.05 per share in the 1980s and $0.04 per share thereafter

+ Fundamental Risk Definition Possibility that the negative-stub-value trade is terminated before prices converge to fundamental values The risk of a terminating event before prices converge is substantial

+ Acquisition Delisting

+ Financing Risk Horizon Risk Increasing the length of the path reduces the arbitrageur's return

+ Financing Risk Margin Risk Forced to post additional collateral or partially liquidate if the arbitrageur faces a margin call Full Sample Results for Individual Investments Portfolio Results

+ Full Sample Results

+ Portfolio Results R p, - R f, = a + b (R m, - R f,) +sSMB, + hHML, + e t

+ Financing Risk Specialization of the Arbitrageur pure negative-stub-value portfolio negative-stub-value portfolio combined with the market portfolio (41% negative stub values, 59% market) negative-stub-value portfolio combined with a merger arbitrage portfolio (15% negative stub values, 85% merger arbitrage)

+ Specialization of the Arbitrageur

+ Arbitrage in Imperfect Capital Markets Costs of Short Selling Low Public Floats Short Rebate The minimum short rebates: -8% - 6% per year The real impediment is not the short rebate, but instead the uncertainty over how long one will be paying it Buy-in Risk Owners of the stock demand that their loaned-out shares be returned

+ Arbitrage in Imperfect Capital Markets Imperfect Information and the Persistence of Negative Stub Values

+ Conclusion Impediments to arbitraging relative mispricing of corporate cross holdings, where the parent firm is worth less than its ownership stake in a publicly traded subsidiary Biggest friction impeding arbitrage Costs associated with imperfect information Imperfect information and transaction costs

+ Comments Limitation Limited Sample Size Imprecise Estimation The ratios do not account for off-balance-sheet liabilities Biased sample T he distribution of "bad outcomes" is not known ex ante

+ THANK YOU