Limited Arbitrage in Equity Markets
MARK MITCHELL, TODD PULVINO, and ERIK STAFFORD*
ABSTRACT
We examine 82 situations where the market value of a company is less than its subsidiary. These situations imply arbitrage opportunities, providing an ideal setting to study the risks and market frictions that prevent arbitrageurs from immediately forcing prices to fundamental values. For 30 percent of the sample, the link between the parent and its subsidiary is severed before the relative value discrepancy is corrected. Furthermore, returns to a specialized arbitrageur would be 50 percent larger if the path to convergence was smooth rather than as observed.
Uncertainty about the distribution of returns and characteristics of the risks
Specialization limits the degree of diversification in the arbitrageur’s portfolio and causes him to bear idiosyncratic risks for which he must be rewarded. For example, if there is a purely random chance that prices will not converge to fundamental value, a highly specialized arbitrageur who cannot diversify away this risk will invest less than one who can.
Furthermore, even if prices eventually converge to fundamental values, the path of convergence may be long and bumpy. While waiting for the prices of the mispriced securities to converge, they may temporarily diverge. If the arbitrageur does not have access to additional capital when security prices diverge, he may be forced to prematurely unwind the position and incur a loss ~DeLong et al. ~1990!, Shleifer and Summers ~1990!, and Shleifer and
Vishny ~1997!!. The prospect of incurring this loss will further limit the amount that a specialized arbitrageur is willing to invest.
To empirically address the limits of arbitrage in equity markets, we construct a sample of situations where a firm’s market value is less than the value of its ownership stake in a publicly traded subsidiary.1 These situations are commonly referred to as “negative stub values” and can arise following equity carve outs of subsidiaries or from the partial acquisition of a publicly traded firm. We track each parent0subsidiary pair until an event occurs that eliminates the link between the two entities or until the