Historical tests of various asset pricing models, especially the CAPM, have given rise to an abundance of well-documented, anomalously priced characteristics in the cross section of stock returns. In theory, we would expect anomalies to be arbitraged away by sophisticated investors. However, in the real world, anomalies can persist because there are limits to arbitrage, such as constraints on short selling.
First, as I have discussed before, many institutional investors (such as pension plans, endowments and mutual funds) are prohibited by their charters from taking short positions.
Second, the cost of borrowing a stock to short it can be expensive. There also can be a limited supply of stocks available to borrow for the purpose of shorting (this can be especially true for small growth stocks).
Third, investors are unwilling to accept the risks associated with shorting because of the potential for unlimited losses. This is prospect theory at work, where the pain of a loss is much larger than the joy of an equal gain.
Fourth, short-sellers run the risk that their borrowed securities are recalled before the strategy pays off. They also run the risk that the strategy performs poorly in the short run, triggering an early liquidation.
Together, these factors suggest investors may be unwilling to trade against the overpricing of securities, allowing anomalies to persist. On the other hand, profiting on underpricing is easy, as investors can simply purchase undervalued securities. This results in asymmetry in arbitrage, because buying is easy (inexpensive) and short-selling can be hard (expensive and riskier).
Examining Arbitrage’s Limits
Filip Bekjarovski contributes to the literature on anomalies with his November 2017 study, “How Do Short Selling Costs and Restrictions Affect the Profitability of Stock Anomalies?” His study, covering the period July 1963 through 2016, examines the profitability of both long-only and long-short portfolios to determine if limits to arbitrage (short-selling constraints) explain seven CAPM anomalies (size, value, profitability, investment, momentum, accruals and net issuance). This allowed him to also determine if long-only strategies can exploit anomalies.
Bekjarovski also tested a low-cost, long-short strategy designed to avoid the high costs that can be incurred in shorting, specifically in small-cap stocks. The strategy is to go long the first decile of an anomaly and then short the total market, which is cheap to do. The long-short strategy minimizes the concentrated exposure to market risk typical of conventional long-only portfolios while providing exposure to the anomaly at a low cost. The net position is long the first decile of the anomaly and short the remaining nine.
Following is a summary of his findings: