Swedroe: Why Stock Price Anomalies Persist

Research suggests anomalies aren’t simply the result of constraints on short-selling.

Larry Swedroe
Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

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:


  • Extensive mispricing exists in long positions. Time-series alphas are large and statistically significant in long-only anomaly portfolios, and including long-only anomalies leads to statistically significant (at the 1% confidence level) improvements in Sharpe ratios (risk-adjusted returns).
  • Momentum, investment and net issuance have significant alphas from both the long and short position. Book-to-market (value) is the only anomaly deriving its alpha primarily from the long side. Operating profitability and accruals get their alpha primarily from the short position.
  • Short-selling costs are avoidable and low relative to short position profitability, meaning short-selling frictions cannot account for the persistence of anomalies.
  • The synthetic-short portfolio dramatically improves Sharpe ratios of long-only strategies, with the improvement being statistically significant at the 2% confidence level.
  • Short selling individual securities in the short leg of anomalies is profitable in the absence of shorting costs. Short alphas capture 63% of long-short profitability. In addition, short selling individual securities provides a large and statistically significant improvement, at the 2% confidence level, in the Sharpe ratio relative to the synthetic-short approach. While the evidence suggests short-selling restrictions on either individual securities or the market can severely reduce the profitability of anomalies, they do not completely eliminate their investment potential.

Bekjarovski also examined how the inclusion of a positive weight in the second-highest alpha portfolio in the synthetic short (reducing the net negative weight assigned to the second-highest alpha portfolio in the overall synthetic-short approach) impacted the strategy. While this did improve results, the improvement was marginal.

How High Are Shorting Costs?

The value-weighted borrowing cost was 46 basis points (bps) annually, which is close to the general collateral rate of 35 bps. However, the equally weighted borrowing fee was 416 bps, nine times larger. Even though 37% of stocks in the data were on special (they were expensive to borrow), they account for only 3% of total market capitalization—high borrowing costs are concentrated in small-cap stocks.

Bekjarovski found that, on a value-weighted basis, borrowing costs of anomaly short positions are small relative to their alphas—only 15% of the average short anomaly alpha. The highest borrowing costs were for the unprofitable (116 bps annually) and loser (110 bps annually) portfolios.

However, the anomalies’ short-selling costs were only a fraction of their gross short alpha, which was 504 bps for profitability and 1,124 bps for momentum. For the remaining five anomalies examined, costs were below 65 bps. In fact, four anomalies (size, value, investment and accruals) had a higher shorting cost in the long position than in the short position.

The results suggest that short-selling costs are small relative to anomaly profitability.

This goes against the hypothesis that claims exploiting short position profitability is too costly, allowing anomalies to persist. But Bekjarovski also found that the average borrowing cost associated with equally weighted anomaly sorts was 974 bps, 14 times larger than its value-weighted counterpart.

Furthermore, Bekjarovski made the important observation that the short-selling costs associated with anomaly strategies can at least be partly offset by revenue received though the lending of stocks in long positions.

These findings led Bekjarovski to conclude both that there is significant profitability in long positions, which serves as evidence against arbitrage asymmetry’s implication that anomaly profitability should be concentrated in short positions, and that even investors who do not short-sell (for whatever reason) can improve performance extensively by including anomalies in their investment universe. He concluded as well that short-selling costs can be easily and extensively reduced using value weights without forgoing any short-position profitability (by shorting the market portfolio instead of the short leg of the anomaly).

Bekjarovski also sought to determine at what cost level shorting individual securities would become unprofitable. He found investors can no longer be confident that a security-short approach will outperform synthetic-short execution when short-selling costs for a portfolio of anomalies exceeds 125 bps annually.

Additionally, he found synthetic-short investing becomes economically more profitable when short-selling costs exceed 300 bps. These estimated cost bounds are much larger than the borrowing cost associated with value-weighted anomalies.

There was another finding that should be of interest: The average correlation between long-short strategies was low. Thus, anomalies provide diversification benefits versus long-only portfolios, where correlations were much higher. For example, individual correlations between the market and operating profitability, investment, accruals and net issuance were all above 0.9 (because they have large exposure to market beta, which dominates their risks), limiting the diversification benefit.


Bekjarovski supplies evidence that there is significant profitability in the long leg of anomalies, and additional improvements in performance can be achieved through a synthetic short. Short-selling costs on individual equities are small relative to their profitability contribution if investors do not extensively rely on small-market-capitalization firms in portfolio construction. Overall, the evidence does not support the view that short-selling frictions can fully account for the persistence of anomalies.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

Larry Swedroe

Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.