Swedroe: The Shorting Premium Puzzle

December 31, 2014

There are a number of well-documented anomalies that cause problems for the efficient markets hypothesis (EMH). These problems arise because the EMH assumes any mispricing in the market will be arbitraged away by rational traders who buy relatively undervalued assets and sell relatively overvalued ones.


Among the biggest problems are the existence of momentum and the relatively poor performance of small growth stocks—as well as any security with a lotterylike (or jackpot) distribution. These anomalies continue to occur even after they become known through the publication of academic research. The question is, Why, then, do such anomalies continue to persist?


One explanation offered by researchers attempting to answer this question is that there are limits to arbitrage, which prevents rational investors from exploiting the anomaly. For example:

  • Many institutional investors (such as pension plans, endowments and mutual funds) are prohibited by their charters from taking short positions.
  • Shorting can be expensive. You have to borrow a stock to go short, and many stocks are costly to borrow because the supply of equities available from institutional investors is low. The largest anomalies tend to occur in small stocks, which are costly to trade in large quantity (both long and especially short); the volume of shares available to borrow is limited, since they tend to be owned by individual investors; and borrowing costs are often high.
  • Investors are unwilling to accept the risks of shorting because of the potential for unlimited losses. Even traders who believe a stock’s price is too high know that, even though they might be correct and the price may eventually fall, they still face the risk the price will go up before it goes down. Such a price move, requiring additional capital, can force traders to liquidate at a loss.


Malcolm Baker, Brendan Bradley and Jeffrey Wurgler—authors of the 2011 study, “Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly”—proposed another explanation; specifically, the typical institutional investor’s mandate to maximize the ratio of excess returns relative to a fixed benchmark without resorting to leverage.


Many institutional investors who are in a position to offset an irrational demand for risky assets have fixed benchmark mandates that are usually capitalization-weighted. Thus, straying from the benchmarks to exploit anomalies creates career risk.


The Fee For Shorting

Arbitrageurs can sell shares short by borrowing them in the stock loan market. The price for doing so is a fee, or rebate, paid by the borrower of the stock to the lender. The size of the fee should reflect underlying demand to short the stock.


Itamar Drechsler and Qingyi Freda Drechsler—authors of the March 2014 study, “The Shorting Premium and Asset Pricing Anomalies”—sought to determine if the shorting fee provided information as to the stock’s expected return. Their study covered the period January 2004 through October 2012, and included 95 percent of stocks in the CRSP database and more than 85 percent of borrowing activity in the U.S. security lending market. Following is a summary of their findings:




  • For each of the top eight deciles by shorting fee, the average shorting fee is below 32 basis points (bps) per year. In other words, 80 percent of stocks are cheap to short. Stocks in the ninth decile are moderately expensive to short (78 bps per year, on average). However, stocks in the tenth decile are expensive to short, with an average fee of 582 bps per year. That’s greater than the size of the value premium, and not that much less than the size of the equity premium.
  • The stocks with almost zero short fees tend to be very large on average. Market capitalization is then, on average, effectively flat, at $2 billion to $3 billion, from the third to the ninth deciles. The expensive-to-short stocks are, on average, the smallest. Yet, even these stocks have a sizable average market capitalization of $1.27 billion. And the aggregate market capitalizations of the expensive-to-short stocks are economically large. The average total market caps of the ninth and tenth deciles are roughly $1.1 trillion and $415 billion. As an interesting aside, Apple’s current market capitalization is about $700 billion.
  • The average returns are flat across the eight cheap-to-short deciles. However, the average return drops sharply for the ninth and tenth deciles. In fact, the average return on the tenth decile is -0.70 percent per month. The average return on a portfolio long in the stocks in the first decile and short in the stocks in the tenth decile—the cheap-minus-expensive (CME) portfolio—is 1.44 percent per month, and highly significant (t-stat 4.94) despite the short sample. This large average return cannot be explained by differential exposures to the conventional four Fama-French factors, as the CME portfolio’s four-factor (FF4) alpha is 1.55 percent (t-stat 7.00).
  • The difference in returns is not accounted for by the shorting fees themselves. While net returns are smaller, the average net return on the tenth decile stocks is -0.17 percent per month, and the average net return of the CME portfolio is a highly significant 0.92 percent per month. Thus, high short-fee stocks earn low returns even after accounting for the shorting fee earned from securities lending.


The authors called this difference in average returns the “shorting premium,” because it represents the extra return earned by a concentrated group of short-sellers as compensation for taking risk. However, the question remains as to why investors want to hold such stocks (the jackpot theory would offer one explanation).


It’s unfortunate, but also understandable, that the time period covered by the study is relatively short. It’s difficult to obtain shorting costs further back in time. The authors tried to correct for this problem by using a proxy for shorting costs (short interest as fraction of shares owned by institutions), which allowed them to extend the period of study back to 1980.


The authors do note that the drawback to using a proxy is that it may provide only a rough measure of shorting fees and hence introduce substantial noise into the analysis. That said, the results produced by the proxy measure were very similar to those produced by the actual shorting fee.


The authors also demonstrated that the shorting fee went a long way in explaining six of the eight well-known anomalies they examined, including financial distress, idiosyncratic volatility and gross profitability. They also found that the anomalies are largely nonexistent within the 80 percent of stocks that have low short fees.


Correlations With Common Factors

The authors found that the CME factor is negatively correlated with the market portfolio. A strategy that calls for shorting high-fee stocks performs relatively poorly when the market is doing well. The authors also found that CME is negatively correlated with the size and value factors, but positively correlated with the momentum factor. Thus, including a CME factor in portfolio design would provide a diversification benefit for portfolios with tilts to small and value stocks.


The research shows that stocks with high short fees have poor returns. A fund wouldn’t have to go short in stocks with high fees to benefit from this information. An alternative strategy would be for long-only mutual funds to avoid buying stocks with high short fees. The evidence suggests that such a strategy would involve no extra costs while improving returns.


For example, a small-cap or value fund could screen out a high short-fee stock from their eligible buy lists even if that stock’s market capitalization or valuation metric (such as price-to-book ratio) would otherwise cause it to be purchased.


In fact, both Bridgeway and Dimensional Fund Advisors account for short fees when considering whether to include stocks in their list of equities eligible for purchase. (Full disclosure: My firm, Buckingham, recommends Dimensional and Bridgeway funds in constructing client portfolios.)


AQR Capital also uses the information in some of their portfolios. A high shorting fee is used as a signal to sell short the hard-to-borrow names, assuming AQR forecasts a positive expected return (net of the fee). They do so based on the academic evidence showing that high short-fee names are predictive of lower returns, even net of their higher fee.


Larry Swedroe is the director of research for the BAM Alliance, a community of more than 150 independent registered investment advisors throughout the country.



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