The authors are the first to model the dynamic risks of short-selling constraints (i.e., the risk that borrowing fees and the availability of stock loans may change while a short position is outstanding). Practitioners may find arbitrage opportunities unexploitable not because of the static costs of short selling but rather because of short-selling risk. Furthermore, the longer it takes for an arbitrage opportunity involving short selling to bear fruit, the greater the short-selling risk and, correspondingly, the greater the possible mispricing and the fewer arbitrageurs willing to take the risk.

The authors use daily equity lending data from Markit for 4,500 US equities from 1 July 2006 through 31 December 2011. The authors construct their short-selling risk (“short risk”) measure by regressing the variance of daily short-selling loan fees for the previous 12 months on a number of lagged variables that include the variance of loan fees for new loans, the variance of the ratio of equity loan supply to demand (i.e., loan “utilization”), measures of extreme loan fees and utilization, and a number of firm-level characteristics. This regression model is used to estimate the level of short risk given available information.

To examine how a stock’s short-selling risk might affect its future returns, stocks are sorted into quintiles based on their prior-month level of short risk. Highest-quintile (i.e., riskier) short risk stocks earn monthly returns of –0.49%, and lowest-quintile short risk stocks earn monthly returns of 0.58%.

After examining other risk factors and firm size, the authors find that a one standard deviation increase in short risk leads to a 40-bp reduction in monthly returns. Higher short risk is correlated with lower future returns, suggesting that arbitrageurs with short positions receive compensation for this short risk. This finding is also consistent with the puzzle that high short interest (which is publicly available information) helps predict lower future returns. The authors find this puzzle to be particularly pronounced for stocks with high short risk, again indicating that the lower future returns are simply compensation for this short risk.

The next analysis considers whether prices for stocks with high short risk display are inefficient or exhibit a predictable “price delay.” Using regression analysis with price delay as the dependent variable and short risk as one of the independent variables, short risk is found to have a positive statistically significant coefficient, indicating that increased short risk contributes to price inefficiency.

Another key result concerns the interaction of an arbitrageur’s time horizon and short risk on arbitrage activity and price inefficiency. By using option prices with different times to expiration, the authors can examine arbitrage opportunities with different time horizons (i.e., 1–30 days, 31–60 days, and 61–90 days). To measure these opportunities relative to a time horizon, the authors calculate the natural log difference between the spot price and the synthetic stock price implied from the put–call parity of a given time to expiration. This measure is termed PutCallDisparity—a positive value indicating an opportunity for an arbitrageur to short the stock and purchase the synthetic stock, expecting convergence at option expiration.

The authors find that PutCallDisparity increases for the combination of stocks with higher short risk and trades involving longer horizons. Further analysis links this combination to lower short-selling volume (i.e., fewer arbitrageurs available).

I find the research interesting because it indicates that even if such short-selling constraints as the uptick rule or naked selling were eliminated, short selling would not necessarily resolve the problem of price inefficiency because of short-selling risk. Given these possible limitations to unconstrained short selling, further research could look at whether derivative securities have similar issues with regard to risk or the ability to resolve some of these risk issues.