What determines the level of short-selling activity?

Financial Management (Financial Management Association), Winter, 2007 by Hung Wan Kot

I merge short interest, institutional holding, and options listings with the CRSP using the historical ticker symbol. To avoid the look-ahead bias for the book-to-market ratio, during the merge of Compustat with the CRSP, I use the latest fiscal year-end values for the book value of equity only if the current month is at least four months after the firms fiscal year-end. For example, if the fiscal year-end month is before September, then I use the book value in calendar year t-1 to compute the book-to-market ratio in calendar year t. Otherwise, I use the book value in calendar year t-2 to compute the book-to-market ratio in calendar year t.

The Nasdaq market contains many small-capitalization stocks. To avoid the small-firm size effect, in each month I exclude the bottom 33% of stocks, based on the market capitalization on the Nasdaq. I exclude observations if any variables are missed in the regression analysis. I also exclude outliers. My final sample comprises 2,506 common stocks in the NYSE with 201,910 observations and 6,020 common stocks in the Nasdaq with 287,573 observations.

B. Variable Construction

I measure the level of short-selling activity on a monthly basis as relative short interest (RSI), which is the volume of short interest divided by the number of shares outstanding. I use RSI as the dependent variable in a regression analysis. I introduce independent variables to analyze the four different hypotheses that explain the motives for short selling.

To test the Trend Hypothesis, I construct PR1Y, which I define as the lagged one-year cumulative returns (PR1Y), as a proxy for the short-term stock returns. As noted above, some investors are trend-traders. Short-sellers will close their position if the stock prices are increasing in the past short-term. On the other hand, short-sellers will open their short position if the stock prices are decreasing in the past short-term. I predict that there is a negative relation between PR1Y and RSI.

To test the Overpricing Hypothesis, I use the book-to-market ratio (BM) as a proxy for the overvaluation. Low fundamental-to-market ratio stocks are relatively overpriced implying a higher level of short-selling. I predict that the relation between BM and RSI is negative.

To test the Arbitrage Hypothesis, I construct three dummy variables as proxies for the arbitrage and hedging demand of short-selling. D_DEBT is the dummy variable of availability of convertible debt and convertible preferred stocks (one for yes and zero for no). I predict that the relation between D_DEBT and short interest level is positive.

D_OPT is the dummy variable of the availability of stock options (one for stock that has underlying options traded, zero for none). Options listing has both a positive and a negative effect on short selling. On the positive side, studies find a positive relation between short interest and options trading (Brent et al., 1990; Figlewski and Webb, 1993; Danielsen and Sorescu, 2001; and Arnold et al., 2005). The reasons could be that shares are sold short to hedge option positions in the stock, or because of the arbitrage opportunity if there is a price difference between options and underlying stocks. On the negative side, options are a substitute for short selling. If an investor wants to profit from decreasing stock prices, he can short the stock, buy a put option, or sell a call option. All three methods achieve the same purpose. Theoretically, the relation between D_OPT and the short-interest level could be positive or negative.