What determines the level of short-selling activity?

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

Table III supports the three trading hypotheses of the short-sellers. Other factors, such as the difference of investors' opinion and the institutional ownership, are also important to determine the short-interest level. In addition, since I standardize all non-dummy variables, the direct comparison of impact from change of one standard deviation to the relative short-interest level is possible. Results show that the arbitrage and hedging demand proxy by D_DEBT and D_OPT, dominates others.

Put/call ratio of the options trading volume is an alternative proxy for the market sentiment. However, only a small proportion of sample stocks have underlying options. I run the regression with the stocks that have underlying options for the 1996-2002 period. The relation between the put/call ratio and the RSI is significant and positive. The coefficient of the put/call ratio is 0.0005 with a t-value of 2.97 on the NYSE and is 0.0011 with a t-value of 4.15 on Nasdaq.

B. Tax-based Trading

I follow the method of Arnold et al. (2005), adding four dummy variables in the regression. D_BJAN and D_BDEC are dummy variables that indicate January and December before TRA97, respectively. D_AJAN and D_ADEC are dummy variables that indicate January and December after TRA97, respectively.

Table IV reports the results. The coefficients of D_BDEC and D_BJAN are both significant and negative on both the NYSE and Nasdaq. The difference between D_BJAN and D_BDEC is statistically less than zero in the NYSE. This result is consistent with the belief that before TRA97, short selling against the box drives up the short-interest level before the end of the year and closes the position in January of the next year (Arnold et al., 2005). But the difference of D_AJAN and D_ ADEC is also statistically less than zero. The Taxation Hypothesis appears to be true prior to the Taxpayer Relief Act of 1997, but has since disappeared due to the introduction of that legislation.

C. Proportion of Variables Contributes to Explanation

Table III shows that there are many variables that affect the level of short selling. However, the proportion of variables that individually contribute to determining the short-selling level is unclear. I use the following method to investigate the issue. First, I run a regression with all nine variables to obtain the sum of square residual (SSR). I then run nine regressions that contain only eight different variables to obtain nine SSRs. I compute the proportion of independent variable contributions to R-square (PCR) as follows. [PCR.sub.i] equals [SSR.sub.i] ([X.sub.i] | control all other variables) divided by SSR (all variables), where [SSR.sub.i] ([X.sub.i] control all other variables) equals SSR (all variables) minus SSR (all variables except [X.sub.i]). The advantage of this approach is that it isolates the pure contribution of individual variables from common contribution with other variables.

Table V reports the results. On the NYSE, D_OPT, SIGMA, and D_DEBT, which are proxies for the arbitrage and hedging demand and the divergence of investors' opinion, contribute the most to explaining the level of short selling. On Nasdaq, arbitrage and hedging demand from D_OPT dominates the other variables. In addition, D_DEBT, BM and LNAGE also play important roles in explaining the short-selling level on Nasdaq.