¹ At any given time, the short interest variable is defined as the number of shares borrowed, sold, and still uncovered or owed. Having no time dimension, the short interest level is a stock variable.

² For a comprehensive discussion of the random walk hypothesis, see Cootner, P. H., ed., The Random Character of Stock Price Behavior (M.I.T. Press, 1964)Google Scholar.

³ Of course, as Baumol has convincingly argued, most traders do not have access to relatively sophisticated statistical studies and may therefore be unable to detect relationships not immediately apparent to the naked eye. To the extent that this is so, the random walk hypothesis should only approximate reality. Baumol, W. J., Economic Efficiency and the Stock Market (Fordham University Press, 1965)Google Scholar.

⁴ “Short Interest: Bearish or Bullish?,” The Journal of Finance, XXII (March 1967), pp. 67–70Google Scholar. Seneca assumed that aggregate stock prices are linearly related to a short interest variable and aggregate dividends, which is an extremely simple and arbitrary theory of equity prices, through no fault of the author. It is this arbitrariness which appears to be the root cause of the disagreement between Seneca and Mark Hanna. See Hanna's comment and Seneca's reply in the Journal of Finance, XXIII (June 1968)Google Scholar.

Seneca's results, like those presented in this paper, do not confirm the Wall Street hypothesis of a positive short interest effect. But, unlike those presented in this paper, the short interest variable emerges with a significantly negative coefficient. The discrepancy between our findings appears to indicate that the results are heavily dependent upon the specification of the regression equation. To cite only one of the possible specification pitfalls, Seneca defines his short interest variable as the ratio of short interest to the volume of transactions (let us call it the short ratio), which is one of the several ways in which financial analysts express the hypothesis. But this specification may be open to serious bias if the common view of the relationship between prices and volume—that they are positively related after the trend and other factors are accounted for—is indeed true. For if this is the case, a spurious negative correlation is set up between prices and the short ratio, a correlation which has nothing to do with the influence of short trading on equity prices. For example, it would be possible to have a negative relationship between the short ratio and equity prices even though a ceteris paribus change in short interest (leaving volume constant) would have no effect whatever on equity prices. For empirical evidence on the positive relationship between prices and volume, see the excellent study by Ying, Charles C., “Stock Market Prices and Volumes of Sales,” Econometrica, XXXIV (July 1966), pp. 676–685CrossRefGoogle Scholar.

⁵ The absolute short interest level was employed for reasons previously given. It was lagged two weeks because Securities and Exchange Commission data on short sales indicate that the average short position is held only about two weeks. Nevertheless, all models were tested using a number of alternative lags. In every case the particular lag assumption made little difference in the results. Hence for the sake of brevity we can safely confine our analysis to the two-week lag.

⁶ With aggregate data, where P_t is a price index already adjusted for stock splits, the dependent variable is P_t rather than P_td_t.

⁷ A first order scheme yields results which are quite similar to those obtained from a second order scheme, but in most cases the first order results are not completely free of serial correlation. For this reason alone the author prefers the second order model. The conclusions of this paper in no way depend upon this choice.

⁸ Since short interest data are available only once a month, the price variable is the average price in the second week after the short interest is reported.

⁹ Although accurate data do not exist, New York Exchange officials, in private communication to the author, have estimated that approximately 60 percent of the growth in listed shares is due to stock distributions. There is no way of knowing whether this relationship is stable over short periods of time or whether it seems to hold only over relatively long periods of time. If the latter is true, this method of correcting for stock splits is questionable at best, and one would want to place greater reliance on results for individual firms and less on results for aggregates.

¹⁰ Certainly if there is a causal relationship between prices and short interest levels, that relationship should be stronger and more visible when one examines firms, for the short interest position in a given stock should directly influence the price of that stock, at least if the hypothesis holds, and only indirectly influence the prices of other stocks.

¹¹ Typically, short trading activities are concentrated in a relatively small number of stocks. In the early 1960's, for example, some 3% of listed firms accounted for 50% of the total short interest. The fourteen firms used in this study have approximately 10% of the total short interest.

¹² The failure to perform the more general test on sets of estimated parameters can result in the loss of potentially useful information and, what is worse, may cause the acceptance of a false hypothesis or the rejection of a true one. To cite one example, the reader is referred to Almarin Philips'recent study, “Evidence on Concentration in Banking Markets and Interest Rates,” federal Reserve Bulletin, 53 (June 1967), p. 920Google Scholar, where the author concludes, on the basis of 20 regressions for different time periods and different loan sizes, that concentration has no significant effect on interest rates. However, had he performed the more general test outlined above he would have found that the hypothesis of a positive relationship between concentration and interest rates could not be rejected at the usual confidence levels. And his results would have been more in accord with evidence presented in Meyer's, Paul, “Price Discrimination, Regional Loan Rates, and the Structure of the Banking Industry,” Journal of Finance, XXII (March 1967), pp. 49–61Google Scholar.

¹³ A distributed lag approach was also attempted by including a lagged price variable on the right hand side of the regression equation. Here again, the short interest coefficients were insignificant.

¹⁴ As stated above, in this study Monte Carlo techniques have a number of advantages over regression techniques. Most of the thorny econometric problems specification, autocorrelation, and the like—are absent, and the results have more direct economic meaning.

¹⁵ This method seems particularly appropriate when there are large numbers of short traders in a given stock. Standard accounting methods such as LIFO and FIFO do not appear satisfactory.

¹⁶ For aggregate price data, which are already corrected for stock splits, Pt must be replaced by P_td_t-1/d_t, since the above expressions assume that the price variable is uncorrected for stock splits.

¹⁷ If the random rearrangement process chooses the jth short interest level (corrected for splits) for the kth period in the simulation, then the simulated short interest level in period k is given by . The computer program used for the simulation generates consecutive numbers from one through n in random order. These random integers define the value of j corresponding to each k and hence the rearrangement of the adjusted short interest levels.

¹⁸ Simulations were run for a large number of discount rate assumptions, and the results did not appear to be sensitive to the particular discount rate chosen.

¹⁹ The F-ratio for testing the equivalence of the sample variance and the T distribution variance is approximately 1.74, which is less than the ratio required for a significant difference at the 95 percent confidence level, 1.97.

²⁰ Short sales are reportedly used for a wide variety of tax purposes. For example, a trader may wish to secure a profit on one of his ordinary stock holdings but does not wish to incur the tax liability in the current year. In order to accomplish both objectives he may sell short in the current year and cover in the following year with his own shares. As might be expected, the legality of many of these arrangements is questionable.