Skewness, short interest and the efficiency of stock prices

ABSTRACT

We examine the association between return skewness, short interest and the efficiency of stock prices. Since preferences for skewness have been shown to impact asset prices, we examine how skewness relates to market efficiency. We find that stocks with positive skewness are less efficient, which might be explained by investor preferences for positive skewness. Next, we document that short interest reduces both total skewness and idiosyncratic skewness. Finally, while research has shown that short selling can improve the efficiency of markets generally, we show that short interest’s ability to improve market efficiency is strongest in stocks with the highest skewness.

KEYWORDS:

• Skewness
• short interest
• market efficiency
• idiosyncratic skewness

JEL CLASSIFICATION:

• G00
• G10
• G12

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Another important exogenous shock to short-sale constraints occurred during the recent financial crisis. The SEC restricted short selling on all financial stocks in late 2008. However, this ban only occurred over a 14-day period. Therefore, obtaining accurate estimates of higher order moments in the return distribution is troublesome.

² The short interest data are obtained by purchase directly from NASDAQ. Therefore, our time period is constrained based on the availability of this data.

³ We recognize the need to control for the technology bubble which, following Ofek and Richardson (2003) and Battalio and Schultz (2006), occurred from first quarter of 1998 until the first quarter of 2000. In unreported tests, we replicate the entire analysis while including controls for this time period. The conclusions that we draw from these unreported tests are similar to those in this article. So for brevity, we do not report these tests in the current version of the article. Instead, we are sure to control for fixed effects by quarter in all of our multivariate tests.

⁴ Hou and Moskowitz (2005) discuss the use of Wednesday-to-Wednesday returns. In particular, these returns are used to control for autocorrelations that are apparent in Friday-to-Friday returns and Monday-to-Monday returns (see e.g. Chordia and Swaminathan 2000).

⁵ Some stock-quarter observations were excluded because fewer than 40 daily observations were available to calculate skewness.

⁶ We note the possibility of multicollinearity throughout our analysis. As seen in the correlation matrix in Table 1, several of the control variables are highly correlated. These results are consistent with the literature that discusses the positive relationship between volume and returns (see the review in Karpoff 1987) and the large literature that discusses the relation between volatility, volume and returns (see e.g. Chen, Firth, and Rui 2001). We conduct a series of unreported tests, where we estimate various econometric specifications while including subsets of control variables to ensure that the conclusions we draw in this study are robust. We also estimate variance inflation factors in each of our specifications to determine whether multicollinearity influences the size of the SEs. In each case, we find that inflation factors are small indicating that SEs seem to be unaffected by potential collinearity. These unreported tests are available from the authors upon request.

⁷ The results in Tables 1 and 2 produce both univariate and multivariate evidence that stocks with the most skewness are the least efficient. Kumar (2009) and Kumar, Page and Spalt (2011) provide another identification of lottery stocks. They argue that stocks with most idiosyncratic skewness, the most idiosyncratic volatility and the lowest stock prices are most likely to resemble lotteries. Following this definition, we create an indicator variable that equals unity for stocks with idiosyncratic skewness greater than the median, idiosyncratic volatility greater than the median and stocks with prices lower than the median. After replicating the analysis in Tables 1, we find that the correlation between delay and this dummy variable is 0.2366 (p value = 0.000). When we include this indicator variable in Equation (4) (instead of our measures of skewness), we find a coefficient equal to 0.01 (p value = 0.000). These results suggest that our results are robust to an alternative definition for lottery-type stocks.

⁸ Although not discussed in Xu (2007), there is the potential for autocorrelated returns, which is being used as an additional control variable. In a relatively efficient market, quarterly returns are not likely to be serially correlated. However, to further test this possibility, we take the average contemporaneous return (across stocks) and estimate an AR process with Durbin–Watson (DW) statistics to determine the degree of autocorrelation in returns. In the results from these unreported tests, we find that DW statistics are relatively low and that returns are neither positively nor negatively autocorrelated.