Short Selling and the Weekend Effect in Nasdaq Stock Returns

Authors


  • We thank the Nasdaq Stock Market for providing the data. J. J. Angel and M. G. Ferri gratefully acknowledge financial support from the Nasdaq Educational Foundation. We greatly appreciate the assistance of members of Nasdaq's Office of Economic Research—especially Jeffrey W. Smith, and Frank Hatheway. We thank Jeff Harris and participants at the 2006 FMA Conference for valuable comments and suggestions. Also, we benefited from discussions with Timothy McCormick and Amy Edwards of the Office of Economic Analysis at the Securities and Exchange Commission. Finally, we acknowledge the substantial help provided by a reviewer for this journal and Editor Arnie Cowan. The views expressed in this paper, however, are those of the authors and do not necessarily reflect the views of the Nasdaq Stock Market, Inc., the Nasdaq Educational Foundation, or anyone else.

* Corresponding author: School of Management, MS 5F5, George Mason University, Fairfax, VA 22030; Phone: (703) 993-1858; Fax: (703) 993-1870; E-mail: mferri@gmu.edu

Abstract

We examine daily short selling of Nasdaq stocks to explore whether speculative short selling causes a significant portion of the weekend effect in returns. We identify a weekend effect in speculative short selling whereby it constitutes a larger percentage of trading volume on Mondays versus Fridays. We find an opposite effect in dealer short selling, consistent with market makers adding liquidity and stability. Our main finding is that speculative short selling does not explain an economically meaningful portion of the weekend effect in returns, even among the firms most that are most actively shorted. This finding contradicts some prior studies.

1. Introduction

An intriguing phenomenon in financial markets is the weekend effect, which is the term for the fact that Monday's returns often are significantly lower than those of the immediately preceding Friday (French, 1980). Keim and Stambaugh (1984) establish that the phenomenon has been a regular feature of the financial landscape for many years, but they uncover no evidence that it is specific to firm size, and they reject the possibility that it arises from measurement error. Lakonishok and Maberly (1990) attribute some of the Monday–Friday puzzle to the different trading patterns of institutions and individuals. Sias and Starks (1995) establish an association between the weekend effect and institutional ownership. Abraham and Ikenberry (1994) and Chan, Leung and Wang (2004) relate Monday's return to a stock's holdings by institutions and individuals. Damodaran (1989) explores whether a tendency of corporations to release bad news on Friday after the markets close could account for depressed Monday share prices; he reports evidence of only a weak connection. Wang, Li and Erickson (1997) find a Monday effect only in the final weeks of the month.

Chen and Singal (2003) propose that short selling may explain a significant part of the weekend effect. They hypothesize that “the inability to trade over the weekend tends to make many short sellers close their speculative positions at the end of the week and reopen them at the beginning of the following week leading to the weekend effect, where the stock prices rise on Fridays as short sellers cover their positions and fall on Mondays as short sellers re-establish new short positions”[page 2—emphasis added]. They find support for the hypothesis in the positive association between stocks' weekend effects and their monthly levels of short interest, which is the ratio of a stock's number of shorted shares, as reported monthly by the exchange where it is listed and traded, to its number of outstanding shares. One strength of this monthly series of short interest, which Chen and Singal (2003) use as an indicator of the relative level of speculative short selling, is the fact that it has been, historically, the only publicly available data on short selling. A second strength is that it is an actual count of the number of a stock's shares that are in short positions.

The data series does, however, have several weaknesses. First, the number of shorted shares is drawn from just one day in the middle of the month, and there is no guarantee that this day is representative of all days in the month or reflective of patterns in the short selling of Mondays and Fridays. Second, short interest is an undifferentiated aggregation of several categories of shorted shares. It includes shares shorted by, among others, dealers who are engaged in market-making, arbitrageurs active in the options markets, and investors who anticipate price decline or relative underperformance. Only the shares of the last category are likely to reflect the speculative activity that, according to Chen and Singal (2003), might be partly responsible for the weekend effect in returns. Finally, the relative sizes of these categories could change substantially over time, with the undetectable result that a stock's reported short interest could rise sharply in a month even if the speculative component of short interest actually declined.

Because of these considerations, the hypothesis that short selling explains a significant part of the weekend effect deserves further examination when new and different data become available. The purpose of this paper is to conduct that examination with the help of an extensive data set of daily trades, including short sales, for a large number of stocks traded through Nasdaq's National Market System (NMS) between September 2000 and July 2001. This rich and precise data set enables us to do several things Chen and Singal (2003) are unable to do. For example, we can separate daily short selling by Nasdaq dealers from the short sales by their customers. This important distinction allows us to assess the different relationship that the weekend effect may have with customer (largely speculative) short sales versus shorting that primarily represents dealer market-making. In addition, our data set allows us to compute the exact difference in a stock's short selling between actual Mondays and Fridays and thus frees us from having to extrapolate possible changes in an issue's short selling on the basis of its monthly measures of short interest. Other contemporaneous papers examining the linkage between short selling and the weekend effect include Blau, Van Ness and Van Ness (2007), and Gao, Kalcheva and Ma (2007).

We can summarize our findings this way. First, the weekend effect in returns, which Chen and Singal (2003) track up to 1999, persists for Nasdaq stocks through our sample period of 2000–2001. Second, customer short selling displays a weekend effect of its own because customer-shorted shares on average constitute a larger percentage of share volume on Monday than on Friday. (This difference is more pronounced for firms of smaller market capitalization.) However, the raw number of shares shorted by customers tends to be greater on Fridays than on Mondays.

Third, short selling by dealers also exhibits a weekend effect, but it is exactly opposite of the weekend effect in customer short selling, because dealer-shorted shares constitute a lower percentage of trading volume on Monday than on Friday. This result for dealers is consistent with certain implications of Griffin, Harris and Topaloglu (2003) and conforms to the notion that dealers actively bring liquidity and stability to the market by selling short when stock prices are rising. Our evidence of this key difference between short selling by dealers and customers is new to the literature and has important implications for anyone engaged in short-selling research.

Our final conclusion is that speculative short selling by customers does not explain an economically meaningful portion of the observed weekend effect in stock returns. Consequently, the weekend effect in returns persists as an unexplained anomaly.

2. Data and sample

2.1. Structure of records in data set

We draw our data from Nasdaq's Automated Confirmation Transaction Service (ACT), which processed the preponderance of transactions in Nasdaq stocks during our study period of September 13, 2000 to July 10, 2001. The data set includes all processed trades (except odd-lot transactions) in the daily 9:30 am–4:00 pm sessions of all stocks listed on the Nasdaq's NMS. We are unaware of any equally rich and detailed data set dealing with the Nasdaq from this or any other period.1 Also, shortly after 2001, the ECNs (Electronic Communication Systems, such as Archipelago and Island) started reporting their trades through other Self-Regulatory Organizations. As a result, ACT files from later years cannot supply the almost comprehensive record of Nasdaq trading and short selling that our data set provides for the 2000–2001 period.

A specific protocol is followed for reporting a trade to ACT: (1) a market maker in a trade with a nonmarket maker reports the trade; (2) the seller in a trade between two market makers files the report; (3) the NASD member in a trade with a non-NASD member reports the trade; and (4) the seller in a trade between two members is responsible for reporting. As described later, this protocol for trade reporting helps us to separate dealer short selling from customer short selling. This separation is important because our objective is to examine the linkage between speculative (rather than market-making) short selling and the weekend effect in stock returns.

In the ACT record, a short sale is indicated by an entry into either the REPORT_SHORT field, which means the reporting entity has flagged the trade as a short sale, or the CONTRA_SHORT field, which means the counterparty has indicated that the trade was short. In addition, the details in the ACT record of a trade include characteristics, such as the stock's ticker, date, time, number of shares traded, trading price, and whether ACT has passed the record of the trade to the “tape” (the public record). This final item is particularly important for trades conducted through an ECN. Each of the trades generates (at least) two records—because the ECN is technically the counterparty for both the buy and sell sides of the trade—but ACT reports only one to the tape.2 To avoid double-counting, we restrict our sample to only the transaction records that were reported to the tape, whether they were executed through an ECN or on another venue.

To distinguish between customer and dealer short sales, we use Nasdaq's daily file of quotations to identify who, during each day, was serving as a market maker in a stock by actively posting bid and ask quotes. With this information, and the trade reporting protocol described earlier, each day's short sales in a stock are broken into two major categories: dealer short selling and customer short selling. Dealer short selling consists of the short selling by NASD members who were functioning as market makers on the day.3 During the time of our sample, NASD rules required market makers to identify all their short sales.4 Market maker compliance with the rules is indicated by the substantial amount of short selling listed in the REPORT_SHORT field of the ACT files. The second category, customer short selling, contains all short sales that, according to the trade reporting rules and trade records, were not made by dealers acting as market makers on the day of the trade.

Within each category of short selling (by dealers and by customers), there is an additional distinction, based on whether the sale was designated as exempt from the Nasdaq Short Sale Rule.5 Regarding customers, Nasdaq allowed the exempt designation for short sales related to certain nonspeculative activities including hedge transactions by qualified options market makers, arbitrage of differences in a stock's price on United States versus foreign stock markets, convertible bond arbitrage, and the hedging of deliveries due in a few days. In these cases, the field CONTRA_SHORT in the ACT record would contain an “X” rather than an “S.”

For dealers, the designation of exempt was designed for short sales executed as part of bona fide market-making at the prevailing inside bid following a down tick. When reporting their trades, dealers were required to specifically distinguish between short and short-exempt transactions, as the instructions from pages 3–4 of Chapter 9 in the Nasdaq Trader Manual (revised 2000) show:

Under revisions to NASD Rule 6130(d)(6) implemented in 1997, Market-makers that are exempt from the rule now must mark their ACT reports to denote when they have relied on a short-sale rule exemption, and thus must denote all short sales—both exempt and nonexempt—as short sales. Accordingly, if you effect a nonexempt short sale (e.g., a short sale during an up bid or a short sale at least 1/16 above a point on a down bid, assuming a spread of 1/16), you must mark your ACT report as a short sale. If you effect a short sale in reliance on an exemption to the rule, you must mark your ACT report as an exempt short sale.

An exempt trade by a market maker would be signified by an “X” in the REPORT_SHORT field; if the dealer did not need to claim the exemption for the short sale (i.e., it did not violate the bid-test) the field would contain an “S.” The reporting of both nonexempt (the majority of dealer trade reports) and exempt (the minority) short sales by active dealers makes our data set quite different from the 2005 SHO-based data discussed by Diether, Lee and Werner (2008), who state that all dealer short trades in their sample are designated in the record as exempt short sales.

We are confident that a consistent review of the report fields, guided by the reporting rules and the quotations file, can accurately fit the sample's large set of daily short sales into a 2-by-2 matrix, for customers versus dealers, and for nonexempt versus exempt. For convenience in exposition, we apply the following labels to the sales (and their shares) in these classes: “customer-shorted,”“customer-shorted exempt,”“dealer-shorted,” and “dealer-shorted exempt.”

Customer-shorted shares were very likely sold in speculative trades by sellers who anticipated subsequent share price decline or relative underperformance. Therefore, they represent the speculative component of overall short selling that Chen and Singal (2003) suggest may be linked to the weekend effect in stock returns. Customer-shorted shares represent speculative trades because any seller engaged in some nonspeculative type of short selling who could have claimed exemption from the Nasdaq Short Sale Rule (i.e., have the right to trade “short exempt”) would likely have done so. The exemption would have allowed the sale to go forward when shorting would otherwise have been prohibited by the bid-test rule.6

The majority of the dealer-shorted (nonexempt) trades, which is our largest category in both number of trades and of shares, were probably market-making moves (or, less likely for our sample period, brokering moves). It is possible, however, that some of a dealer's short nonexempt trades represented proprietary investing for either the dealer's desk or some other unit within the firm. Though we are not able to identify these trades directly, we can test whether a stock's total of dealer-shorted nonexempt shares tended to have a consistently substantial number of speculatively shorted shares. The details of the testing are in the Appendix; they lead us to conclude that dealer-shorted shares in our sample primarily resulted from market-making.

For most of our analysis, we normalize each category of a stock's shorted shares on a day by dividing the shares by the stock's trading volume on that day. Asquith, Pathak and Ritter (2005, p. 249) argue that the question being addressed determines whether shorted shares should be normalized by outstanding shares or by total shares traded. The central question of our paper is whether weekend short selling has a link to weekend share price movements. Thus, the question revolves around the establishment of prices by the interplay of buyers and sellers. The importance of short selling to that interplay is best reflected by the percentage of trading volume that customer- or dealer-shorted shares account for. Boehmer, Jones and Zhang (2005) and Diether, Lee and Werner (2008) also take this approach.

2.2. Formation of sample

The stocks we analyze are drawn from an initial sample of all the companies (over 3,000) listed on the Nasdaq and covered by ACT between September 13, 2000 and July 10, 2001. To minimize the potential for drawing improper inferences from thinly traded stocks, we delete any stock that (a) does not trade every day and (b) has average daily volume of fewer than 50 trades in the sample period. These criteria reduce the sample to 1,314 stocks. During this period, the value of numerous Nasdaq stocks changed dramatically, and the Nasdaq value-weighted index fell by approximately 45%. By contrast, the Nasdaq equally-weighted index during the period was almost unchanged. The movement of this latter index suggests that, because our tests do not weight returns by firm size, the sample period does not bias weekend returns in a negative direction. (Nonetheless, to verify that our findings are not an artifact of a generally declining market, we also conduct some tests for separate sub-samples of our time period.) CRSP is the source for all data on returns of stocks and the indexes.

We define the week as Wednesday to the following Tuesday. For example, the first sample week runs from Wednesday, September 13, through Tuesday, September 19. Further, we consider only weeks in which the Nasdaq was open for each of the five trading days (Wednesday, Thursday, Friday, Monday and Tuesday). As a result, the final sample consists of 35 five-day trading weeks for the 1,314 stocks.7

We conduct tests on this full sample, as well as on two subsamples of stocks that were subjected to frequently high amounts of speculative short selling during the sample period. The two subsamples are the upper half and the top quartile of the 1,314 stocks, as ranked by the median of each stock's daily ratio of customer-shorted shares to outstanding shares within the sample period. In forming these subsamples, we normalize short selling by outstanding shares because we are trying to gauge a stock's general tendency and availability to be the subject of short selling over the entire sample period. Testing with these subsamples is important because some of the 1,314 stocks experience very little short selling during the sample interval. A careful evaluation of the Chen and Singal hypothesis must include a direct exploration of the sub-samples of stocks that are often subjected to substantial speculative shorting.

Table 1 presents, for each day of the week, the sample's mean and median of return, trading volume, shorted shares in each of the four categories of short selling (customer-shorted, dealer-shorted, etc.), and the number of shorted shares normalized by trading volume. Panel A of Table 1 presents descriptive statistics for the entire sample of 45,990 observations (or 1,314 stocks over 35 weeks); Panel B pertains to the 22,995 observations on the 657 stocks in the upper half of the sample (657 stocks across 35 weeks); Panel C presents statistics for 11,515 observations, or the top quartile of stocks (329 over 35 weeks).

Table 1. 
Day-of-the-week values for returns, trading volume, and short selling by customers and dealers: Nasdaq stocks from September 13, 2000 to July 10, 2001
The cells labeled M, T, etc., contain the means and medians of daily percentage stock returns, trading volume, and measures of short selling for different days of the week. Return (%) is percentage stock return. Customer-shorted shares are shares sold short by speculators. Dealer-shorted shares are shares sold short by dealers acting as market makers in the stock. Dealer-shorted exempt shares are shares sold short by dealers acting as market makers in the stock, where the sale was executed at the prevailing “inside” bid following a down tick. Panel A has 45,990 observations for the full sample of stocks, or 35 five-day weeks × 1,314 stocks. Panels B and C have observations for the 657 and 329 stocks that are in the upper half, and top quartile of sample stocks, respectively, based upon each stocks median value during the sample period for daily shares sold short by customers normalized by outstanding shares.
 MTWThF
Panel A: Full sample (n = 45,990)
Return (%)−0.6510.358−0.3950.034−0.054
−0.5740.000−0.544−0.182−0.400
Volume (000s of shares)1,1121,2191,3601,3081,286
224236248241239
Customer-shorted shares40,90744,22448,90747,90544,169
2,7392,6002,9002,7002,700
Customer-shorted shares as % of volume3.153.023.023.013.01
1.241.141.171.131.14
Dealer-shorted shares217,598240,888265,505256,807257,191
45,05448,50050,54148,85149,475
Dealer-shorted shares as % of volume21.1521.4021.2321.1821.66
20.4520.6720.5420.3820.88
Customer-shorted exempt shares94810701,3051,3211,938
00000
Customer-shorted exempt shares as % of volume0.060.050.060.050.15
0.000.000.000.000.00
Dealer-shorted exempt shares25,15627,49630,36429,25131,754
2,8583,0003,2003,1003,125
Dealer-shorted exempt shares as % of volume2.232.262.232.212.45
1.211.191.201.181.24
Panel B: Stocks in the upper half of the sample, by median ratio of shares shorted by customers to outstanding shares (n = 22,995)
Return (%)−0.6920.468−0.2390.135−0.097
−0.6500.197−0.532−0.222−0.498
Volume (000s of shares)1,9832,1772,4462,3482,303
449477508500489
Customer-shorted shares77,84684,17793,35391,49383,889
12,30012,44113,30012,70012,615
Customer-shorted shares as % of volume4.484.314.294.324.33
2.72.552.582.532.52
Dealer-shorted shares383,372425,887472,831456,142455,496
93,710100,980105,951103,301102,294
Dealer-shorted shares as % of volume20.9521.1621.0520.9921.35
20.3220.5020.4620.2520.63
Customer-shorted exempt shares1,7912,0632,4842,5463,529
00000
Customer-shorted exempt shares as % of volume0.080.070.080.070.14
0.000.000.000.000.00
Dealer-shorted exempt shares43,28247,23752,91650,86754,448
5,7006,0006,7006,3006,388
Dealer-shorted exempt shares as % of volume1.971.961.971.932.13
1.251.221.251.231.27
Panel C: Stocks in the top quartile of the sample, by median ratio of shares shorted by customers to outstanding shares (n = 11,515)
Return (%)−0.7400.568−0.1940.097−0.181
−0.8110.255−0.589−0.354−0.548
Volume (000s of shares)2,8873,1993,6043,4343,312
842908988960915
Customer-shorted shares126,843137,606152,974149,050136,739
33,10034,21738,31036,70035,684
Customer-shorted shares as % of volume5.365.195.175.245.23
3.713.583.633.633.54
Dealer-shorted shares547,468613,259682,613655,341642,024
174,410186,963203,773194,011193,598
Dealer-shorted shares as % of volume20.5020.6920.5520.4520.83
19.8920.0919.9919.7520.19
Customer-shorted exempt shares2,4262,8293,5253,5454,653
00000
Customer-shorted exempt shares as % of volume0.090.080.100.090.14
0.000.000.000.000.00
Dealer-shorted exempt shares61,12467,88676,47772,57675,283
11,80012,80013,80012,80013,290
Dealer-shorted exempt shares as % of volume1.901.901.861.862.01
1.341.331.321.321.35

Though we report and discuss our statistical tests later, some features of Table 1 deserve special notice. First, in all panels, mean and median returns are lower on Monday than on any other weekday, including Friday. Thus, our data set appears to be consistent with that of Chen and Singal (2003), who uncover the traditional weekend effect in Nasdaq returns as late as 1999. Second, volume results recall Lakonishok and Maberly (1990), in that Monday's total shares traded is lower than that of any other day, in all three panels.

A third feature common to all panels in Table 1 is that the customer-shorted shares present a very complex weekend effect. For example, Monday's customer-shorted shares are on-average fewer than those of Friday's. This finding is exactly opposite what is expected generally if the weekend effect is due (at least partially) to speculative short-selling activity where a speculator closes a short position on Friday and then reestablishes a short position consisting of the same number of shares on Monday. In contrast, customer-shorted shares as a percent of trading volume is higher on Mondays than on any other day of the week, which might be consistent with a linkage between speculative short selling and the weekend effect. These seemingly contradictory results arise because trading volume on Mondays tends to be so much lower than trading volume on other days of the week that customer shorting as a percentage of volume ends up being the highest on Mondays.

Fourth, the number of dealer-shorted shares and their percentage of volume are large, and both measures are lower on Mondays than on other days. Fifth, while the customer-shorted exempt category is very small, the dealer-shorted exempt shares amount to more than one-tenth of the number of dealers' nonexempt shares. Finally, for the full sample (Panel A), the percentage of trading volume attributable to the combined four categories of short selling (customer, dealer, customer exempt, and dealer exempt) is approximately 25% on each day of the week. This is similar to the percentage of overall shorting to volume reported by Diether, Lee and Werner (2008) in their analysis of SHO data from early 2005.

3. Tests and results

3.1. Weekend effects in returns

To explore whether returns exhibit the weekend effect, it is not sufficient to compare average returns on Mondays to average returns on Fridays. Instead, it is necessary to compute the difference between each stock's return on Monday and its return on the preceding Friday. Table 2 reports the mean and median of the difference over the 35 weeks for the entire sample of stocks (Panel A), stocks with above-median ratios of shares shorted to outstanding shares (Panel B), and stocks in the top quartile by the same ratio (Panel C). In every panel, the mean and median value for Return (%) is negative, and the corresponding t-test (of the mean) and sign test (of the median) reject the hypothesis of no difference between the Monday and the preceding Friday returns. In sum, these results strongly indicate the presence of a weekend effect in returns for our sample of Nasdaq stocks.

Table 2. 
Weekend effects in returns and short selling by customers and dealers: Nasdaq stocks from September 13, 2000 to July 10, 2001
Each variable is computed as Monday's value minus the previous Friday's value. Return (%) is percentage stock return. Customer-shorted shares as % of volume are shares sold short by speculators, normalized by daily share volume. Dealer-shorted shares as % of volume are shares sold short by dealers acting as market makers in the stock, normalized by daily share volume. Total dealer-shorted shares as % of volume are dealer-shorted shares plus dealer-shorted exempt shares (cases where the sale was executed at the prevailing “inside” bid following a down tick), normalized by daily share volume. A cell contains a mean with the p-value in parentheses corresponding to t-statistic or a median with the p-value in parentheses from a sign test. Panel A has 45,990 observations for the full sample of stocks, or 35 five-day weeks × 1,314 stocks. Panels B and C have observations for the 657 and 329 stocks that are in the upper half, and top quartile of sample stocks, respectively, based upon each stocks median value during the sample period for daily shares sold short by customers normalized by outstanding shares.
 MeanMedian
Panel A: Full sample (n = 45,990)
Return (%)−0.597−0.277
(0.000)(0.000)
Customer-shorted shares as % of volume0.1330.000
(0.000)(0.000)
Dealer-shorted shares as % of volume−0.505−0.412
(0.000)(0.000)
Total dealer-shorted shares as % of volume−0.728−0.537
(0.000)(0.000)
Panel B: Stocks in the upper half of the sample, by median ratio of shares shorted by customers to outstanding shares (n = 22,995)
Return (%)−0.595−0.313
(0.000)(0.000)
Customer-shorted shares as % of volume0.1560.048
(0.000)(0.000)
Dealer-shorted shares as % of volume−0.393−0.325
(0.000)(0.000)
Total dealer-shorted shares as % of volume−0.553−0.420
(0.000)(0.000)
Panel C: Stocks in the top quartile of the sample, by median ratio of shares shorted by customers to outstanding shares (n = 11,515)
Return (%)−0.560−0.384
(0.000)(0.000)
Customer-shorted shares as % of volume0.1270.073
(0.016)(0.002)
Dealer-shorted shares as % of volume−0.325−0.325
(0.000)(0.000)
Total dealer-shorted shares as % of volume−0.442−0.411
(0.000)(0.000)

3.2. Weekend effects in short selling

The second row of each panel in Table 2 reports the values for the mean and median of the difference between each stock's (speculative) customer-shorted shares as a percentage of trading volume on Monday versus the preceding Friday. These numbers reveal a weekend effect in short selling, as customer-shorted shares constitute a higher percentage of Monday's trading volume than of Friday's in the full sample and the two subsamples. Every mean is positive and statistically significant with low p-values; two of the medians are positive and also significant. The median in Panel A requires some explanation: The reported value is zero yet the corresponding p-value is low and indicates that the population median is different from zero. The reason for this result is twofold: (1) 5,561 of the total of 45,990 observations had zero values, because some stocks in the full sample did not experience any short selling before and after some weekends; (2) but 20,761 observations were positive, while 19,578 were negative. Because positive values outnumber negatives by 1,200, the sign test supports rejecting the hypothesis of a zero population median. A complementary point is that, among stocks with some regular speculative short selling (Panels B and C), Monday's value of customer shorted to total traded shares is above Friday's in the majority of observations.

The third and fourth rows of Table 2 present tests for a weekend effect in (a) dealer-shorted shares as a percentage of volume and (b) total dealer-shorted shares (equal to dealer-shorted nonexempt shares plus dealer-shorted exempt shares) as a percentage of volume. Both percentages exhibit a weekend pattern as both are substantially and significantly higher on Friday than on Monday. Therefore, both categories of short selling appear to be positively linked to volume, because on Fridays, when volume tends to be higher than on Mondays, total dealer-shorted exempt and nonexempt shares tend to be more common. Additionally, both categories of shorted shares move in the opposite direction from customer-shorted shares and they clearly represent, as we have stated, trading of a different type and motivation. For this reason, our separation of customer from dealer short selling and the determination of their individual relationships to the weekend effect provide insights that cannot be obtained from other more highly aggregated data.

3.3. Tests of the linkage between weekend effects in returns and in short selling

We next investigate through ordinary least squares (OLS) and panel regressions whether the Monday–Friday pattern in returns is associated with weekend effects in the types of short selling. The regressions take the form:

image(1)

where (M–F) designates the Monday less the preceding Friday value, R refers to daily return, CustSSVol is the customer-shorted shares as a percentage of trading volume, TDeaSSVol is the total dealer-shorted shares (the sum of dealer exempt and nonexempt shorted shares) as a percentage of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. (Both daily return and the measures of short selling are given in percentage, not decimal, form.)

If, as Chen and Singal (2003) argue, speculative short selling is at least partly responsible for the stock return weekend effect, returns should move in the opposite direction of speculative short selling's portion of trading volume. We should therefore expect to find a significantly negative parameter estimate for CustSSVol(M–F), and the variation in weekend stock returns should be meaningfully explained by the variation in weekend short selling. This hypothesized link between short selling and returns is consistent with short selling bringing about a shift in the supply curve for shares, which does not necessarily cause or accompany an offsetting shift in demand. Thus, short sales at any time, with all else being equal, should (a) prevent a stock's price from rising much above its current level or (b) force the price down from its current level. Several papers that focus on longer horizons provide evidence that at least indirectly supports this view. Asquith, Pathak and Ritter (2005) report that abnormal monthly returns are negatively related to their previous month's short interest.8D'Avolio (2002), Geczy, Musto and Reed (2002), and Jones and Lamont (2002) find that costly-to-short shares post low average returns over time. Similarly, Boehme, Danielsen and Sorescu (2006) show overvaluation is likely in stocks that are difficult to short and are the subjects of widely dispersed opinions.

Equation (1) incorporates the variable TDeaSSVol(M–F), which represents all dealer short selling, rather than a variable based on only dealer-shorted nonexempt shares because exempt sales differ from nonexempt only in terms of the location of the bid price. When we run regressions with only dealer-shorted nonexempt shares in place of TDeaSSVol(M–F), the results (available on request) are quantitatively very similar to those presented here. That is not surprising since, as Table 2 shows, dealer-shorted exempt is a small part of total dealer short selling.

We expect to find a positive value for the coefficient of TDeaSSVol(M–F) if dealers' short selling is fundamentally transactional and related to market-making. Such behavior provides liquidity and does not have the dampening impact on price that nonexempt short selling by customers would have. This argument draws support from Griffin, Harris and Topaloglu (2003). Analyzing Nasdaq trades from May 2000 to February 2001 (an interval that is quite close to our September 2000–July 2001 sample period), they find that increases in a stock's price prompt institutions to surprisingly quick purchases of shares but individuals to equally quick sales. If (plausibly) institutions transact in larger trade sizes, institutional volume will be greater, and will create an imbalance in demand and supply. Dealers accommodating this imbalance as part of market-making activity would need to use a substantial number of shorted shares to provide liquidity and stability to the market. This shift in the supply curve of shorted shares therefore meets an unanticipated upward shift in demand, with the result that a stock's ratio of dealer-shorted shares to trading volume will be relatively high on days of rising prices and low when prices fall.9 Because many stocks post a higher return on Friday than on Monday, Friday's ratio of dealer-shorted shares to trading volume should be higher than Monday's, which is consistent with the summary statistics in Table 2. Therefore, we would expect that our regression of the weekend difference in return on the weekend difference in dealer-shorted shares to trading volume to produce a positive coefficient.

Before turning to the results, we want to explain why short selling by either customers or dealers is not an endogenous variable (i.e., influenced by the dependent variable of return) and why our regression equation is correctly specified. We recognize that some short sales occur in quick response during the trading day to upward as well as downward changes in prices. However, that fact regarding intra-day short selling does not undermine our regressions, which analyze aggregated daily data and not individual trades within a day. All our recorded short selling and other transactions in a stock take place during the 9:30 am–4:00 pm session, while the stock's daily return reflects the price in the day's last Nasdaq print and the previous day's last print. Therefore, the values of the variables for volume and shorted shares are “fixed” in the classic econometric sense: they are predetermined and hence independent of the value of daily return (Greene, 1993, p. 581). The only way that the price of a stock's last print could be contemporaneous with the day's short selling or volume is if all that short selling and all that volume were to take place in the day's last recorded trade. None of the 45,990 observations in our sample is a day with only a single trade.

Table 3 reports the results of regressions with OLS and techniques based on one-way fixed-effects (for time, which is the weekend) and two-way fixed-effects (for time and the individual firm). In each of Table 3's panels, the first column for each technique is devoted to a regression where the only independent variable is customer-shorted shares, and the second column includes both customer-shorted shares and dealer-shorted shares as independent variables. (In the fixed-effects regressions, the fixed-effect parameter estimates are not reported.)

Table 3. 
OLS and panel regressions of weekend returns on weekend short selling by customers and dealers: Nasdaq stocks from September 13, 2000 to July 10, 2001
The regression equation is R(M−F)it01 CustSSVol(M−F)it2 TDeaSSVol(M−F)it+eit, where (M–F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. OLS, one-way (time) fixed-effects, and two-way (time and firm) fixed-effects regressions. Panel A has 45,990 observations for the full sample of stocks, or 35 five-day weeks × 1,314 stocks. Panels B and C have observations for the 657 and 329 stocks that are in the upper half, and top quartile of sample stocks, respectively, based upon each stocks median value during the sample period for daily shares sold short by customers normalized by outstanding shares. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Standard errors are in parentheses.
 OLS One-way fixed-effect Two-way fixed-effect 
  1. ***, **, * indicate statistical significance at the 0.01, 0.05 and 0.10 level, respectively.

Panel A: Full sample (n = 45,990)
β0−0.590***−0.554***NANANANA
(0.046)(0.046)    
CustSSVol(M–F)−0.049***−0.042***−0.031***−0.029***−0.035***−0.031***
(0.009)(0.009)(0.008)(0.008)(0.008)(0.008)
TDeaSSVol(M–F) 0.051*** 0.041*** 0.041***
 (0.004) (0.003) (0.003)
R20.0010.0050.1130.1160.1440.150
Panel B: Stocks in the upper half of sample, by median ratio of shares shorted by customers to outstanding shares (n = 22,995)
β0−0.586***−0.554***NANANANA
(0.059)(0.059)    
CustSSVol(M–F)−0.057***−0.050***−0.030**−0.025***−0.033***−0.028***
(0.010)(0.010)(0.009)(0.009)(0.010)(0.010)
TDeaSSVol(M–F) 0.060*** 0.045*** 0.045***
 (0.006) (0.005) (0.005)
R20.0010.0060.1790.1820.2070.210
Panel C: Stocks in the top quartile of the sample, by median ratio of shares shorted by customers to outstanding shares (n = 11,515)
β0−0.550***−0.519***NANANANA
(0.084)(0.084)    
CustSSVol(M–F)−0.078***−0.069***−0.025*−0.018−0.026**−0.020
(0.015)(0.015)(0.013)(0.013)(0.013)(0.013)
TDeaSSVol(M–F) 0.073** 0.058*** 0.057***
 (0.006) (0.013) (0.008)
R20.0020.0080.2180.2220.2490.252

Several aspects of these estimates merit attention. One is that, although the coefficients for CustSSVol(M–F) are negative in every case and statistically significant in 16 of the 18 regressions, there are two factors that argue against concluding that speculative short selling has a meaningful link to the weekend effect in stock returns. First, the coefficient estimates obtained from the regressions are rather small. Across all 18 regression estimations, the maximum parameter estimate (in absolute value) is only 0.078 (see Panel C, OLS regression results which are for the sub-sample of stocks in the top quartile based upon median ratio of shares shorted to customers to outstanding shares). That coefficient implies that a firm with a 0.127 value for CustSSVol(M–F) would have an associated weekend effect in returns of only −0.010%. (We use 0.127 in this illustration because it represents the mean value of CustSSVol(M–F) for the stocks in that sub-sample—see Table 2, Panel C.) Therefore, despite the statistical significance of many of the coefficients for CustSSVol(M–F), the implied economic connection between the two weekend effects (speculative short selling and returns) seems slight.

The second, and more important, factor is that our sample size is quite large (a maximum of 45,990 observations in the full sample estimations) and that increases the likelihood of rejecting the null hypothesis of no relationship, even when the null is true (Lindley, 1957). Therefore, it is appropriate to examine the amount of variation in the dependent variable that is explained by variation in the independent variable(s). For example, the R2 in each of the OLS regression is quite low (less than 1%). And, though the R2 for the panel regressions is higher at 20%–25%, the bulk of that increase is clearly due to the inclusion of the time (weekend) variable, because the two-way fixed-effects (both time and the firm) regressions have little additional explanatory power. These results indicate that much of the weekend effect in a stock's returns is systematic, or reflective of market-wide phenomena, and not closely related to customer short selling.

Indeed, to further investigate the linkage between speculative (customer) short selling and the weekend effect in returns, we examine the R2 from estimating the three one-way fixed-effects specifications while only including TDeaSSVol(M–F). In each of these estimations, the R2is equivalent to the R2 shown in each panel of Table 3 (0.116, 0.182, and 0.222 in Panels A, B, and C, respectively). Therefore, during the time period we examine, the inclusion of customer short selling as an independent variable in our estimations adds no additional explanatory power for understanding the variation in weekend stock returns. In sum, the results do not support the Chen and Singal (2003) hypothesis that short selling by speculators can explain a meaningful portion of the observed weekend effect in stock returns.

A final aspect of the estimations that merit attention is the set of parameter estimates associated with dealer short selling (TDeaSSVol(M–F)). In each of the nine specifications that include this variable, it is statistically significant and positive. The positive sign, which reflects the dealer's use of shorted shares in market-making, shows that dealer short selling has the opposite link to weekend returns from that of customer shorting, which posts only negative coefficients in the regressions. Other researchers should be cognizant of this finding: nonexempt short selling is clearly not a homogenous category. As illustrated by these results, there are distinct differences between customer and dealer shorting activities.

3.4. Check for robustness: Subsamples based on firm size

To determine whether our inability to find an economically meaningful link between the weekend effects in returns and speculative short selling is due to sample aggregation issues, we repeat the full array of tests on three subsamples based on firm size, as measured by median market capitalization during the sample period. Our large-cap subsample consists of the 357 firms with median market capitalization above $1 billion; the medium-cap subsample consists of the 244 with median market capitalization between $500 million and $1 billion; and the small-cap subsample consists of the 713 firms with median market capitalization below $500 million. This partitioning conforms to the spirit of Chen and Singal (2003) who control for market capitalization by sorting stocks into size deciles. Further, it recognizes a key feature of the market for equity lending: D'Avolio (2002) shows that shares of the large firms are more readily available (or cheaper or both) for borrowing by short sellers, because institutional investors, who make shares available for lending, are more likely to hold the stocks of large firms than of small firms.

Table 4 contains the descriptive statistics and estimation results for only the small-cap subsample of stocks. (The complete set of statistics and results for the mid- and large-cap subsamples are available from the authors.) The descriptive statistics in Panel A show that the mean and median weekend effect in returns for small-cap stocks is quite pronounced (−0.701% and −0.378%, respectively). Though not reported in the table, generally similar results obtain for the mid-cap subsample (−0.703% and −0.209%, respectively), whereas the effect is less pronounced for large-cap stocks (−0.316% and −0.142%, respectively). The panel also records that the percentage of volume attributable to customer-shorted shares is, on average, larger on Monday than on the preceding Friday. By contrast, the percentages of volume for both dealer-shorted (nonexempt) shares and total dealer-shorted shares are higher on Friday than on Monday.

Table 4. 
Univariate statistics and regression results for Nasdaq stocks with median market capitalization below $500 million: September 13, 2000 to July 10, 2001
Panel A contains weekend Returns and Short selling by customers and dealers for 713 small-cap sample stocks. Each variable is computed as Monday's value minus the previous Friday's value. Return (%) is percentage stock return. Customer-shorted shares as % of volume are shares sold short by speculators, normalized by daily share volume. Dealer-shorted shares as % of volume are shares sold short by dealers acting as market makers in the stock, normalized by daily share volume. Total dealer-shorted shares as % of volume are dealer-shorted shares plus dealer-shorted exempt shares (cases where the sale was executed at the prevailing “inside” bid following a down tick), normalized by daily share volume. A cell contains a mean with the p-value in parentheses corresponding to t-statistic or a median with the p-value in parentheses from a sign test. Panel B contains results from OLS, one-way (time) fixed-effects, and two-way (time and firm) fixed-effects regressions for this equation: R(M–F)it01 CustSSVol(M–F)it2 TDeaSSVol(M–F)it+ eit. Here, (M–F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Standard errors are in parentheses.
Panel A: Descriptive statistics (n = 24,955)
Return (%)−0.701−0.378
(0.000)(0.000)
Customer-shorted shares as % of volume0.1720.000
(0.000)(0.000)
Dealer-shorted shares as % of volume−0.494−0.466
(0.000)(0.000)
Total dealer-shorted shares as % of volume−0.752−0.578
(0.000)(0.000)
Panel B: Regression results (n = 24,955)
 OLS One-way fixed-effect Two-way fixed-effect 
  1. *** indicates statistical significance at the 0.01 level.

β0−0.693***−0.653***NANANANA
(0.069)(0.069)    
CustSSVol(M–F)−0.048***−0.040***−0.041***−0.035***−0.043***−0.037***
(0.013)(0.013)(0.013)(0.013)(0.013)(0.013)
TDeaSSVol(M–F) 0.055*** 0.046*** 0.044***
 (0.005) (0.005) (0.005)
R20.0010.0060.0850.0880.1170.120

Panel B presents results from estimating Equation (1) for the subsample. The coefficient estimates reported in the table are mostly similar in size and sign to those of earlier tests. The OLS R2 values are again low and show that, even for small-cap firms, the weekend effects in both types of short selling have only a very limited association with the weekend effect in returns. As before in Table 3, the inclusion of the dummy variables for the weekends (the one-way fixed-effects regression) creates the most substantial improvement in explanatory power, and this is a further indication that the weekend effect in returns is market-wide, rather than a phenomenon induced by speculative short selling. We also examine the R2 that results from estimating the one-way fixed-effects specification while only including TDeaSSVol(M–F) (i.e., not including CustSSVol(M–F)) and find that it was equivalent to the R2 shown (0.088) in the panel of Table 4. Consequently, the inclusion or exclusion of speculative short selling in the model has no impact on the specification's ability to explain the variation in the weekend effect in stock returns.10

3.5. Arbitrage strategies and nonexempt customer short selling

Asquith, Pathak and Ritter (2005) point out that much of the arbitrage-related short selling involves either convertible bonds or efforts at mergers and acquisition. Convertible bond arbitrage consists of buying the (inefficiently priced) convertible bonds of a company while simultaneously shorting the underlying stock. Subject to certain conditions, such as the establishment of an arbitrage account with a broker-dealer, NASD rules exempt short selling related to this arbitrage from the bid-test (see NASD Notice to Members 94–68.) However, some arbitrageurs may be reluctant to utilize the exemption because of aggravations associated with (i) setting up the accounts or (ii) facing potential future audit of the legitimacy of the claim. Therefore, some portion of the customer short sales that could have qualified as “exempt” might be recorded in our database as “nonexempt” short selling, which we treat as largely “speculative.” Of course, since this activity involves a full hedge, it is not at all speculative, and there is therefore no reason to expect the investor would close the short position on Friday (and to reopen it on Monday) in order to guard against the potential disclosure of unfavorable information over the weekend.

If some sales that could have been exempt are labeled as nonexempt, then that misclassification could introduce noise into our tests of the relationship between speculative short selling and the weekend effect in returns. We do not, however, anticipate that the impact of this potential mis-categorization on our findings is substantial. One reason is that, once the arbitrage strategy is in place, the short position would be held until the realignment of prices or conversion of the bond. Further, the short sales which would initiate such hedged position could take place on any day of the week, and we have no reason to think that more of them would occur on Monday or Friday than on other weekdays.

Nonetheless, to investigate whether cases of this arbitrage strategy might be affecting our test results and conclusions, we delete the 255 sampled firms that reported convertible debt on a balance sheet at any year-end between 1999 and 2001 and re-estimate Equation (1). Table 5 contains the results of this re-estimation with the remaining 1,059 stocks. The results are quite similar to what we present in Table 3: the estimated coefficients for CustSSVol(M–F) are rather small, and the R2 values are generally quite low. The greatest improvement in R2 across the different specifications once again comes from the inclusion of the weekend dummy variable in the one-way fixed-effects regressions. In addition, although not reported in Table 5, we conduct similar estimations using the stocks in the upper half, and quartile, of the sample (based upon the median ratio of shares shorted by customers to outstanding shares). These results are similar to the findings in Table 3, Panels B and C.

Table 5. 
OLS and panel regressions of weekend returns on weekend short selling by customers and dealers: Nasdaq stocks from September 13, 2000 to July 10, 2001. Sample excludes firm with convertible debt outstanding in 1999, 2000, or 2001
The regression equation is R(M−F)it01 CustSSVol(M−F)it2 TDeaSSVol(M−F)it+ eit, where (M−F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. OLS, one-way (time) fixed-effects, and two-way (time and firm) fixed-effects regressions. The number of observations is 37,065, or 35 five-day weeks × 1,059 stocks. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Standard errors are in parentheses.
 OLS One-way fixed-effect Two-way fixed-effect 
  1. *** indicates statistical significance at the 0.01 level.

β0−0.578***−0.542***NANANANA
(0.050)(0.050)    
CustSSVol(M−F)−0.049***−0.044***−0.038***−0.033***−0.039***−0.035***
(0.010)(0.010)(0.009)(0.009)(0.009)(0.009)
TDeaSSVol(M−F) 0.051*** 0.041*** 0.041***
 (0.004) (0.004) (0.004)
R20.0010.0060.1090.1120.1390.142

We conduct a similar investigation into the potential impact of merger-based arbitrage on our test results and conclusions. According to Securities Data Company, 80 of the 1,314 sampled stocks announced efforts at mergers or acquisitions during our sample period. The results from estimating Equation (1) with data that do not include the observations of these 80 firms are also very similar to the results reported already in this study. (We do not report the details here, but the results are available from the authors.) In sum, we conclude that the lack of evidence of an economically meaningful linkage between speculative short selling and the weekend effect in stock returns is not due to the potential inclusion in our measure of speculative short selling of short sales motivated by arbitrage involving either convertible bonds or mergers.

3.6. Partitioning the sample period into sub-periods

During our September 13, 2000 to July 10, 2001 sample period, the starting and ending values of the Nasdaq equally-weighted index are essentially equal. In contrast, over the same period the Nasdaq value-weighted index declined. We have argued that, because our tests do not weight returns by firm size, the fact that the value-weighted index was generally in decline does not introduce bias into our tests and results. It must be noted, however, that since the equally-weighted Nasdaq index contains all Nasdaq stocks while our sample selection criterion limits our analysis to only those with 50 or more trades on average during each sample month, we may actually be eliminating from our sample many small firms with high idiosyncratic risk. Those firms are likely to have contributed substantially to the flatness that characterized the equally-weighted index at the start and end of our sample period.

Therefore, to verify that our findings are not an artifact of a generally declining market, we examine three sub-periods of our sample period. The first sub-period contains the first 12 (out of 35) sample weekends. The mean (median) return for our full sample of stocks over these 12 weeks is −0.244% (−0.285%). The second sub-period contains the middle 11 sample weekends. The mean (median) return for our full sample of stocks over these 11 weeks is −0.207% (−0.229%). The third sub-period contains the final 12 weekends. The mean (median) return for our full sample of stocks over these final 12 weeks is 0.190% (0.141%).

Table 6 presents results from estimating Equation (1) for each sub-period for the full sample of stocks. To facilitate presentation, we include only results from the OLS and one-way fixed-effects regressions for the version of Equation (1) that contains both independent variables (CustSSVol(M–F) and TDeaSSVol(M–F)).

Table 6. 
OLS and panel regressions of weekend returns on weekend short selling by customers and dealers: Partitioning the Sample of Nasdaq stocks from September 13, 2000 to July 10, 2001 into sub-periods
Results from estimating R(M−F)it01 CustSSVol(M−F)it2 TDeaSSVol(M−F)it+eit, where (M−F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. OLS, and one-way (time) fixed-effects regressions. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Standard errors are in parentheses.
 First 12 weeks (n = 15,768)Middle 11 weeks (n = 14,454)Last 12 weeks (n = 15,768)
OLSOne-way fixed-effectOLSOne-way fixed-effectOLSOne-way fixed-effect
  1. ***, **, * indicate statistical significance at the 0.01, 0.05 and 0.10 level, respectively.

β0−1.866***NA1.399***NA−1.021***NA
(0.077) (0.076) (0.083) 
CustSSVol(M−F)−0.034**−0.026*−0.028*−0.025*−0.054***−0.037**
(0.015)(0.014)(0.015)(0.014)(0.015)(0.015)
TDeaSSVol(M−F)0.040***0.044***0.045***0.054***0.062***0.031***
(0.007)(0.007)(0.006)(0.006)(0.006)(0.005)
R20.0030.0750.0040.0910.0090.125

The results shown for each sub-period are consistent with the results shown earlier. There is a negative relationship between speculative short selling by customers and the weekend effect in stock returns, and a positive relationship between dealer short selling and the weekend effect in returns. However, as above, the R2 from the OLS estimations are low—indicating low explanatory power, and the increase in R2 for the one-way fixed-effects (weekend) specifications indicates that the weekend effect in returns is mostly driven by market-wide factors rather than speculative short selling. Similar results pertain when the model is estimated for the upper half, and upper quartile of sample stocks (based upon median ratio of shares shorted by customers to outstanding shares). In sum, these tests indicate that the generally declining level of the Nasdaq market during the sample period is not responsible for the results reported in this study.

3.7. Final robustness tests

We also conduct estimations (not reported here) on partitions of our sample by trading volume, forming groups of the highest, middle, and lowest third of sample stocks according to their average daily number of shares traded during the sample period. The results, which are available on request, are very similar to those reported earlier. That is, the goodness-of-fit test detects very little connection between weekend effects in returns and the types of short selling, and the coefficients for the variables of short selling are quite small in importance from an economic perspective.

In addition, we repeat our analysis using the Fama and MacBeth (1973) procedure over the 35 weeks of our sample. Petersen (2008) reports that, in the presence of a time effect, the Fama-MacBeth approach yields unbiased inferences. Table 7 presents results of these estimations for the full sample of stocks, and for stocks in the upper half and top quartile of the sample based upon the firm's median ratio of shorted to outstanding shares. As with the OLS and fixed-effects regression results presented earlier, these estimations result in low values for average R2, with the bulk of the low average R2 values attributable to the inclusion of TDeaSSVol(M–F) in the estimations. For the subsample of stocks in the top quartile, the average CustSSVol(M–F) parameter estimate in the model containing both the speculative (customer) and dealer short-selling variables is not significantly different from zero (estimate =−0.018, standard error = 0.014). In sum, the Fama-MacBeth estimation results are consistent with the results presented previously; variation in speculative short selling does not seem to explain much of the variation in the weekend effect of stock returns.

Table 7. 
Fama-MacBeth regressions: Nasdaq stocks from September 13, 2000 to July 10, 2001
Fama-MacBeth estimations over 35 weeks of R(M−F)i01 CustSSVol(M−F)i2 TDeaSSVol(M−F)t+eit, where (M−F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock, and e is the disturbance term. The Full Sample results present the mean of the parameter estimates from 35 weekly regressions for 1,314 stocks. The stocks in the upper half of the sample results present the mean of the parameter estimates from 35 weekly regressions for the 658 stocks that are in the upper half of sample stocks based upon each stock's median value during the sample period for daily shares sold short by customers normalized by outstanding shares. The stock in the top quartile of the sample results present the mean of the parameter estimates from 35 weekly regressions for the 329 stocks that are in the top quartile of sample stocks based upon each stocks median value during the sample period for daily shares sold short by customers normalized by outstanding shares. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Standard errors are in parentheses.
  Full sample Stocks with above-median values of customer-shorted shares to outstanding shares  Stocks with above-75th quartile values of customer-shorted shares to outstanding  
  1. ***, **, * indicate statistical significance at the 0.01, 0.05 and 0.10 level, respectively.

β0−0.590−0.613−0.607−0.585−0.599−0.589−0.562−0.568−0.571
(0.572)(0.586)(0.585)(0.661)(0.665)(0.665)(0.734)(0.737)(0.737)
CustSSVol(M−F)−0.034*** −0.029***−0.029*** −0.023**−0.023* −0.018
(0.010) (0.010)(0.011) (0.010)(0.014) (0.014)
TDeaSSVol(M−F) 0.045***0.044*** 0.048***0.047*** 0.065***0.063***
 (0.007)(0.007) (0.008)(0.008) (0.010)(0.010)
Average R20.0010.0060.0070.0020.0070.0090.0040.0090.013

In a final robustness check, we focus on the sample observations that have the most pronounced weekend effects in either returns or customer short selling. The reason is that a link between weekend effects in the two variables, which our earlier tests do not detect, could well emerge from an analysis of the observations containing their extreme values. Thus, we estimate Equation (1) for (i) the lowest quartile of sample observations according to the Monday–Friday difference in returns (R(M–F) ≤−4.97830%) and then (ii) for the highest quartile according to the Monday–Friday difference in customer-shorted shares as a percentage of volume (CustSSVol(M–F) ≥ 1.11071%). Each quartile contains 11,497 observations, and Table 8 contains the results of these regressions. The parameter estimate for CustSSVol(M–F) is not significantly different from zero in any of the four OLS estimations. In the fixed-effects regressions, several of the CustSSVol(M–F) estimates are significant, but generally similar in magnitude to estimates reported earlier. In sum, these findings support and corroborate our earlier conclusion that there is not an economically significant link between speculative short selling and the weekend effect in returns.

Table 8. 
OLS and panel regressions for Nasdaq stocks in the lowest quartile by weekend effect in returns and in the highest quartile by customer-shorted shares as a percentage of volume: Nasdaq stocks from September 13, 2000 to July 10, 2001
OLS, and one-way (time) fixed-effects regressions for this equation: R(M−F)it01 CustSSVol(M−F)it2 TDeaSSVol(M−F)it+eit, where (M−F) is the Monday–Friday difference, R is percentage stock return, CustSSVol is the customer-shorted shares as % of trading volume, TDeaSSVol is the total dealer-shorted shares (exempt and nonexempt) as % of trading volume, i refers to the stock and t to the weekend, and e is the disturbance term. The dependent and independent variables are computed as the Monday value less the previous Friday's value. Panel A reports results for the 11,497 observations that comprise the lowest quartile of the sample in terms of R(M−F). Panel B presents results for the 11,497 observations that constitute the highest quartile in terms of CustSSVol(M−F). The corresponding breakpoints for these quartiles are ≤4.97830% and ≥1.11071%, respectively. Standard errors are in parentheses.
 OLS One-way fixed-effect Two-way fixed-effect 
  1. *** and ** indicate statistical significance at the 0.01 and 0.05 level, respectively.

Panel A: Quartile with lowest weekend effects in returns, R(MF) (n=11,497)
β0−11.891***−11.843***NANANANA
(0.077)(0.078)    
CustSSVol(M−F)−0.015−0.0120.0010.001−0.001−0.001
(0.015)(0.015)(0.015)(0.015)(0.015)(0.015)
TDeaSSVol(M−F) 0.023*** 0.008 0.013**
 (0.006) (0.006) (0.006)
R20.0000.0010.0730.0740.2160.217
Panel B: Quartile with highest weekend effects in customer-shorted shares as a percentage of volume, CustSSVol(MF) (n=11,497)
β0−1.087***−1.025***NANANANA
(0.123)(0.121)    
CustSSVol(M−F)−0.026−0.020−0.040***−0.036**−0.049***−0.044***
(0.017)(0.017)(0.016)(0.016)(0.017)(0.017)
TDeaSSVol(M−F) 0.060*** 0.044*** 0.045***
 (0.007) (0.007) (0.007)
R20.0000.0060.1410.1440.2590.262

4. Conclusion

We use daily short-selling data to examine the possible linkage between the weekend effect in stock returns and speculative short selling. Our analysis focuses on a large and detailed data set of daily transactions in Nasdaq stocks between 2000 and 2001. The data set is unique because it allows short sales by speculating customers to be distinguished from those by dealers, and short sales that are exempt from the Nasdaq bid-test to be separated from those that are not. During our sample period, the stocks display a substantial weekend effect in returns, with the effect being largest for the smallest firms.

We find that short selling by customers (speculative short selling) displays a weekend effect, because this type of short selling constitutes a larger percentage of volume on Monday than on Friday; again, this difference is higher in the smaller firms. This weekend effect is due primarily to the fact that share volume (the denominator in the metric) is relatively low on Mondays because the raw number of speculatively shorted shares on Mondays tends to be lower than the number shorted on Fridays.

We also find that short selling by dealers contains a weekend effect, but it is distinctly different from (and opposite to) the effect for customers because dealer-shorted shares consistently make up a larger portion of volume on Friday than on Monday. The use of short selling by dealers to bring liquidity and stability to the market via their market-making activities is the reasonable explanation for this phenomenon. The distinct differences between customer and dealer short selling suggest that these two categories should not be treated as homogenous in academic research.

Finally, although we examine a variety of econometric specifications and consider several different stratifications of the sampled stocks, our estimations indicate that speculative short selling does not account for an economically meaningful portion of the weekend effect in returns, even among the firms that are most actively shorted. Instead, the weekend effect seems to be the result of other market-wide, systematic factors. Consequently, the specific cause of the weekend effect in stock returns remains an unresolved phenomenon.

Appendix

The ACT reporting protocol does not allow us to claim definitively that speculative short sales account for none (or at most very few) of the recorded dealer-shorted nonexempt shares in a stock. We believe, however, that it is possible to craft a test that reveals the likelihood that market-making rather than speculation largely determines the number of dealer-shorted shares. That test measures the strength of the daily association between the number of dealer-shorted nonexempt shares and the number of customer-shorted nonexempt shares in a stock. The rationale for the test is that a stock's nonexempt customer-shorted shares result largely, if not exclusively, from speculative short selling and that day-to-day changes in this variable reliably convey changes in investors' readiness to speculate on the stock. (See our discussion of the structure and interpretation of ACT data.) If speculative short selling by dealers typically accounts for a substantial number of reported dealer-shorted shares, then the test should uncover at least some synchronicity in the daily movement of the two sets of nonexempt shorted shares.

Two facts support this presumption of a measurable amount of synchronicity. First, dealers monitor all their customers' orders and can exploit the information contained in them. A sudden increase in short-sell orders for a stock might prompt a dealer to take similar positions, while a dealer might well be reluctant to engage in short selling when customers are placing few or no orders for short sales. Such behavior by dealers would resemble the “payment for order flow” that became a prominent feature of the stock market some years ago (Battalio, Jennings and Selway, 2001). Second, dealers who want to profit from short selling have the same means as their customers of finding attractive targets. There is no reason to believe that these dealers would be systematically faster or slower—or, even more absurdly, always either faster or slower—than customers in locating potentially over-priced stocks and selling the shares short. Given that dealers can readily augment their own research by surveying customer short-sell orders, the probability is high that speculation by dealers, if it is a substantial portion of their overall nonexempt short selling, has some correlation with speculation by customers.

The test, therefore, consists of finding—for each stock—the extent of the connection between the daily number of dealer-shorted shares and the daily number of customer-shorted shares. The equation used in the test is

image((A1))

where DeaSSVol is dealer-shorted nonexempt shares as a percentage of volume, CustSSVol is customer-shorted nonexempt shares similarly normalized, subscripts i and t refer to the stock and to the day, and η is the disturbance term. With OLS regressions, we fit this equation to 207 days of data for each of the 1,314 stocks in our sample (a total of 1,314 regression estimations). If dealers in a stock do regularly engage in a meaningful amount of speculative short selling, then γ1 for that stock should be positive and significant and the regression should produce a convincing goodness-of-fit statistic. If, on the other hand, this regression for a stock generates a statistically insignificant coefficient for CustSSVol and a low R2, there would be little reason to believe that a substantial portion of dealer-shorted shares in that stock is regularly attributable to speculation.

Table A1 reports the results of the test, which reveal very little similarity in the daily patterns of short selling by customers and by dealers across the stocks in our sample. Most of the 1,314 estimates of γ1 are quite small and only 5% of them are both statistically significant and positive.11 Also, the values of R2 are so low that customer short selling seems almost completely divorced from dealers' decisions to sell short. In our view, the obvious conclusion to be drawn from the test is that there is only a limited probability that a meaningful number of the recorded dealer-shorted nonexempt shares regularly reflect speculation.

Table A1. 
Regression tests of daily association between customer-shorted and dealer-shorted shares in Nasdaq stocks: September 13, 2000 and July 10, 2001
The table reports key aspects of the regression DeaSSVolit01 CustSSVolitit. DeaSSVol is dealer-shorted shares as a percentage of volume, CustSSVol is customer-shorted shares as a percentage of volume, i refers to the stock, and t to the day. In all, 1,314 regressions are conducted, each based on 207 daily observations.
 Estimates of γ0Estimates of γ1R2
Mean/standard deviation21.53/2.76−0.06/0.320.01/0.02
Number positive/negative1,314/0489/825
Number positive and significant at 5% or lower1,31468

Footnotes

  • 1

    Boehmer, Jones and Zhang (2005) describe a large, detailed, and proprietary data set that applies to short and other trades on the NYSE for the 2000–2004 interval.

  • 2

    An ECN-reported trade could include up to three records depending on the side(s) of the trade reported.

  • 3

    We exclude trades reported by ECNs from our measure of dealer short selling.

  • 4

    As page 3 of Chapter 9 in Nasdaq Trader Manual (revised January 2000) states: “Under revisions to NASD Rule 6130(d)(6) implemented in 1997, Market-makers … must denote all short sales … as short sales.”

  • 5

    Nasdaq's Short Sale Rule (Rule 3350) was, in our sample period, analogous to the “uptick” rule for NYSE-listed securities, though Rule 3350 used a bid-test instead of the NYSE's tick-test. Generally, the rule prohibited short selling at the bid if it was lower than the preceding bid. See NASD's Notices to Members, 94-68 and 94-83, and interpretations (IMs) to the rule contained in IM-3350 of NASD Manual.

  • 6

    It is quite unlikely that any customer-shorted or dealer-shorted trades marked as exempt are speculative. The exemption is only available for nonspeculative activities, and trades marked as exempt could be subject to eventual audit for potential abuse.

  • 7

    This restriction leads us to drop the weeks including Thanksgiving, Christmas, New Years, Martin Luther King Day, President's Day, Easter, and Memorial Day. Keim and Stambaugh (1984, Table 1, Note b) impose a similar control when they exclude cases of multiple-day returns for individual weekdays and Monday returns extending over three days. Chen and Singal (2003) define a weekend as the time between the first trading day of the week less the last trading day of the preceding week.

  • 8

    For additional evidence, see Desai, Ramesh, Thiagarajan and Balachandran (2002) as well as Dechow, Hutton, Meulbroek and Sloan (2001) and Boehmer, Jones and Zhang (2005).

  • 9

    Diether, Lee and Werner (2008) also indicate that short selling by dealers is likely to be contrarian because of their role as intermediaries.

  • 10

    Though not reported in the table, we also find similar results for the mid-cap and large-cap subsamples. The R2 from estimating the one-way fixed-effects model is essentially unaffected by the inclusion or exclusion of CustSSVol(M–F) in the specification.

  • 11

    Few of these regressions suffer from auto-correlation in the error terms.

Ancillary