Review of Derivatives Research

, Volume 18, Issue 1, pp 51–73 | Cite as

Are put-call ratios a substitute for short sales?

Article

Abstract

Prior research argues that pessimistic traders can use options as substitutes for short sales particularly when stocks are expensive to short. Motivated by this contention, we examine the relation between put-call ratios, short-selling activity, and constraints to short selling. Results show that (1) put-call ratios are inversely related, instead of directly related, to proxies for short-sale constraints and (2) the significant negative relation between current put-call ratios and future returns (Pan and Poteshman in Rev Financ Stud 19:871–908, 2006) is orthogonal to proxies for short-sale constraints. These results indicate that short-sale constraints do not influence bearish option activity. While prior studies show that short sellers are generally contrarian in contemporaneous and past returns, we find that put-call ratios follow periods of negative returns. However, any observed return predictability contained in put-call ratios is driven by ratios that follow periods of positive returns.

Keywords

Options Short sales Short sale constraints Informed trading 

JEL Classification

G10 G14 

1 Introduction

Recently, Pan and Poteshman (2006) document that unfavorable information about future stock prices is contained in put-call ratios. The idea that informed investors trade in the options market has been a topic of both theoretical and empirical research for over 30 years (e.g. Black 1975; Diamond and Verrecchia 1987; Figlewski and Webb 1993; Mayhew et al. 1995; Danielsen and Sorescu 2001). The theoretical justification for informed option trading is based on two arguments. The first argument, discussed in Black (1975), is that informed investors may be attracted to the options market because of higher leverage available in options. The second argument for informed option trading is based on the substitutability between short sales and bearish option strategies. Prior research argues that short sellers, who are shown to be informed about future stock price movements (Senchack and Starks 1993; Aitken et al. 1998; Dechow et al. 2001; Desai et al. 2002; Diether et al. 2009), can substitute short sales by buying put options and/or writing call options. In particular, Diamond and Verrecchia (1987) argue that options can be used instead of short sales when shorting becomes expensive. Others (Danielsen and Sorescu 2001) argue that when options are introduced, short-sale constraints (or short-sale costs) are mitigated because the demand for short sales decreases and shorting costs subsequently decrease. Other studies have examined the migration of informed trading from the stock market to the options market both theoretically (Easley et al. 1998) and empirically (Mayhew et al. 1995).

Motivated by the idea that investors with unfavorable information may prefer options to short sales, we seek to answer the following three research questions. First, is the most informed bearish option activity driven by stocks that are most likely to face short sale constraints? Second, are the short-term trading strategies of short sellers—as documented in Diether et al. (2009)—similar to the short-term trading strategies of informed option traders? Third, what factors explain the return predictability in both short sales and bearish option activity? To answer these questions, we examine daily short-selling activity and daily put-call ratios for a sample of stocks during 2005 and 2006. Our motivation for this analysis is driven by a simple theoretical argument that is implied in other studies (Diamond and Verrecchia 1987; Danielsen and Sorescu 2001). In order to short a stock, the investor must borrow the stock from a lender. The lender charges, what D’Avolio (2002) denotes as a stock loan fee. The investor leaves collateral, generally cash, with the lender and charges the lender interest on the collateral. When the short position is closed, the investor returns the borrowed shares of stock and the lender rebates the difference between the collateral interest and the stock loan fee. When this rebate rate (the difference between the collateral interest rate and the stock loan fee) decreases or becomes negative to a reservation rate that no longer incentivizes traders to short, short-sale constraints are said to bind. In the case of a decreasing rebate rate, it may be profit maximizing for the investor to short the stock synthetically in the options market. Among other things, the choice between short sales and say, put options depends on the equity borrowing costs. Ceteris paribus, as equity borrowing costs increase, the informed investor is more likely to choose to trade in the options market.

In this simple example, the theory predicts that bearish option volume is increasing in short-sale constraints. Further, the information contained in bearish option volume is also increasing in the severity of short-sale constraints. One of the objectives of this analysis is to test these predictions. A second objective is to compare characteristics of short selling with characteristics of put-call ratios in order to better understand the substitutability between short sales and options.

D’Avolio (2002) documents a direct relation between several stock characteristics (institutional ownership, market capitalization, price, turnover, and book-to-market ratios) and the equity loan supply, which is an inverse measure of short-sale constraints. Similarly, we show that short-selling activity is generally increasing in our direct proxies of the equity loan supply. In answer to the first research question we ask, we do not find that put-call ratios are decreasing in these proxies of the equity loan supply. In fact, our regression results almost uniformly show a positive relation between put-call ratios and proxies of the equity loan supply. These results question whether short-sale constraints drive the substitutability between options and short sales.

Because we find that short-sale constraints do not explain bearish option activity, we begin to compare some of the short-term trading strategies of short sellers—found in Diether et al. (2009)—to the short-term trading strategies of bearish option traders. First, we observe that shorting activity relates directly with contemporaneous share turnover, return volatility, and price volatility. We also find that put-call ratios have a similar positive relation, with the exception of price volatility. However, we report an important asymmetry in our results. We find that shorting activity is positively related to contemporaneous returns and past returns, which is consistent with findings in Diether et al. (2009) and suggests that short sellers are contrarian in contemporaneous and past returns. When examining put-call ratios, we find a significant negative relation between put-call ratios and both contemporaneous and past returns suggesting that bearish option traders are not contrarian and instead follow periods of negative returns. Several explanations exist. One possible explanation is that short sellers and put-option traders are trading on different information. Another explanation is that put-option volume is predominately made up from hedging activity by long investors who, when stock prices begin to decline, have a greater propensity to purchase put options to hedge against downside risk.1 These results provide an answer to our second research question and seem to indicate that the contrarian trading strategies of short sellers are very different from the trading strategies of bearish option traders.

A natural extension to our analysis is to run tests similar to Pan and Poteshman (2006) to determine the level of information contained in put-call ratios.2 Pan and Poteshman show that current put-call ratios relate inversely with future stock returns at the daily level. In addition, we attempt to determine whether the information in put-call ratios is driven by stocks that are most likely to face severe borrowing costs. Theory predicts that when borrowing costs are high, informed investors will migrate to the options market (Diamond and Verrecchia 1987). This migration should manifest itself in higher levels of information in put-call ratios for stocks that are most likely to face binding short-sale constraints. After closely following (Pan and Poteshman 2006), we find consistency with the idea that information is contained in put-call ratios as we also document a significant negative relation between current put-call ratios and future returns. However, we do not find that these results are driven by stocks that are most likely constrained. When compared to a subsample of stocks that are least likely to face binding short-sale constraints, we find that the return predictability of put-call ratios is statistically similar.

The final set of tests in this study examines the interaction of contrarian trading and the level of return predictability. In particular, we test whether the return predictability of short-selling activity and put-call ratios is increasing or decreasing in prior stock price performance. The purpose of these tests is to better determine the source of the information contained in put-call ratios. Results from these tests provide some evidence that short sellers’ ability to predict negative returns is increasing in their contrarian behavior. That is, as past returns are higher, the negative relation between current short selling and next-day returns is strengthened. This result strongly supports the arguments made in Campbell et al. (1993), and Avramov et al. (2006) that contrarian trading strategies are generally executed by informed investors. Similarly, we find that the negative relation between current put-call ratios and next-day returns, documented in Pan and Poteshman (2006), is also increasing in past returns. Relating these findings to our third research question, our results suggest that while the degree of short-sale constraints do not explain the level of information contained in bearish option activity, the level of contrarian trading does.

The rest of the paper follows. Section 2 discusses the data used in the analysis. Section 3 describes our empirical tests and the results from those tests while Sect. 4 concludes.

2 Data description

The data used in this analysis come from several sources. In response to the Securities and Exchange Commission’s (SEC) Regulation SHO, short-sale transactions data is made available from the NYSE. We aggregate the data to the daily level. We note that short-sale data is only available from the beginning of 2005 until the first part of 2007, therefore, our sample time period is from January 2005 to December 2006. The SHO data allows us to distinguish each short sale as either an exempt short sale or a non-exempt short sale. Exempt short sales are shorts that are exempt from the uptick rule. Generally, these short sales are thought of as market maker short sales (Edwards and Hanley 2009; Christophe et al. 2010). Partitioning the data this way becomes important in our study because several of the exempt short sales may be from option market makers who are attempting to hedge the other side of bearish option trades (Danielsen and Sorescu 2001) and are therefore less informed than non-exempt short sales (Engelberg et al. 2010).

From the Center of Research on Security Prices (CRSP), we obtain daily returns, volume, prices, market capitalization, and shares outstanding. We also restrict our sample to ordinary common stocks (CRSP share code 10 or 11) and stocks that trade every day of the sample time period. From Thompson’s Spectrum database, we obtain the number of shares held by institutions from the 13f filings. Book value of equity is obtained from Compustat and the daily options data come from Bloomberg.3 After including the initial restrictions and combining the SHO data, CRSP data, the institutional holdings data, the Compustat data, and options data, the number of stocks in our sample is 1,186 stocks that are listed on the NYSE.

Table 1 provides a summary of statistics for the sample used in the analysis. Panel A reports the price of the average stock is $36.58 while the market cap is $9.4 billion. We also show that the average book-to-market ratio is 0.386 and nearly 77 % of outstanding shares are held by institutions. Following Diether et al. (2009), we calculate price volatility as the difference between the daily high price and the daily low price scaled by the daily high price. Further, return volatility is measured as the standard deviation of daily returns from day \(t\) to \(t-10\), where day \(t\) is the current trading day. Turnover is the daily CRSP volume divided by the number of shares outstanding in percent. We observe that the mean price volatility is 0.024, the mean return volatility is 0.017, and the average turnover is 0.889 % in Table 1.
Table 1

Summary statistics

 

Price

Market capitalization

Book-to-market

Institutional ownership

Price volatility

Return volatility

Turnover

 

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Panel A. Stock characteristics

Mean

36.58

9.4303

0.3858

0.7652

0.0240

0.0171

0.8885

SD

22.48

25.6699

0.7609

0.1878

0.0084

0.0064

0.5635

Min

2.46

0.0317

\(-\)0.0618

0.0011

0.0012

0.0006

0.0679

Max

366.59

381.4018

2.3369

0.9887

0.0834

0.0713

4.9070

\(N\)

1,186

1,186

1,186

1,186

1,186

1,186

1,186

 

Non-exempt short turnover

Exempt short turnover

Call volume

Put volume

Put-call ratio

 

(1)

(2)

(3)

(4)

(5)

Panel B. Option and short-selling characteristics

Mean

0.1835

0.0130

1,457.11

921.00

0.3500

SD

0.1439

0.0180

4,369.46

2,896.02

0.1016

Min

0.0063

0.0000

0.01

0.00

0.0000

Max

1.1999

0.1318

82,476.83

57,966.70

0.8387

\(N\)

1,186

1,186

1,186

1,186

1,186

The table reports statistics that describe the sample. Panel A reports stock characteristics the 1,186 stocks included in our sample. Price is the daily ending price in CRSP. Market capitalization (000s) is the CRSP market cap. Book to market is the ratio of the Compustat book value of equity relative to the market value of equity. Institutional holdings are obtained from the Spectrum 13f filings and are scaled by the number of shares outstanding. Price volatility is the difference between the daily high price and the daily low price divided by the daily high price following Diether et al. (2009). Return volatility is the standard deviation of daily returns from day \(t-10\) to \(t\), where day \(t\) is the current trading day. Turnover is the daily volume divided by the shares outstanding. In Panel B, we report characteristics of short selling and put option activity. Non-exempt short turnover is the non-exempt short volume divided by the shares outstanding (in percent). Exempt short turnover is the exempt short volume divided by the shares outstanding, in percent. Call (put) volume is the number of call (put) option contracts traded per day according to Historical data obtained from Bloomberg. The put-call ratio is the put volume divided by the sum of the put volume and call volume, which is similar to the ratio used in Pan and Poteshman (2006)

Panel B reports summary statistics for short-selling and option characteristics. Following prior literature (Asquith et al. 2005; Christophe et al. 2010), we scale daily short volume by shares outstanding.4 Non-exempt short turnover is the non-exempt short volume divided by the number of shares outstanding in percent while exempt short turnover is the daily exempt short volume scaled by shares outstanding in percent. We find that nearly 0.2 % of shares outstanding are shorted on a particular day as 0.184 % is made up from non-exempt short turnover and 0.013 % is made up from exempt short turnover. We also report that the average stock trades 1,457 call-option contracts, and 921 put-option contracts daily. Following Pan and Poteshman (2006), we define the put-call ratio as put volume scaled by the sum of call volume and put volume. The mean put-call ratio is 0.35 suggesting that 35 % of all option volume is made up from put options.

3 Empirical tests and results

As described above, Pan and Poteshman (2006) argue that information about future stock price movements is contained in put-call ratios. Further, Pan and Poteshman document that information contained in put-call ratios is driven by non-public information and directly related to the level of leverage options provide. Black (1975) suggests that leverage in options may motivate informed investors to trade in the options market. Other research suggests that a portion of the information contained in option volume is due to short sellers migrating from the stock market to the options market because of high equity borrowing costs (Diamond and Verrecchia 1987; Danielsen and Sorescu 2001). While Pan and Poteshman (2006) test Black’s (1975) initial contention, the short-sale constraints contention has not been tested. In this section, we provide these tests.

3.1 Short activity, put-call ratios, and proxies for short-sale constraints

We begin by examining the relation between both short turnover and put-call ratios and the direct proxies of the equity loan supply. Table 2 reports the results from sorting non-exempt short turnover (Panel A), exempt short turnover (Panel B), and put-call ratios (Panel C) into quartiles and examining the five constraint proxies across each quartile.
Table 2

Relation between trading activity and proxies for equity loan supply

 

Q I

Q II

Q III

Q IV

Q IV–Q I

 

(1)

(2)

(3)

(4)

(5)

Panel A. Sort by non-exempt short turnover

InstOwn

0.6318

0.7425

0.8159

0.8716

0.2398***

(0.000)

Size

24.0624

6.1944

4.2372

3.1916

\(-\)20.8708***

(0.000)

Price

36.39

32.86

38.06

38.99

2.60

(0.191)

Turn

0.4181

0.6279

0.8718

1.5574

1.1393***

(0.000)

B/M

0.3625

0.4264

0.2775

0.4760

0.1135**

(0.027)

Panel B. Sort by exempt short turnover

InstOwn

0.7296

0.7819

0.7529

0.7970

0.0674***

(0.000)

Size

14.4955

8.5513

10.0704

4.6009

\(-\)9.8946***

(0.000)

Price

37.91

36.35

34.26

37.78

\(-\)0.13

(0.940)

Turn

0.6016

0.7788

0.9810

1.1123

0.5107***

(0.000)

B/M

0.4162

0.3718

0.4103

0.3436

\(-\)0.0726

(0.245)

Panel C. Sort by put-call ratios

InstOwn

0.7339

0.7550

0.7696

0.8031

0.0692***

(0.000)

Size

2.4102

6.6701

16.0391

12.5994

10.1892***

(0.000)

Price

25.00

35.02

40.26

46.05

21.05***

(0.000)

Turn

0.8010

0.8176

0.8320

1.0235

0.2225***

(0.000)

B/M

0.4540

0.3851

0.3298

0.3730

\(-\)0.0810

(0.276)

The table reports InstOwn, Size,Price Turn, and \(B/M\) across portfolios sorted by non-exempt short turnover (Panel A), exempt short turnover (Panel B), and put-call ratios (Panel C). The five stock characteristics are included as direct approximations for the equity loan supply (or inverse measures of equity borrowing costs) following D’Avolio (2002). The difference between the stock characteristics for the high quartiles and the low quartiles are reported with the corresponding \(p\) value. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

Panel A reports that institutional ownership, which is defined as the percentage of shares outstanding held by institutions, is increasing monotonically across non-exempt short turnover quartiles. In column (5), the difference between extreme quartiles is significant at the 0.01 level (difference = 0.2398, \(p\) value = 0.000). We find that the difference between extreme quartiles is also positive for price, turnover, and book-to-market ratios although the price difference is not significant at the 0.10 level. We find that market cap is decreasing monotonically across increasing non-exempt short turnover quartiles. The difference between extreme quartile is \(-\)$20.87 billion (\(p\) value \(=\) 0.000). The negative relation between non-exempt short turnover and market cap is consistent with findings in Boehmer et al. (2008) who show that short volume as a percentage of trade volume relates negative with market cap. However, we recognize that the negative relation between short turnover and size is a function of the construction of both variables. Short turnover is scaled by shares outstanding while market cap is price multiplied by shares outstanding. We therefore sort stocks into quartiles based on unscaled short volume and find that size is 1.36, 2.64, 6.37, and 27.31 across increasing short volume quartiles. The difference between extreme quartiles is 25.95 (\(p\) value \(=\) 0.000) indicating that short volume and market cap are directly related thus providing some support for the use of market cap as an inverse proxy for short-sale constraints (D’Avolio 2002; Xu 2007).

Results in Panel B are generally consistent with findings in Panel A. Panel C reports the results for put-call ratio sorts. If short-sale constraints drive the migration of informed investors from the stock market to the options market, then we expect a negative relation between put-call ratios and our direct proxies of the equity loan supply. On the contrary, Panel C shows that institutional ownership, market cap, prices, and turnover are each increasing monotonically across increasing put-call ratio quartiles. Results for book-to-market ratios are mixed. Findings in Panel C indicate that put-call ratios are higher for stocks that are least likely constrained instead of stocks that are most likely constrained and seem to contradict the idea that informed investors will migrate from the stock market to the options market when shorting becomes costly. Several explanations for our findings exist. For instance, perhaps only a small portion of put-call ratios come from this type of market migration and the data is unable to identify this type of market migration. Another explanation may be that short-sale constraints are not binding. D’Avolio (2002) reports that, for nearly 90 % of his sample, equity borrowing costs are less than 1 % per annum. However, D’Avolio also find that the other 10 % of his sample are very costly to short which should be picked up in our results.

We continue our analysis using a cross-sectional regression. In particular, we estimate the following equation.
$$\begin{aligned} Activity_{i }&= \beta _{0} + \beta _{1} InstOwn_{i} + \beta _{2} ln(size_{i}) + \beta _{3}price_{i}^{-1} \nonumber \\&+\, \beta _{4} turn_{i} + \beta _{5}B/M_{i}+ \varepsilon _{i} \end{aligned}$$
(1)
The dependent variable Activity is defined as either the cross-sectional mean of the non-exempt short turnover, exempt short turnover, or the put-call ratio. As independent variables, the percentage of outstanding shares held by institutions \(({InstOwn}_{i})\), the natural log of market cap in $billions \(( ln(size_{i}))\), the inverse of the stock price \(( price_{i}^{-1})\), the percentage of shares outstanding that are traded each day \(( turn_{i})\), and the book-to-market ratio (\(B/M_{i})\) are included. When Activity is defined as non-exempt short turnover, the expected signs of the estimates for InstOwn, size, turn, and \(B/M (price^{-1})\) are positive (negative). If market migration makes up a substantial portion of put volume, then the opposite is true when Activity is defined as the put-call ratio.

After controlling for conditional heteroskedasticity in the standard errors as documented by White (1980), we find that the regression results are qualitatively similar to our univariate results in Table 2. The only exception is in column (9) when the positive estimate for B/M is not significant at the 0.10 level (\(p\) value \(=\) 0.145). The regression results again do not support the idea that a substantial portion of put activity is driven by investors migrating from the stock market to the options market because of high equity borrowing costs.

3.2 Short activity, put-call ratios, and contrarian trading behavior

In this subsection, we examine some additional characteristics that determine the level of short-selling activity and put-option activity. Diether et al. (2009) document a positive relation between current short selling and both contemporaneous and past returns suggesting that short sellers are contrarian in contemporaneous and past returns. We extend this analysis to put-call ratios. Our purpose in doing so is to begin to examine the information contained in put-call ratios. Prior research argues that contrarian trading strategies are generally executed by informed traders attempting to profit from short-term price reversals (Campbell et al. 1993; Avramov et al. 2006). The findings in Diether et al. (2009) support the contention that informed investors execute contrarian trading strategies (Table 3).
Table 3

Cross sectional regressions

 

Non-exempt short turnover

Exempt short turnover

Put-call ratios

 

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Panel A. Dependent variable is short turnover

Intercept

\(-\)0.0480***

0.2124***

\(-\)0.0223***

0.0040*

0.0154***

0.0057**

0.2866***

0.3276***

0.2765***

(0.000)

(0.000)

(0.003)

(0.064)

(0.000)

(0.014)

(0.000)

(0.000)

(0.000)

InstOwn

0.3025***

 

0.0163**

0.0117***

 

\(-\)0.0081***

0.0830***

 

0.0467***

(0.000)

 

(0.030)

(0.000)

 

(0.002)

(0.000)

 

(0.004)

Ln(size)

 

\(-\)0.0256***

\(-\)0.0068***

 

\(-\)0.0021***

\(-\)0.0009**

 

0.0199***

0.0193***

 

(0.000)

(0.000)

 

(0.000)

(0.028)

 

(0.000)

(0.000)

\(\hbox {Price}^{-1}\)

  

\(-\)0.3936***

  

\(-\)0.0107

  

\(-\)0.4315***

  

(0.000)

  

(0.428)

  

(0.000)

Turn

  

0.2483***

  

0.0175***

  

0.0374***

  

(0.000)

  

(0.000)

  

(0.000)

B/M

  

0.0045**

  

\(-\)0.0007

  

0.0038

  

(0.023)

  

(0.257)

  

(0.145)

\({\hbox {Adj}. R}^{2}\)

0.1550

0.1926

0.8748

0.0141

0.0255

0.2475

0.0227

0.0709

0.1571

The table reports the results from estimating the following equation

\(Activity_{i } = \beta _{0} + \beta _{1}InstOwn_{i} + \beta _{2} ln(size_{i}) + \beta _{3} price_{i}^{-1}+ \beta _{4}turn_{i}+ \beta _{5}B/M_{i} + \varepsilon _{i}\)

The dependent variable Activity is defined as the cross-section mean of the non-exempt short turnover [columns (1) through (3)], exempt short turnover [columns (4) through (6)], and put-call ratios [columns (7) through (9)]. The independent variables used in the equation are the institutional ownership (InstOwn), the natural log of market cap (Ln(size)), the inverse of the average daily price \(( Price^{-1})\), the turnover (Turn), and the book-to-market ratio (\(B/M)\). \(P\) values are obtained from White (1980) robust standard errors although qualitatively similar results are found controlling for clustering in the error terms. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

We begin by sorting stocks into portfolios similar to our sorts in Table 2 and then reporting both contemporaneous and past returns across each quartile. Table 4 reports the results of the sorts.5 Panel A shows the results of the non-exempt short turnover sorts while Panel B reports the results for the exempt short turnover sorts. Similar to Diether et al. (2009), we find that returns monotonically increase across increasing short turnover quartiles indicating that short sellers are indeed contrarian in contemporaneous and past returns. We do note that the difference between extreme quartiles is much larger in magnitude in Panel A than in Panel B suggesting that non-exempt short sales drive the contrarian behavior documented in Diether et al. (2009). This result is somewhat expected if exempt short turnover is generally executed by option market makers attempting to hedge against bearish option volume using shorts (Evans et al. 2009).
Table 4

Relation between daily trading activity and both contemporaneous and past returns

 

\(Q I\)

Q II

Q III

Q IV

Q IV–Q I

 

(1)

(2)

(3)

(4)

(5)

Panel A. Sort by non-exempt short turnover

\({{ret}_{t}}\)

\(-\)0.0018

\(-\)0.0002

0.0011

0.0033

0.0051***

(0.000)

\({{ret}_{t-5,t-1}}\)

\(-\)0.0001

0.0021

0.0039

0.0061

0.0062***

(0.000)

Panel B. Sort by exempt short turnover

\({{ret}_{t}}\)

0.0005

0.0001

0.0004

0.0013

0.0008***

(0.000)

\({{ret}_{t-5,t-1}}\)

0.0014

0.0020

0.0030

0.0056

0.0042***

(0.000)

Panel C. Sort by put-call ratios

\({{ret}_{t}}\)

0.0012

0.0028

\(-\)0.0000

\(-\)0.0022

\(-\)0.0034***

(0.000)

\({{ret}_{t-5,t-1}}\)

0.0043

0.0065

0.0024

\(-\)0.0024

\(-\)0.0067***

(0.000)

The table reports both contemporaneous returns \((ret_{t})\) and past returns \((ret_{t-5,t-1})\) across quartiles formed by sorting stock-day observations based on non-exempt short turnover (Panel A), exempt short turnover (Panel B), and put-call ratios (Panel C). The difference between returns for the high quartiles and the low quartiles is reported with the corresponding \(p\) value. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

Panel C shows the results for the put-call ratio sorts. Contrary to the short turnover results, we find that returns are generally decreasing across increasing put-call ratio quartiles. The difference between the extreme quartiles is consistently negative and significant indicating that put-option traders trade on days with negative returns and tend to follow periods of negative returns. This new result requires some explanation. One possible reason for this asymmetry between short selling and put-option activity is that each types of trader is trading on different information. The findings seem to suggest that the two types of traders have different intentions. Another possible explanation is that the majority of the put activity is motivated by the propensity of long investors to hedge against downward price movements particularly after periods of negative returns.6 In either case, the observed difference in trading behavior by short sellers and put-option traders makes the case for short-selling migration to the options market less compelling.

We recognize that other factors influence the level of short selling and put-option activity so we estimate the following equation using panel data.
$$\begin{aligned} Activity_{i,t}&= \beta _{0} + \beta _{1}{ret}_{i,t} + \beta _{2}{ret}_{i,t-5,t-1} + \beta _{3}{turn}_{i,t } + \beta _{4}{turn}_{i,t-5,t-1}\nonumber \\&+\, \beta _{5}{rvolt}_{i,t} + \beta _{6}{rvolt}_{i,t-5,t-1}+ \beta _{7}{pvolt}_{i,t }\nonumber \\&+\,\beta _{8}{pvolt}_{i,t-5,t-1}+ \varepsilon _{i,t} \end{aligned}$$
(2)
The dependent variable Activity, is defined as before with the exception that the data is now pooled. That is, we examine the daily short-selling/put-option activity for each stock on each day during the entire sample time period. Similarly, we include contemporaneous returns \(({ret}_{i,t})\) and past 5-day cumulative returns \(( ret_{i,t-5,t-1})\). The returns used in Eq. (2) are CRSP raw returns although similar (unreported) results are found when examining market-adjusted returns. In addition, both current and past turnover, return volatility, and price volatility are included as additional controls. A Hausman test rejects the presence of random effects. However, an \(F\)-test reveals observed differences across both stocks and days so we report the two-way fixed effects estimates although similar results are found using pooled OLS while controlling for conditional heteroskedasticity and clustering in the error terms.
Table 5 reports the results from estimating equation (2). Columns (1) through (4) report the results for the different measures of short turnover. As before, results show that both non-exempt and exempt short turnover are positively related to contemporaneous and past returns supporting the idea that short sellers are contrarian traders. Further, columns (5) and (6) provide evidence consistent with our univariate results as current put-call ratios relate inversely with both current and past returns. These results are robust when controlling for turnover and volatility measures. When examining the coefficients on these variables, a few results are noteworthy. First, we find that both non-exempt short turnover and the put-call ratio generally have the same sign for each of the turnover and volatility measures. The only exception is that the coefficient on contemporaneous price volatility is positive for non-exempt short turnover but negative for put-call ratios. These results suggest that, in general, the level of shorting activity and bearish option activity respond to both trading activity and volatility. However, Table 5 suggests that bearish option activity follows negative returns while short-selling activity does not.
Table 5

Panel regressions

 

Non-exempt short turnover

Exempt short turnover

Put-call ratio

 

(1)

(2)

(3)

(4)

(5)

(6)

Intercept

0.1810***

\(-\)0.0232***

0.0127***

\(-\)0.0031***

0.2974***

0.3143***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\({{ret}_{t}}\)

1.0625***

0.8062***

0.0269***

0.0144***

\(-\)1.0838***

\(-\)1.1175***

(0.000)

(0.000)

(0.000)

(0.021)

(0.000)

(0.000)

\(ret_{t-5,t-1}\)

0.2093***

0.2504***

0.0231***

0.0270***

\(-\)0.4419***

\(-\)0.4819***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(turn_{t}\)

 

0.2177***

 

0.0113***

 

0.0251***

 

(0.000)

 

(0.000)

 

(0.000)

\(turn_{t-5,t-1}\)

 

0.0293***

 

0.0031***

 

0.0739***

 

(0.000)

 

(0.000)

 

(0.000)

\(rvolt_{t}\)

 

1.1692***

 

\(-\)0.0333***

 

0.6402***

 

(0.000)

 

(0.183)

 

(0.000)

\(rvolt_{t-5,t-1}\)

 

\(-\)1.8069***

 

\(-\)0.0178**

 

\(-\)1.2862***

 

(0.000)

 

(0.351)

 

(0.000)

\(pvolt_{t}\)

 

1.2545***

 

0.1337***

 

\(-\)0.2710***

 

(0.000)

 

(0.000)

 

(0.000)

\(pvolt_{t-5,t-1}\)

 

\(-\)1.0854***

 

0.0498***

 

\(-\)3.5521***

 

(0.000)

 

(0.000)

 

(0.000)

Adj. \(R^{2}\)

0.0093

0.6503

0.0014

0.1486

0.0089

0.0428

Stock fixed effects

Yes

Yes

Yes

Yes

Yes

Yes

Day fixed effects

Yes

Yes

Yes

Yes

Yes

Yes

The table reports the results from estimating the following equation

\(Activity_{i,t}= \beta _{0}+ \beta _{1} ret_{i,t}+ \beta _{2} ret_{i,t-5,t-1 }+ \beta _{3}turn_{i,t } + \beta _{4}turn_{i,t-5,t-1 }+ \beta _{5}rvolt_{i,t }+ \beta _{6} rvolt_{i,t-5,t-1 } + \beta _{7}pvolt_{i,t}+ \beta _{8} pvolt_{i,t-5,t-1}+ \varepsilon _{i,t}\)

The dependent variable Activity is defined as the daily non-exempt short turnover [columns (1) and (2)], exempt short turnover [columns (3) and (4)], and put-call ratios. The independent variables are the contemporaneous return \((ret_{i,t})\) and past returns \(( ret_{i,t-5,t-1})\), the contemporaneous turnover \((turn_{i,t})\) and past turnover \(( turn_{i,t-5,t-1})\), the contemporaneous return volatility \(( rvolt_{i,t})\) and past return volatility \(( rvolt_{i,t-5,t-1})\), and the contemporaneous price volatility \((pvolt_{i,t})\) and past volatility \((pvolt_{i,t-5,t-1})\). Returns are daily CRSP returns. Turnover is defined as the daily trade volume scaled by the number of shares outstanding. Return volatility is the standard deviation of daily returns from day \(t\) to \(t-10\), where day \(t\) is the current trading day. Price volatility is difference between the daily high price and the daily low price divided by the daily high price. In response to a Hausman test, we report the two-way fixed effects estimates with robust standard errors. Similar results are found using pooled OLS controlling for conditional heteroskedasticity. \(P\) values are reported in parentheses. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

Next, we attempt to determine whether short-sale constraints drive our results by estimating equation (2) for stocks in the lowest institutional ownership quartile and stocks in the highest institutional ownership quartile.7 Stocks in the lowest institutional ownership quartiles represent stocks that are most likely to face binding short-sale constraints while stocks in the highest quartile are stocks that are least likely to face binding constraints. Table 6 reports the results of the two-way fixed effects regression. Columns (1), (3), and (5) [(2), (4), and (6)] report the results from estimating the equation for the least (most) constrained stocks for non-exempt short turnover, exempt short turnover, and put-call ratios, respectively. The variables of interest are the contemporaneous and lagged returns. Interestingly, the results in Table 6 show that the contrarian behavior of short sellers is more pronounced in stocks that are least likely to face binding short-sale constraints. An \(F\)-statistic tests for equality between the estimates in the two subsamples. The \(F\)-statistics are sufficiently large enough to reject the null hypothesis that the estimates are equal and indicating that the direct relation between current short selling and both current returns and past returns is stronger for stocks that are least likely constrained. This is possibly explained by the idea that short sellers may have difficulty shorting stocks that are most likely constrained in attempt to profit from short-term price reversals. In columns (5) and (6), we find that the negative relation between current put-call ratios and both current and past returns is also driven by stocks that are least likely constrained. However, the significant negative relation is present in both subsamples.
Table 6

Panel regressions

 

Non-exempt short turnover

Exempt short turnover

Put-call ratio

 

High institutional ownership

Low institutional ownership

High institutional ownership

Low institutional ownership

High institutional ownership

Low institutional ownership

 

(1)

(2)

(3)

(4)

(5)

(6)

Intercept

\(-\)0.0132

\(-\)0.0322***

0.0267***

\(-\)0.0003

0.3970***

0.1796***

(0.339)

(0.000)

(0.000)

(0.856)

(0.000)

(0.000)

\(ret_{t}\)

1.4335***

0.5426***

0.0368***

0.0024

\(-\)1.0209***

\(-\)0.8168***

(0.000)

(0.000)

(0.000)

(0.442)

(0.000)

(0.000)

\(ret_{t-5,t-1}\)

0.4549***

0.1511***

0.0296***

0.0178***

\(-\)0.3899***

\(-\)0.3368***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(turn_{t}\)

0.2314***

0.1783***

0.0092***

0.0129***

0.0097***

0.0127***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(turn_{t-5,t-1}\)

0.0131***

0.0102***

0.0006***

0.0042***

0.0189***

0.0197***

(0.000)

(0.000)

(0.003)

(0.000)

(0.000)

(0.000)

\(rvolt_{t}\)

3.1071***

0.2166***

0.3034***

\(-\)0.1035***

0.2666

\(-\)0.0761

(0.000)

(0.000)

(0.000)

(0.000)

(0.121)

(0.175)

\(rvolt_{t-5,t-1}\)

\(-\)3.1499***

\(-\)0.6176***

\(-\)0.2315***

0.0198**

\(-\)0.1321

0.1472

(0.000)

(0.000)

(0.000)

(0.048)

(0.411)

(0.330)

\(pvolt_{t}\)

2.4455***

0.6162***

0.1516***

0.0882***

0.5330***

0.5195***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(pvolt_{t-5,t-1}\)

\(-\)0.9971***

\(-\)0.3624***

0.0071

0.0187**

\(-\)0.5011***

\(-\)0.0355

(0.000)

(0.000)

(0.594)

(0.024)

(0.004)

(0.754)

\(\hbox {Adj. } R^{2}\)

0.6824

0.6652

0.4305

0.4272

0.2268

0.2049

Stock fixed effects

Yes

Yes

Yes

Yes

Yes

Yes

Day fixed effects

Yes

Yes

Yes

Yes

Yes

Yes

\(\hbox {F-stat}_{Hi =Lo}^{ret}{}_{t}\)

108.61***

71.83***

23.89***

(0.000)

(0.000)

(0.000)

\(\hbox {F-stat}_{Hi=Lo}^{ret}{}_{t-5,t-1}\)

62.89***

40.81***

7.86***

(0.000)

(0.000)

(0.004)

The table reports the results from estimating the following equation

\(Activity_{i,t}= \beta _{0}+ \beta _{1} ret_{i,t}+ \beta _{2} ret_{i,t-5,t-1 }+ \beta _{3}turn_{i,t } + \beta _{4}turn_{i,t-5,t-1 }+ \beta _{5}rvolt_{i,t }+ \beta _{6} rvolt_{i,t-5,t-1 } + \beta _{7}pvolt_{i,t}+ \beta _{8} pvolt_{i,t-5,t-1}+ \varepsilon _{i,t}\)

The dependent variables and independent variables are defined as before. Again, two-way fixed effects estimates are reported with \(p\) values from robust standard errors although similar results are found using pooled OLS. We partition the sample into portfolios consisting of stocks with the highest level of institutional ownership [columns (1), (3), and (5)] and stocks with the lowest level of institutional ownership [columns (2), (4), and (6)] in order to determine whether stocks that are least likely constrained or stock that are most likely constrained drive our results. \(P\) values are reported in parentheses. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

Combined, Tables 4, 5 and 6 reveal an important asymmetry when comparing short-selling and put-option activity. While short sellers generally follow periods positive returns, put-option traders generally follow negative returns, which is robust to subsamples of stocks that most likely constrained and stocks that are least likely constrained. These findings question the level of information contained in put-call ratios. We attempt to further answer this question in the following subsection.

3.3 Return predictability of short-selling and put-option activity

While Pan and Poteshman (2006) document that stocks with high put-call ratios underperform stocks with low put-call ratios, in this subsection, we attempt to extend their findings and test theory that predicts that the information contained in options is driven by a migration of short sellers to the options market because high equity borrowing costs.8 The following equation is estimated using pooled data.
$$\begin{aligned} ret_{t+1,t+j}&= \beta _{0 } + \beta _{1}{ turn}_{i,t } + \beta _{2}{rvolt}_{i,t} + \beta _{3}{pvolt}_{i,t} + \beta _{4}{ ret}_{i,t-5,t-1} \nonumber \\&+\, \beta _{5}{Activity}_{i,t} + \varepsilon _{i,t+1,t+j} \end{aligned}$$
(3)
Following Pan and Poteshman (2006), the dependent variable is defined as the four-factor risk-adjusted return on day \(t+1\). For robustness, we also report results using the four-factor risk-adjusted return from day \(t+1\) to \(t+5\). Similar results are found for different values of \(j\). The independent variables are defined as before. The variable of interest is Activity, which is defined as non-exempt short turnover, exempt short turnover, and put-call ratios. After controlling for factors that influence next-day returns, prior research finds that both current shorting activity and current put-call ratios relate inversely with future returns (Diether et al. 2009; Pan and Poteshman 2006). Table 7 reports the results from estimating equation (3) using a two-way fixed effects regression in response to a Hausman test. Similar results are found using pooled OLS after controlling for conditional heteroskedasticity and clustering in the errors. Panel A presents the results when the dependent variable is defined as \({ret}_{t+1}\) while Panel B shows the results for the dependent variable \({ret}_{t+1,t+5}\). We note an important difference in Eq. (3) and similar tests in Diether et al. (2009). To compensate for the possibility of bid-ask bounce in their results, Diether et al. (2009) defined the dependent variable as the return on day \(t+2\). In unreported results, we follow this specification and find results that support the main conclusions documented in this paper.
Table 7

Panel regressions—next day returns

 

Non-exempt short turnover

Exempt short turnover

Put-call ratio

 

Full sample

High InstOwn

Low InstOwn

Full sample

High InstOwn

Low InstOwn

Full sample

High InstOwn

Low InstOwn

 

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Panel A. Dependent variable:\(ret_{t+1}\)

Intercept

0.0000

\(-\)0.0001

0.0000

0.0000

0.0000

0.0000

0.0001

0.0000

0.0001

(0.417)

(0.277)

(0.904)

(0.964)

(0.744)

(0.688)

(0.158)

(0.841)

(0.646)

\(turn_{t}\)

0.0887***

0.0689***

0.1348***

0.0288***

0.0289***

0.0348*

0.0304***

0.0336***

0.0297

(0.000)

(0.000)

(0.000)

(0.000)

(0.001)

(0.098)

(0.000)

(0.000)

(0.139)

\(rvolt_{t}\)

0.0054

0.0087

\(-\)0.0007

0.0067

0.0085

0.0018

0.0060

0.0088

0.0011

(0.347)

(0.194)

(0.966)

(0.247)

(0.204)

(0.907)

(0.299)

(0.189)

(0.945)

\(pvolt_{t}\)

\(-\)0.0124***

\(-\)0.0168***

\(-\)0.0102

\(-\)0.0144***

\(-\)0.0199***

\(-\)0.0118

\(-\)0.0152***

\(-\)0.0198***

\(-\)0.0125

(0.002)

(0.006)

(0.333)

(0.000)

(0.001)

(0.264)

(0.000)

(0.001)

(0.234)

\(ret_{t-5,t-1}\)

\(-\)0.0021**

\(-\)0.0018

\(-\)0.0028

\(-\)0.0028***

\(-\)0.0024*

\(-\)0.0036

\(-\)0.0030***

\(-\)0.0024**

\(-\)0.0038

(0.020)

(0.199)

(0.282)

(0.002)

(0.083)

(0.174)

(0.001)

(0.081)

(0.145)

\(sh\_{turn_{t}}\)

\(-\)0.2595***

\(-\)0.1455***

\(-\)0.5609***

      

(0.000)

(0.000)

(0.000)

      

\(E\_sh\_turn_{t}\)

   

\(-\)0.1055

0.2686

\(-\)0.4485

   
   

(0.412)

(0.165)

(0.358)

   

PC_ratio\(_{t}\)

      

\(-\)0.0443**

\(-\)0.0295*

\(-\)0.0478***

      

(0.000)

(0.056)

(0.007)

Adj. R\(^{2}\)

0.0065

0.0054

0.0081

0.0022

0.0031

0.0011

0.0024

0.0031

0.0020

Stock FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Day FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

F-Stat \(_{Hi=Lo}\)

50.10***

7.42***

1.02

(0.000)

(0.005)

(0.336)

Panel B. Dependent variable:\({ret}_{t+1, t+5}\)

Intercept

\(-\)0.0014***

\(-\)0.0018***

\(-\)0.0016***

\(-\)0.0012***

\(-\)0.0015***

\(-\)0.0017***

\(-\)0.0009***

\(-\)0.0012***

0.0015***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.001)

\(turn_{t}\)

0.1951***

0.1758***

0.2903***

0.0555***

0.0767***

\(-\)0.0209

0.0599***

0.0969***

\(-\)0.0378

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.632)

(0.000)

(0.000)

(0.352)

\(rvolt_{t}\)

0.0427***

0.0584***

0.0403**

0.0456***

0.0567***

0.0481*

0.0441***

0.0583***

0.0474***

(0.000)

(0.000)

(0.135)

(0.000)

(0.000)

(0.077)

(0.000)

(0.000)

(0.083)

\(pvolt_{t}\)

0.0045

\(-\)0.0189

0.0225

\(-\)0.0002

\(-\)0.0273**

0.0176

\(-\)0.0018

\(-\)0.0264**

0.0165*

(0.573)

(0.108)

(0.296)

(0.980)

(0.020)

(0.411)

(0.817)

(0.024)

(0.443)

\(ret_{t-5,t-1}\)

\(-\)0.0009

\(-\)0.0009

0.0043

\(-\)0.0024

\(-\)0.0026

0.0020

\(-\)0.0028

\(-\)0.0026

0.0016

(0.628)

(0.745)

(0.391)

(0.184)

(0.362)

(0.682)

(0.111)

(0.365)

(0.742)

\(sh\_turn_{t}\)

\(-\)0.6011***

\(-\)0.3362***

\(-\)1.7224***

      

(0.000)

(0.000)

(0.000)

      

\(E\_sh\_turn_{t}\)

   

\(-\)0.1847

1.2922***

\(-\)1.1390

   
   

(0.470)

(0.000)

(0.256)

   

\(PC\_ratio_{t}\)

      

\(-\)0.1010***

\(-\)0.1093***

\(-\)0.0494*

      

(0.000)

(0.002)

(0.257)

\(\hbox {Adj. } R^{2}\)

0.0089

0.0088

0.0173

0.0030

0.0071

0.0036

0.0044

0.0067

0.0033

Stock FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Day FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

F-Stat \(_{Hi=Lo}\)

113.00***

17.26***

2.21

(0.000)

(0.000)

(0.141)

The table reports the results from estimating the following equation

\(ret_{t+1,t+j} = \beta _{0} + \beta _{1}turn_{i,t }+ \beta _{2} rvolt_{i,t } + \beta _{3} pvolt_{i,t }+ \beta _{4}ret_{i,t-5,t-1 }+ \beta _{5} Activity_{i,t }+ \varepsilon _{i,t+1,t+j}\)

The dependent variables is the four-factor risk-adjusted return on day \(t+1\) (Panel A) and the four-factor risk-adjusted return from day \(t+1\) to \(t+5\) (Panel B). The independent variables are defined as before. The independent variable Activity is defined as non-exempt short turnover in columns (1) through (3), exempt short turnover in columns (4) through (6), and put-call ratios in columns (7) through (9). After estimating the equation for the full sample in columns (1), (4), and (7), we partition the sample into subsamples consisting of stocks with the highest level of institutional ownership [columns (2), (5), and (8)] and stocks with the lowest level of institutional ownership [columns (3), (6), and (9)] in order to determine whether stocks that are least likely constrained or stock that are most likely constrained drive our results. In response to a Hausman test, we report two-way fixed effects estimates with \(p\) values from robust standard errors although similar results are found using pooled OLS after controlling for conditional heteroskedasticity. \(P\) values are reported in parentheses. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

Panel A column (1) shows that, similar to both Diether et al. (2009), next-day returns are directly related to turnover. We also find some evidence that return (price) volatility is positively (negatively) related to next-day returns and that lagged returns are negatively related next-day returns. The latter result is similar to findings in Pan and Poteshman (2006). Consistent with Diether et al. (2009), we find that current short selling predicts negative next-day returns as the estimate for short turnover is \(-\)0.2595 (\(p\) value \(=\) 0.000). In columns (2) and (3), we report the results from estimating equation (3) for the subsamples of stocks capturing whether constraints have a higher likelihood of binding. Results show negative estimates for short turnover in both columns (2) and (3) although the short turnover estimate for stocks that are most likely constrained is 3.8 times more negative than the estimate for stocks that least likely constrained. An \(F\)-statistic, testing for equality between the two estimates is 50.10 (\(p\) value \(=\) 0.000), indicates that the return predictability of short-selling activity in stocks that are most likely constrained is higher than in stocks that are least likely constrained. This finding is consistent with theory in Diamond and Verrecchia (1987). Columns (4) through (6) show the results for exempt short turnover. When using the full sample, we do not find that exempt short selling is able to successfully predict negative next-day returns as the estimate is insignificant (\(p\) value \(=\) 0.412), which is consistent with results in Engelberg et al. (2010). This result is somewhat expected if exempt short selling is made up from hedging activity by market makers.

Columns (7) through (9) report the regression results for the put-call ratio. Consistent with findings in Pan and Poteshman (2006), we find that current put-call ratios are negatively related to next-day returns as the estimate is \(-\)0.0433 (\(p\) value \(=\) 0.000). This observation is consistent with the idea that information about future stock price movements is contained in put-call ratios. The objective of this test is to determine whether short-sale constraints drive informed investors from the stock market to the options market. If this assertion is true then the return predictability of put-call ratios should be driven by stocks that most likely to face binding short-sale constraints. The estimate for put-call ratios is \(-\)0.0295 (\(p\) value \(=\) 0.056) for stocks that are least likely constrained [column (8)] and \(-\)0.0478 (\(p\) value \(=\) 0.007) for stocks that are most likely constrained [column (9)]. While the estimate in column (9) is more negative, the \(F\)-statistic is not sufficiently large enough to reject equality of the two estimate (\(F\)-stat \(=\) 1.02, \(p\) value \(=\) 0.336). This result indicates that short-sale constraints do not drive the return predictability of put-call ratios and contradicts the argument that informed short sellers will migrate from the stock market to the options market when equity borrowing costs increase.

Panel B reports the regression results when the dependent variable is defined as the risk-adjusted return from day \(t+1\) to \(t+5\). Results in columns (1) through (6) are generally consistent with results reported in Panel A. In column (7), the put-call ratio also produces a significant negative estimate (estimate = \(-\)0.1010, \(p\) value \(=\) 0.000), which is consistent with Pan and Poteshman (2006) who document that the return predictability of put-call ratios lasts for more than a week. In columns (8) and (9), we find that the negative estimate for the put-call ratio is significant for both subsamples, but is more negative for stocks that are least likely to face binding constraints. However, the \(F\)-statistic is 2.21 (\(p\) value \(=\) 0.141), which is not significant at the 0.10 level. The results in Panel B are less supportive of the idea that short-sale constraints drive the return predictability contained in put-call ratios.

3.4 What drives the return predictability of short-selling and put-option activity

While Pan and Poteshman (2006) document significant return predictability in put-call ratios, they are only able to find some evidence that the information contained in put-call ratios is non-public. In Sect. 3.3, our results show that the return predictability of put-call ratios is independent of the severity of short-sale constraints. The source of the information contained in put-call ratios remains an empirical question. In this subsection, we take a step in this direction by testing whether the return predictability in put-call ratios depends on the recent short-term performance of the underlying stock. Results in Sect. 3.2 show that bearish option traders tend to follow periods of negative returns while short sellers are contrarian in past returns. While prior research argues that contrarian trading strategies are generally executed by informed traders (Campbell et al. 1993; Avramov et al. 2006), observing a negative relation between current put-call ratios and past returns is puzzling especially after showing that current put-call ratios are able to predict negative returns in Sect. 3.3. In this subsection, we test the idea that contrarian option trading strategies are more informed than momentum strategies by conditioning the return predictability of put-call ratios on the prior stock performance. In particular, we estimate the following equation using panel data.
$$\begin{aligned} {ret}_{t+1,t+j}&= \beta _{0 } + \beta _{1}{ turn}_{i,t } + \beta _{2}{ rvolt}_{i,t } + \beta _{3}{pvolt}_{i,t} + \beta _{4}{ret}_{i,t-5,t-1 } \nonumber \\&+\, \beta _{5}{ Activity}_{i,t } + \beta _{6}{ Activity}_{i,t} \times ret_{i,t-5,t-1 } + \varepsilon _{i,t+1,t+j} \end{aligned}$$
(4)
The dependent variables and independent variables are defined as before in Eq. (3). However, we interact Activity with lagged returns \((Activity_{i,t} \times ret_{i,t-5,t-1})\) in order to determine whether the common negative relation between current short selling/put-call ratios and next-day returns is strengthened by contrarian strategies. Recall that both non-exempt short turnover and put-call ratios relate inversely with next-day returns so if contrarian strategies strengthen the return predictability, the interaction estimate is expected to be negative.
Table 8 reports the results of the two-way fixed effects estimates.9 After controlling for other factors that influence next-day returns, we find that the interaction between non-exempt short turnover and lagged returns produces a negative estimate that is not reliably different from zero in column (1) (estimate \(=\) \(-\)0.2074, \(p\) value \(=\) 0.473). This results indicates that contrarian short selling drives the return predictability documented in Diether et al. (2009). Column (2) shows that the interaction between exempt short turnover and lagged returns produces estimates that are statistically similar to zero. Column (3) reports the results for the put-call ratio. We also find that the interaction between put-call ratios and lagged returns results in a negative estimate although the estimate is not reliably different from zero (estimate \(=\) \(-\)0.2701, \(p\) value \(=\) 0.366). Columns (4) through (6) report the results when the dependent variable is defined as the return from day \(t+1 \)to \(t+5\). Results are stronger as the interaction estimate for non-exempt short turnover is \(-\)0.8271 (\(p\) value \(=\) 0.069) and \(-\)1.9493 (\(p\) value \(=\) 0.002) for put-call ratios. Combined, the results in columns [4] and [6] show that the return predictability contained in both non-exempt short selling and put-call ratios is stronger after periods of positive returns. Said differently, trading profits to both short sellers and put-option traders appear to be captured during bull markets. This observation is particularly interesting as it relates to the results in Pan and Poteshman (2006) that show that put-call ratios predict negative returns. Our findings suggest that this result is driven by contrarian put-option strategies, which supports theory in Campbell et al. (1993).
Table 8

Panel regressions—next day returns

 

\(ret_{t+1}\)

\(ret_{t+1, t+5}\)

 

Non-exempt short turnover

Exempt short turnover

Put-call ratio

Non-exempt short turnover

Exempt short turnover

Put-call ratio

 

(1)

(2)

(3)

(4)

(5)

(6)

Intercept

0.0000

0.0000

0.0001

\(-\)0.0014***

\(-\)0.0012***

\(-\)0.0009***

(0.411)

(0.962)

(0.158)

(0.000)

(0.000)

(0.000)

\(turn_{t}\)

0.0886***

0.0288***

0.0303***

0.1946***

0.0556***

0.0593***

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

\(rvolt_{t}\)

0.0053

0.0067

0.0059

0.0424***

0.0455***

0.0437***

(0.354)

(0.246)

(0.302)

(0.000)

(0.000)

(0.000)

\(pvolt_{t}\)

\(-\)0.0124***

\(-\)0.0144***

\(-\)0.0152***

0.0046

\(-\)0.0002

\(-\)0.0020

(0.002)

(0.000)

(0.000)

(0.566)

(0.979)

(0.803)

\(ret_{t-5,t-1}\)

\(-\)0.0015

\(-\)0.0028***

\(-\)0.0022*

0.0017

\(-\)0.0018

0.0029

(0.228)

(0.005)

(0.093)

(0.484)

(0.368)

(0.274)

\(sh\_turn_{t}\)

\(-\)0.2578***

  

\(-\)0.5942***

  

(0.000)

  

(0.000)

  

\(sh\_turn_{t} \times ret_{t-5,t-1}\)

\(-\)0.2074

  

\(-\)0.8271*

  

(0.473)

  

(0.069)

  

\(E\_sh\_turn_{t}\)

 

\(-\)0.1074

  

\(-\)0.1667

 
 

(0.410)

  

(0.517)

 

\(E\_sh\_turn_{t}\times ret_{t-5,t-1}\)

 

0.2907

  

\(-\)2.7330

 
 

(0.903)

  

(0.524)

 

\(PC\_ratio_{t}\)

  

\(-\)0.0444***

  

\(-\)0.1014***

  

(0.000)

  

(0.000)

\(PC\_ratio_{t} \times ret_{t-5,t-1}\)

  

\(-\)0.2701

  

\(-\)1.9493***

  

(0.366)

  

(0.002)

Adj. \(R^{2}\)

0.0063

0.0024

0.0022

0.0083

0.0039

0.0043

Stock FE

Yes

Yes

Yes

Yes

Yes

Yes

Day FE

Yes

Yes

Yes

Yes

Yes

Yes

The table reports the results from estimating the following equation

\({ret}_{t+1,t+j}= \beta _{0}+ \beta _{1}turn_{i,t }+ \beta _{2} rvolt_{i,t} + \beta _{3}pvolt_{i,t} + \beta _{4}ret_{i,t-5,t-1}+ \beta _{5} Activity_{i,t }+ \beta _{6}Activity_{i,t} \times ret_{i,t-5,t-1 } + \varepsilon _{i,t+1,t+j}\)

The dependent variables is the four-factor risk-adjusted return from \(t+1\) to \(t+j\), where \(j = 1\) or 5. The independent variables are defined as before. The independent variable Activity is defined as non-exempt short turnover in column (1) and (4), exempt short turnover in columns (2) and (5), and put-call ratios in columns (3) and (6). In response to a Hausman test, we report two-way fixed effects estimates with \(p\) values from robust standard errors although similar results are found using pooled OLS after controlling for conditional heteroskedasticity. \(P\) values are reported in parentheses. ***,**,* Statistical significance at the 0.01, 0.05, and 0.10 levels, respectively

4 Summary

In this study, we examine the substitutability and return predictability of short sales and put-call ratios. Motivated by the theoretical argument that when short-sale constraints bind, informed short sellers will migrate from the stock market to the options market (Diamond and Verrecchia 1987; Danielsen and Sorescu 2001), the analysis in this paper finds that put-call ratios are negatively related, instead of positively related, to proxies of short-sale constraints indicating that short-sale constraints do not increase put-option activity. A possible explanation is that short-sale constraints are not binding or, perhaps, the leverage benefit options provide (Black 1975) is not enough to motivate short sellers to trade in the options market when short selling is costly.

When examining the informativeness of both short activity and put-call ratios, we first find an important asymmetry. While short sellers are generally contrarian in contemporaneous and past returns (Diether et al. 2009), results in this study show that put-option traders follow periods of negative returns possibly indicating that either put traders and short sellers trade on different information or a substantial portion of put activity is made up from long investors hedging against the downside as stocks prices begin to decrease. Either explanation makes the case for constraint-induced put-option activity less compelling.

Our final set of tests examines the negative relation between both short activity and put-call ratios and next-day returns. Similar to Diether et al. (2009), we show that current short selling is inversely related with future returns at the daily level. Furthermore, results in this study are similar to Pan and Poteshman (2006) as current put-call ratios also negatively related to next-day returns. However, we show that the return predictability of short selling is driven by short selling of stocks that are most likely constrained, which is consistent with theory in Diamond and Verrecchia (1987). Consistent with conclusions we draw from earlier tests, the common negative relation between current put-call ratios and future returns is not substantially different for stocks that most likely constrained and stocks that are least likely constrained. Results do show that the return predictability of both short-selling activity and put-call ratios is increasing in size of past returns indicating that contrarian trading strategies drive the return predictability of both short-selling activity and put-call ratios. To our knowledge, this study is the first to determine whether the information contained in put-call ratios depends on the severity of short-sale constraints in the stock market. Further, our findings provide some of the initial framework in determining what drives the return predictability found in put-call ratios.

Footnotes

  1. 1.

    Bodie et al. (2009) argue that during periods of down markets, investors are likely underhedged and therefore investors will attempt to purchase more put options to protect their long positions.

  2. 2.

    We note that not all option trading activity should be considered informative trading. Blau et al. (2014) show that the ratio of call option volume relative to put-option volume is directly related to characteristics of the underlying stock that resemble lotteries. These results suggest that some option activity might reflect investors’ preferences for lottery-like distributions. We follow Pan and Poteshman (2006) in order to isolate what might be considered informed option trading activity.

  3. 3.

    Bloomberg data contains volume for both call and put options across all strike prices and across all expirations.

  4. 4.

    We also examine the short ratio which is defined as the percentage of trading volume that is made up from short volume, which is commonly used in prior studies. Our results are qualitatively similar. In each of our regression specifications, we control for some form of trading activity so we prefer to result the short-turnover results for brevity.

  5. 5.

    We report CRSP raw returns in the paper. However, in unreported result we examine two types of market-adjusted returns. EW_adj_ret are CRSP raw returns less the equally weighted CRSP index return while VW_adj_ret are the CRSP raw returns less the value-weighted CRSP index return. The results using these alternative returns produce findings that are qualitatively similar to those reported in this paper.

  6. 6.

    An examination of hedging activity during bull and bear markets might be a fruitful area for future research. However, these tests are beyond the scope of this paper. See Bodie et al. (2009), p. 742, for example.

  7. 7.

    We also sort stocks by the other proxies of short-sale constraints and the results are generally similar with the exception of turnover sorts, which produce mixed results. The institutional ownership proxy is given a heavier weight based on arguments in D’Avolio (2002), Asquith et al. (2005), Nagel (2005), and Xu (2007).

  8. 8.

    Recent theory in Bakshi et al. (2010) suggesting that short selling can affect option prices. Here, we are examining both short selling and option activity on the prices of underlying securities instead of the prices on the options. While outside the scope of this study, perhaps a fruitful area for future research might be to examine the effect of short selling on option returns.

  9. 9.

    Similar results are obtained when using pooled OLS while controlling for conditional heteroskedasticity and clustering in the error terms.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Huntsman School of BusinessUtah State UniversityLoganUSA

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