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Speculation Spillovers
Yu-Jane Liu
Professor of Finance Guanghua School of Management
Peking University Beijing, China
Zheng Zhang Associate Professor of Finance
Guanghua School of Management Peking University
Beijing, China [email protected]
Longkai Zhao
Associate Professor of Finance Guanghua School of Management
Peking University Beijing, China
First draft: December 15, 2008 This version: October 9, 2010
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Speculation Spillovers
Abstract
This paper demonstrates that investor irrationality can be contagious across markets. Studies addressing the pros and cons of opening derivatives markets have failed to pay sufficient attention to the roles of speculative activities. This paper investigates how trading activities that are unrelated to fundamentals affect the impact of derivatives on stock markets. By using unique data from the Chinese warrants market, we document that there are speculation spillovers in an unsophisticated individual- dominated market. Our findings indicate that a higher turnover of underlying stocks is associated with higher unexpected warrants turnover and a larger price deviation of warrants from theoretical prices that cannot be fully attributed to better information revelation or hedging needs. We suggest that behavioral biases may contribute to the contagious speculation between warrants and stock markets. Our paper contributes the debate over derivatives by taking speculation behavior into account.
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I Introduction
There has always been a concern that the engineering of complex financial
derivatives is a double-edged sword. It provides market participants with low-cost,
low-margin, and high-liquidity instruments that they can trade on, thus facilitating
information flow with less market friction and helping to stabilize financial markets.
Danthine (1978) and Turnovsky (1983) present models in which futures markets are seen as
a stabilizing influence. However, Stein (1987) document how the introduction of a new
group of speculators into the spot market for a commodity (corresponding to the opening of
a futures or options market) can destabilize prices. The aforementioned inconsistency is
largely based on the implicit assumption that derivative traders are rational and sophisticated
(Danthine (1978), Turnovsky (1983), Stein (1987), Back (1993), and Kraus and Smith
(1996)).
As the recent financial turmoil involving credit derivatives shows, the same
convenient features of derivatives may encourage excessive speculations that lead to the
destabilization of financial markets. In a natural experimental environment, Xiong and Yu
(2010) study 16 put warrants in China. These put warrants are so deeply out-of-the-money
that their fundamental value is certainly zero. Xiong and Yu find that many
deep-out-of-the-money put warrants were traded at prices so high that they can only be
explained by irrational behavior. Complementarily, recent empirical evidence also suggests
that behavioral biases exist in derivatives markets (Heath et al. (1999), Poteshman (2001),
Horst and Veld (2008), Haigh and List (2005), Liu, Wang, and Zhao (2010)).
What are the impacts of behavioral biases in derivatives trading on the underlying
asset? This paper addresses this question by examining the impact of warrant trading in
China on the underlying stocks. We find that speculation in the warrants market has a
significant spillover effect on the underlying stocks. The underlying stocks are traded
significantly more after the introduction of warrants, and the stocks are traded more
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extensively when the warrant speculation is more severe. The increased stock trading cannot
be fully explained by reasons such as information and hedging. We also find that the
spillover effect is intensified when the divergence of investors’ beliefs is more pronounced.
Our results are consistent with the explanation that the resale option value for stocks
increases with the warrant bubble. Miller (1977), Harrison and Kreps (1978), and
Scheinkman and Xiong (2003) examine the case where short sales of assets are constrained
and investors hold heterogeneous beliefs about an asset’s fundamentals. They suggest that
prices may hold their value due to the possibility that an optimist expects to sell the asset at
an even higher price to even more optimistic investors. The institutional setting of China’s
stock market satisfies the two necessary ingredients of the resale option theory: short-sale
constraints and heterogeneous investors.
The Chinese stock markets were only recently reopened in the early 1990s after
being closed for nearly half a century. Investors in the Chinese market were not allowed to
sell short during our sample period. The markets are still under development, with only a
limited participation of institutions, and most domestic investors are individuals who are
new to stock trading and are likely to be subject to behavioral biases, including
overconfidence. Baily, Cai, Cheung and Wang (2009) document that individual investors in
China’s stock market are less informed and more subjective to behavioral biases than
institutional investors.
The introduction of warrants and the subsequent speculation on warrants may result
in a greater divergence of investors’ beliefs due to the following effects. First, a lack of
knowledge about warrants contributes to the dispersion of beliefs among stock investors.
The warrant was the first equity derivative in China’s capital market. Many investors, even
warrant investors, do not fully understand the nature of warrants. Although warrants’
fundamentals can be readily derived from the publicly observable underlying stock prices,
the derivation requires a sufficient degree of understanding about the warrant contracts.
Inference of information about underlying stocks from the warrant prices requires further
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sophistication. Because China’s warrants market is also dominated by inexperienced
individual investors and individual investors consistently generate more than 99.5% of
warrant transactions, the speculative nature of warrants makes the job even more difficult.
Harris and Raviv (1993) and Kandel and Pearson (1995) discuss that a dispersion of
heterogeneous beliefs can be generated when investors have different economic models that
lead them to interpret the news differently. Therefore, the complexity of warrants may create
another layer for the cause of heterogeneous beliefs.
Second, heterogeneous beliefs among stock traders may be attenuated by the
introduction and trading of warrants due to their limited attention, particularly for
unsophisticated investors. In China’s capital market, warrants, which are the only type of
equity derivative, attract media attention by constantly exhibiting extreme returns and
trading volume. Moreover, the warrants usually share the first two Chinese characters with
the underlying stocks in their trading ticker symbols.1 Therefore, the attention to warrants
might spread to the underlying stocks. There have been theoretical frameworks (Sims (2003),
Hirshleifer and Teoh (2003), and Peng and Xiong (2006)) and empirical studies (Barber and
Odean (2008), Hou, Peng, and Xiong (2009), Yuan (2008)) suggesting that limited attention
has an effect on stock returns. More attention to warranted stocks brings more investors and
exaggerates the heterogeneity of investors trading in the underlying stocks.
The speculation spillover can be explained by a greater divergence of beliefs among
stock traders, which is the consequence of limited attention and lack of warrants knowledge
when warrants are traded in frenzied speculation. Hong, Scheinkman and Xiong (2006)
develop a model that shows that the asset float (number of tradable shares) has a negative
effect on the size of the bubble. Following Hong et al. (2006), we develop tests to examine
the behavioral explanations of the speculation spillover. Our evidence supports Hong,
Scheinkman and Xiong’s (2006) model in that there is a weaker association between warrant
speculation and stock turnover when the share float of the underlying stock is larger. 1 For example, Wu Gang Gu Fen is a ticker symbol that consists of four Chinese characters. There were two warrants issued on this stock with ticker symbols of Wu Gang JTP1 (a put warrant) and Wu Gang JTB1 (a call warrant). These warrants share the first two Chinese characters in their ticker symbols.
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Another further examination relies on market optimism. When the market is
dominated by optimistic investors, the resale option value is higher, as the investors
anticipate that the possibility of reselling the asset in the future to even more optimistic
investors is high (Harrison and Kreps (1978), Scheinkman and Xiong (2003)). Our data
cover a sample period in which China’s stock market experienced both boom and rapid
decline. We find that in the bull market, the speculation spillover effect is much stronger
than in the bear market. In a bull market, optimists can drive out pessimists more easily,
which results in higher speculation spillover.
Still, there are other explanations for the association of warrant trading and stock
trading. Theoretical models (e.g. Back (1993), Stein (1987)) suggest that there are two
sources of linkages between stock markets and warrant markets: information and hedging.
Stock investors can infer information about the underlying stock from the warrant trading
when the warrant is a non-redundant option. In the present case, put warrants are
non-redundant due to the no-short-sale regulation in the underlying market. Investors can
learn more from put warrants; therefore, the speculation spillover effect should be weaker
for put warrants.
These reasons are unlikely to have a significant influence due to the market condition
in China. Warrants traders are individual investors who are less likely to possess private
information; the no-short-sale rule applies to both the stock market and the warrant market.
Nevertheless, we consider the information revelation and hedging in our investigation. We
consider the effect of hedging and information by including a proxy for information
revelation (put dummy) and hedge ratio in our aforementioned analysis.
Harrison and Kreps (1978), Morris (1996), Scheinkman and Xiong (2003), and Hong,
Scheinkman and Xiong (2006) all suggest that short-sale constraints prevent negative
information from being incorporated in prices. While short-sales are prohibited in the
Chinese stock market, the put warrant might be the only security that can be used to utilize
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negative information regarding the underlying stock. Therefore, put warrants might reveal
some negative information that cannot be realized in stock markets. The availability of put
warrants mitigates the short-sale constraint in the stock market, which may result in less
speculation in the underlying stock.
Additionally, investors may use warrants to construct option-like strategies, such as a
protective put strategy. They need to rebalance their position simultaneously in stock and
warrants markets. We calculate the hedge ratio using the Black-Scholes formula and take the
difference between the hedge ratios of two adjacent days as a variable, i.e., the Δhedge ratio.
If hedging is indeed the link between the stock market and the warrants market, there should
be a positive relationship between the Δhedge ratio and stock turnover. Our results confirm
that information transmission and hedging may explain a small proportion of the link
between stock trading and warrant trading. However, the speculation spillover still prevails
when these effects are controlled.
To completely rule out the possibility of the hedging and information effects, we also
examine the deep-out-of-the-money put warrants, which are similar to the sample used in
Xiong and Yu (2010). This sample is completely free from information and hedging effects;
these put warrants are so deeply out-of-the-money that their fundamental value is zero with
certainty. There is no information contained in these put warrants prices and there is no
hedging need at all. In this clean sample, we find that stock trading is still more intensive
when the warrant speculation is more severe. Therefore, we find that speculation spillover
exists when there is no information or hedging effect.
Our findings suggest that behavioral biases in one market can be transferred to
another one, resulting in a contagious speculation. Huberman and Regev (2001) document
that the contagious speculation exists in one market among different stocks. They examine
the stock-market behavior of a single biotechnology firm, EntreMed. A Sunday New York
Times article reports a potential cancer research breakthrough of EntrMed. The enthusiasm
spills over to other biotechnology stocks, even though there is no genuinely new information
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from the article. Our paper distinguishes from them in that this paper is the first study that
link behavioral biases in derivatives and in the underlying stocks. Besides, we are able to
highlight the mechanism through which the speculation is spilled over.
Our paper also contributes to the literature that examines the impact of speculations on
price. As surveyed by Mayhew (2000), researchers typically examine whether the
introduction of derivatives (or the expiration of derivatives) changes underlying market
characteristics, and they study lead-lag relationships between cash and derivative markets.
The empirical findings have not provided a firm conclusion. In fact, without further
exploring the sources of trading motivations, many empirical findings are difficult to
interpret. For example, some studies test whether volatility has changed and associate
increased volatility with destabilization. However, the interpretation is only justified if
changes in volatility are associated with noise trading rather than trading on information.
Our study corroborates these studies by highlighting investor irrationality in addition to
information and hedging as critical drivers of assets market transmission. Complementarily to
Xiong and Yu (2010), who point out “the large endogenous inflow of inexperienced investors as
an additional factor in prolonged price bubbles,” we find that price bubbles in the warrants
market cause more behavioral biases in the underlying stock market, thus creating a speculation
spillover effect.
In the next section, we introduce China’s warrants market. Section III presents our data
and empirical results. Section IV concludes.
II China’s Warrants Markets
China’s stock market was established around 1992,2 while derivatives appeared much
later. The establishment of China’s warrants market traces back to August 2005 when the
first warrant, BaoGang JTB1 (trading code 580000.SH), was issued. As the first derivative
2 Please see Mei, Scheinkman, Xiong (2009) and Baily, Cai, Cheung and Wang (2006), among others, for a thorough introduction of China’s stock market.
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product in China’s financial market, warrants quickly become a favorite target for
speculators. Less than three months later, on December 6, 2005, the total value of warrants
transacted reached 10.18 billion Yuan with only six warrants issued, whereas the total
trading volume of more than 1,300 listed stocks was just 7.89 billion Yuan on the same day.
In the first year after being issued, the trading volume of NanHang JTP1 (580989.SH) was
2,391.2 billion Yuan, which was nearly 10% of China’s GDP.
China’s warrants market surpassed that of Hong Kong in 20073 and has become the
largest warrants market in the world in terms of total trading value and number of
transactions. Noticeably, this extremely high transaction value was achieved with only 17
outstanding warrants in China by the end of 2007, whereas Hong Kong’s market has more
than 4,500 warrants.4
Warrant trading involves a commission fee but no stamp duty tax, which reduces
transaction costs by 50% compared to A-share trading. The T+0 rule, which states that
securities bought on day T can be sold the same day at the earliest, applies to warrant trading,
whereas the trading of stocks has to conform to T+1 rule. There is a price-limit rule in warrant
trading that is based on the absolute price, not the percentage price. The warrant price limit
usually is much larger than the stock price limit, which is usually 10% for A-share trading.
These features of warrant trading attract individual investors who trade heavily but are
inexperienced with warrants and possess less fundamental information than institutional
investors.
Various issues of the monthly report of the Shanghai Stock Exchange reveal that
institutional traders account for less than 0.2% of warrant trading. Individual investors
generate the most transactions in the warrants market due to their heavy trading. The reports
show that more than 50% of accounts have an asset turnover ratio higher than 500% and are
thus classified by the stock exchanges as dangerous or extremely risky groups. In our sample, 3 See Chan and Wei (2001) for an introduction to derivative warrants in Hong Kong. 4 Table 1 presents general statistics for the two markets. There are 34 warrants that were traded once in 2007, although not all warrants were traded during the whole year.
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the median of daily warrant turnovers is 0.540, which is much higher than the median of
daily stock turnovers (0.025).
Warrants are similar to options but issued and guaranteed by the company. In China’s
warrants market, so-called derivative warrants or covered warrants also exist. Covered
warrants, which are issued by an investment bank or a similar financial institution, allow the
holder to buy or sell a specific amount of equities from the issuer at a specific price and time,
whereas equity warrants are standard warrants issued by firms. In China, a covered warrant
can only be issued when a warrant is already issued by the company, and the covered
warrant has to have the same contract features as the original equity warrant. Under a
controversial rule, a covered warrant is traded under the same trading code as its
corresponding original equity warrant. Financial institutions frequently issue covered
warrants. For example, 1.4 billion shares of NanHang JTP1 (580989.SH) were originally
issued, but 12 billion more shares were later issued by 26 financial institutions. Unlike
options, individual investors cannot open a position by writing a warrant (or shorting a
warrant). However, the institutional setting of covered warrants enables institutional
investors to write warrants up to a quota approved by the stock exchange. At the same time,
the issuer of covered warrants can always buy back and write off warrants to an amount less
than its issuance or wait for expiration. This arrangement puts institutional investors in better
trading positions against individual investors in the warrants market, especially considering
that institutional investors are better informed. In fact, anecdotal evidence suggests that the
issuance of covered warrants generates great profits for institutional investors, who have no
interest in warrant trading at all. Noticeably, the exercise value of NanHang JTP1 was zero
on the expiration day, as was that of many other covered warrants.
Restrictions on short sales and the lack of other financial instruments make any attempt
to act or arbitrage on the price deviation from the fundamental caused by noise traders
extremely difficult, if not impossible, in China’s stock market. For the same warrant
mentioned in the previous example, the price was far above zero with one month left before
expiration. Because the price limit of 10% applies to the underlying stock, its value is
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already determined to be zero with certainty at that time. The limiting of arbitrage prevents
rational speculators from profiting on trades against noise traders.
Xiong and Yu (2010) analyze 16 put warrants that were so deep-out-of-the-money that
they were certain to expire worthless. Those warrants were traded with extremely high
turnover ratios and at substantially inflated prices. Xiong and Yu (2010) find evidence
supporting the resale option theory of bubbles: investors overpay for a warrant and hope to
resell it at an even higher price to a greater fool. They suggest that there exists a substantial
amount of inexperienced investors who lack an understanding of the warrant contracts.
China’s warrants market is a highly speculative market with individual investors as the
dominating player. Its institutional setting provides us an opportunity to directly study the
impact of speculation on the underlying market.
III. Empirical Investigation
Data
The warrant data used in this study are provided by WIND, which is a commercialized
financial data provider.5 The available information of warrant characteristics includes the
following: the trading code of the underlying stocks, the date of warrant listing (or issuance),
the expiration date of the warrant, whether it is an equity warrant or a covered warrant, the
call/put feature, the exercise price, and the stock exchange listed. We also collect daily
closing prices, the highest and lowest prices in a daily range, and the daily trading volume of
warrants. We also collect data about the A-share market capitalization.
In China’s warrants market, covered warrants can only be issued by investment banks
when an equity warrant already exists in the market. The newly issued covered warrants
5 We verify the data using other data providers such as SinoFin and CSMAR. The data are consistent.
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must have the same features as the existing equity warrant and are traded in the same stock
trading code. Investment banks receive their quota of warrant issuance after the approval of
the stock exchange. However, the exact date and size of their issuance to the market are not
publicly available. Still, we have daily data of warrants outstanding and thus can measure
warrant turnover.
As shown in Panel A of Table 2, warrants in the sample are issued on 41 underlying
stocks. In total, 23 of them have only the call feature, 12 firms have issued put warrants, and
6 firms have issued both call and put warrants. In Panel B, the dataset consists of the
complete observations of 50 warrants that are listed in Shanghai Stock Exchange and
Shenzhen Stock Exchange between August 2005 and June 2008. In total, 32 warrants are
equity warrants, and 18 warrants are covered warrants6. For equity warrants, there are more
call warrants (25) than put warrants (7). Out of 10 covered warrants, 7 have a call feature.
The speculative component is the non-fundamental component in stock prices. Mei,
Scheinkman, and Xiong (2009) examine the Chinese A-B share premium and find that the
share turnover rate of A-share can explain a large portion of the cross-sectional variation in
the A-B share premium. A-shares, which can only be held by domestic investors, and
B-shares, which can only be traded by foreigners, have identical rights. The A-B share
premium largely captures the non-fundamental component. Mei, Scheinkman, and Xiong
show that the importance of A-share turnover in explaining the A-B share premium is not
substantially affected by factors such as market capitalization and various risks and is not
due to liquidity. Hong and Stein (2007), Scheinkman, Xiong and Hong (2004), and Hong
and Yu (2009) also use turnover to measure speculation. In this paper, we will use A-share
turnover as the measure of speculation in the underlying market.
6 Covered warrants are trading in the same trading codes with their corresponding equity warrants. Therefore, the covered warrants here are referring to the covered warrants that can be issued. In fact, all of the equity warrants that are eligible for covered warrants issuance have been issued with covered warrants in our sample.
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Descriptive statistics
In Table 3, we report the descriptive statistics of the variables used in our study.
Normally, warrants issued by Chinese companies are of a long tenure of one or two years.
Panel B of Table 3 shows that the average tenure of warrants in our sample is 1.3 years. In
China’s warrants market, the warrants’ prices are always much higher than their theoretical
prices. To measure the difference, we define the variable implied price difference (IPD) as
)__
__log(priceltheoreticawarrant
pricemarketwarrantIPD = .
For each warrant, we calculate the daily IPDs and then take the average as the warrant’s IPD.
The average warrant’s IPD is 1.32 in our sample, which means that on average, warrants are
traded at 3.74 times their theoretical prices. The minimum IPD is 0.035, which means the all
warrants are priced above the Black-Scholes model. Most of the warrants are nominally
Bermudan but essentially European options, as they can only be exercised within five days
of their maturity. Thus, we use the Black-Scholes option pricing formula to calculate
theoretical prices, with volatility defined as the standard deviation of daily stock returns in a
250 trading period ending 10 days before the warrant announcement. We admit that the
Black-Scholes model may not be the perfect model, given its strict assumptions. We also
tried other trading periods to calculate the volatility. The results are similar in scale and do
not change our subsequent results. In addition, WIND also reports similar IPD but without
explicit explanation of the model used. We use the IPD measure in WIND for a robustness
check, and it provides similar results.
Warrants exhibit a high turnover rate. On average, 65.4% of outstanding warrants are
traded every day, whereas the turnover rate of the underlying A-shares is only 2.3%. Warrant
trading also appears to be more volatile. We use two measures of volatility: Vol1 is the
standard deviation of daily stock (or warrant) returns in the sample period, and Vol2 is the
daily price range normalized by the daily closing price. In both measures, the volatility is
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much higher in warrants than it is in stocks.
In Figure 1, we plot the average weekly stock turnover and warrant turnover in our
sample. The average warrant turnover peaks almost at the same time as the average stock
turnover. Simple observation suggests a positive association between warrant turnover and
stock turnover. We further equally divide our sample to three groups according to the
average daily warrant turnover over each half year and plot the corresponding average daily
stock turnovers of the three groups. The pattern in Figure 2 clearly indicates that high
warrant turnover is always associated with high stock turnover.
Introduction of warrants
To explore whether the introduction of warrants affects the turnover of underlying
stocks, we examine the change of stock turnovers around the introduction of warrants. We
choose the listing date as the event date. Chan and Wei (2001) study both issuance
announcement and listing. However, in our sample period, the issuance announcement of
equity warrants is associated with Non-Tradable Shares (NTS) reform.7 It is difficult, if not
impossible, to highlight the effect of warrants from the announcement.
We formulate three pre-event periods, i.e., (-45, -15), (-90, -30), and (-180, -30), and
three symmetric post-event periods around event day 0. We avoid days close to the event day
and adopt long pre-event and post-event periods for several reasons. First, in NTS reform,
public investors are compensated with additional shares, which are also listed with warrants
at the same time. Second, we are more interested in the long-term or permanent effects.
Third, investment banks usually issue covered warrants within the first two weeks of listing.
To account for possible market-wide phenomena, we adjust our measure of turnover by
subtracting the corresponding industry median.
7 NTS refers to the process in which Chinese State-Owned Enterprises (SOEs) offer additional shares or funds to private investors as compensation for potential losses in the value of their portfolios when these SOEs free all their previously non-tradable shares. Li, et al. (2010) have provided detailed research on this issue.
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Table 4 reports the results. Panels A, B and C of Table 4 show the pre-event and
post-event adjusted turnovers of the underlying stocks and their differences with the
significance reported. For each warranted stock, we calculate its average turnover in the six
windows specified above and report the mean of 41 stocks’ average turnover. An unpaired
two-sample t-test is then used to examine the significance of the difference between the pre-
and post-event periods with the same length.
We find that the adjusted turnover of warranted stocks increases significantly in the
post-event periods. For example, in the full sample (Panel A of Table 4), the adjusted
turnover increases by more than 50% in the 30-day window, which is highly significant.
Similar observations can be found for both call warrants and put warrants. The increase in
turnover is generally more significant for put warrants than for call warrants. For example,
when comparing the window (-45, -15) to (15, 45), the adjusted turnover almost doubles for
stocks with put warrants, whereas the counterparty for call warrants increases by only 30%.
This finding is not very consistent with the information effect introduced by warrants. If the
information effect dominates, put warrants ideally can convey negative information better
than call warrants and thus are more likely to ease speculation in stocks. What we find here
is the opposite.
Overall, in the comparison between the pre-event and post-event period, we see some
evidence that warranted stocks are traded much more.
Speculation spillover
We use 41 warranted stocks as the sample in our analysis. For each stock, to measure
how actively warrants are traded, we construct a variable, warrant turnover, that is calculated
as the trading volume divided by the outstanding warrants shares. IPD is used as a measure
of the speculative extent for warrants. To control the time-series pattern of warrant turnover
and IPD, we run the auto-regression of both warrant turnover and IPD with a one-day lag
and take the residuals as unexpected warrant turnover and unexpected IPD, respectively. The
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results are not sensitive to the choice of lags.
To control other factors, we construct a covered dummy that is set to be 1 if the stock
has a covered warrant and 0 otherwise. We control the number of days left before the
warrant’s expiration (warrant duration). We also include stock liquidity (see Amihud (2002)),
stock market capitalization (the natural logarithm of a firm’s market capitalization), market
volatility, stock market turnover, and industry dummies. When applicable, variables are on a
daily basis.
The correlations of the variables are presented in Table 5. Table 5 shows that IPD and
warrant turnover is highly correlated, which is consistent with Xiong and Yu (2010). The
correlation coefficient between unexpected warrant turnover and warrant turnover is 0.551,
which suggests that a large proportion of warrant turnover cannot be predicted from the past.
This is also the case for IPD.
In the sample that consists of 41 warranted stocks, we run a pooling regression. The full
specification of the model is as follows:
iitittit SWY εββα +++= 21 .
Here, we choose the stock turnover rate as the dependent variables. Sit stands for a vector of
control variables including the covered dummy, warrant duration, stock liquidity, stock
market capitalization, market volatility, stock market turnover, and industry dummies. Wit is
a vector of independent variables of interest, including unexpected warrant turnover and IPD,
among others, in various specifications.
The results are shown in Table 6. In all specifications, the coefficients of unexpected
warrant turnover are significantly positive, which suggests that higher stock turnover is
positively associated with higher warrant turnover. For example, the coefficient of
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unexpected warrant turnover is 0.385 with a t-statistic of 12.2 in specification (1). The
inclusion of control variables does not change the result. Similarly, the coefficients of
unexpected IPD are also significantly positive in all specifications. The results suggest that
stock turnovers are positively associated with warrant turnovers and the speculation of
warrant prices.
For the control variables, the coefficient of the covered dummy is negative, which
suggests that allowing institutional investors to issue new warrants eases the speculation in
stocks. The original intention of regulators for covered warrants was to increase the supply
of warrants and ease the speculation in the warrants market. However, the results here
suggest that covered warrants also have a similar impact on stock speculation. The
coefficient of the warrant duration is significantly positive. There has been no rational model
suggesting this relationship. Time-to-maturity as an exogenous contracting feature may only
affect the value of warrants in option-like pricing models. However, it is consistent with the
argument that a larger duration may allow a greater diversity of opinion regarding the value
of warrants, which results in a steeper downward-sloping demand curve for stocks (Hong,
Scheinkman, and Xiong (2006)). For a steeper downward-sloping demand curve, demand
shocks without information content can cause higher price fluctuations.
Information and hedging effect
There are several reasons that the trading in the warrants market may affect the trading
of the underlying stocks: warrants may reveal more information about the underlying stocks,
and investors may simultaneously trade stocks and warrants for risk management purposes
or hedging. To consider information and hedging effects, we construct a put dummy variable.
The put dummy is set to be 1 if the stock has a put warrant and 0 otherwise. Because short
selling is prohibited, put warrants might be the only security that can be used to utilize
negative information regarding an underlying stock. Therefore, put warrants might reveal
some negative information that cannot be realized in stock markets. The availability of put
warrants mitigates the short-sale constraint in the stock market, which may result in less
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speculation in the underlying stock. If this is the case, we expect to see a negative sign
before the put dummy.
Regarding the hedging effect, we calculate the hedge ratio using the Black-Scholes
formula and take the absolute value of the difference between the hedge ratios of two
adjacent days as a variable, i.e., the Δhedge ratio. If hedging is indeed the link between the
stock and warrants market, we expect to see a positive sign for the Δhedge ratio. The results
are shown in Table 7.
Table 7 consists of various panels depicting the information effect and the hedging
effect. In Panel A, we examine the information effect, and the results show that the
coefficients of the put dummy are significantly negative in all specifications. This implies
that stocks with put warrants have lower turnover, which might be because put warrants can
reveal negative information that cannot be achieved by other stocks. Noticeably, in
specifications (3) and (4), the coefficients of unexpected warrant turnover and unexpected
IPD remain significantly positive, which suggests that the information effect cannot fully
explain the association between warrant trading and stock trading.
Regarding the hedging effect, the coefficients of the Δhedge ratio are positive in Panel
B, as we expect. Similar to the result of the information effect, inclusion of the hedging
effect does not alter the result that unexpected warrant turnover and IPD are significantly
positively associated with stock turnovers. In Panel C, specifications (9) and (10) include
both the information effect and the hedging effect. The coefficients of warrant turnover and
IPD are still positive and significant in both specifications.
To completely rule out the effect of information and hedging, we adopt the sample used
by Xiong and Yu (2010) to re-run the above analysis. The advantage of their sample is that
there is no need for any information or hedging concern. Xiong and Yu’s (2009) sample
consists of 16 put warrants that are so deep-out-of-the-money that they will certainly expire
worthless. One measure that they use to quantify the warrants’ fundamental value is based
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on the Black-Scholes model. They only include a warrant when its Black-Scholes value
drops to economically negligible levels below half of the minimum trading tick of 0.1
pennies. A Black-Scholes value of less than 0.05 pennies is a reliable indication that the
warrant only has a tiny probability, if any, of being in the money at expiration and that it has
virtually no value, especially when the 10% price limit rule applies.
In this sample of warrants, the underlying stocks should receive no information
regarding the stock value from the warrants, as the warrant price is purely the speculative
bubble. Additionally, the hedging need does not exist, as the hedge ratio is fixed. Here, we
replace IPD with the warrant price. The results are shown in Table 8. In this sub-sample,
without the concerns of information and hedging, the warrant turnover and the extent of
warrant speculation are still positively associated with stock turnover. The coefficients are
significantly smaller than those in the previous case. The linkage of information or hedging
between two markets is irrelevant here. Still, the stock turnover is positively associated with
speculation in warrants.
Overall, in the multivariate analyses, we find that when warrants are traded more
frequently and warrants are more speculative, the turnover of stocks is higher. The
speculation spillover remains when information revelation and hedging are considered.
Behavioral explanations
What is the channel for the speculation spillover? How does the speculation spillover
happen? The warrants market introduces a new group of speculators into the market. Stein
(1987) develops a model that shows that even when all agents are rational and risk-averse
competitors who make the best possible use of their available information, their trading can
create a misinformation effect. This effect can result in more noise in stock prices. The
warrants market and the stock market are often considered to be two segmented markets by
practitioners in China. Warrant traders are mostly individual investors who often do not trade
in the underlying market at all. The usual link suggested by the aforementioned theoretical
18
models loses its ground in this unique market.
Xiong and Yu (2010) demonstrate that the resale option theory can explain the trading
behavior in China’s warrants market. The institutional setting of China’s warrants market
satisfies the two necessary ingredients of the resale option theory: short-sales constraints and
heterogeneous investors. Miller (1977) suggests that in a static setting, the asset’s price is
biased toward the optimists’ belief. Harrison and Kreps (1978) show that in a dynamic
setting, an optimist is willing to pay more than his already optimistic belief of asset
fundamentals, anticipating the possibility to resell the asset in the future to even more
optimistic investors. Scheinkman and Xiong (2003) show that overconfident investors trade
assets with each other under short-sales constraints. Their continuous-time model provides a
sharp prediction that the magnitude of the price bubble is positively correlated with trading
frequency.
The observed speculation spillover can also be explained by the resale option theory.
There also exist heterogeneous investors and short-sales constraints in China’s stock market.
The introduction and trading of warrants exaggerate the conditions through several
mechanisms, including the limited attention of investors and their lack of sophistication.
Kahneman (1973) suggests that attention is a scare cognitive resource and that investors
have limited attention. Sims (2003), Hirshleifer and Teoh (2003), and Peng and Xiong (2006)
develop theoretical framework in which limited attention can affect asset pricing statics and
dynamics. Various measures have been used for investor attention, including extreme returns
(Barber and Odean (2008)), trading volume (Barber and Odean, 2008, and Hou, Peng, and
Xiong, 2009), and news and headlines (Barber and Odean, 2008, and Yuan, 2008). Warrants
have all of the above characteristics in China’s capital market. More importantly, the
underlying stocks usually share the first two Chinese characters with the warrant in their
trading tickers. The attention to the warrant may spread to the underlying stock. Hong and
Stein (2007) suggest that limited attention can lead to disagreement among investors.
19
Even if a given piece of news is made publicly available to all investors simultaneously,
and even if they all pay attention to it, the news can nevertheless increase their disagreement
about the fundamental value of the stock in question. As Harris and Raviv (1993) and
Kandel and Pearson (1995) discuss, this outcome will occur if investors have different
economic models that lead them to interpret the news differently. The warrant is the first
type of derivative introduced to China’s capital market. Even many warrant traders do not
fully understand the nature of warrants (Xiong and Yu (2010)). Stock investors are more
likely to form heterogeneous priors (Hong and Stein (2007)).
Although Xiong and Yu (2010) provide a natural experimental environment to study the
resale option theory, this case is rare and unrepresentative. The introduction of warrants can
serve as an exogenous shock to the resale option of stock speculation, as warrant trading
exaggerates the extent of heterogeneous belief among stock investors and attracts more
attention. An indirect test of the resale option theory in stock markets would test the
hypothesis that the speculation spillover effect should be stronger when the condition for the
high resale option is better met.
To formally test this hypothesis, we choose two conditional variables that contribute to
the value of resale option. The first is asset float. Hong, Scheinkman and Xiong (2006)
develop a model to show that asset float (the number of tradable shares) has a large effect on
the size of bubble. The implication is that there exists a negative relationship between resale
option value and asset float. If the mechanism of speculation spillover is consistent with our
argument above, we expect to see a stronger speculation spillover effect when the stock has
a smaller float as well. In Table 9, we construct an interaction between asset float and
warrant turnover (IPD). We expect that a larger float reduces the speculation spillover, or the
sign of the interaction should be negative. The results show that warrant turnover and IPD
are positively associated with stock turnover; therefore, the speculation spillover effect
exists. However, the effect is reduced when the stock has a larger asset float. The interaction
is always negative in all specifications.
20
The second conditional variable we look into is market sentiment. When the market is
dominated by optimistic investors, it is easier to drive out pessimists. The resale option value
is higher (Harrison and Kreps (1978), Morris (1996), Scheinkman and Xiong (2003), and
Hong, Scheinkman and Xiong (2006)). Our data period covers the historical bull market in
China’s stock market as well as the significant decline that followed. China’s stock market
experienced a historical bull run from 2005 to mid 2007. In this period, the Shanghai
Composite Index increased from 998 to 6,124, reaching its highest point in its history. The
market quickly dropped after that. By the end of our sample period, the index was around
2,736. We thus divide our sample into a bull market and bear market period using October
16, 2007 as the cutting point.
We compare the speculation spillover in two market conditions and present the results
in Table 10. For unexpected warrant turnover, the speculation spillover is significantly
positive in both market conditions. However, the coefficient in the bull market period (0.372)
is significantly larger than that in the bear market (0.250). More interestingly, in the bear
market period, IPD, with a coefficient of -0.082, is no longer positively associated with
stock turnover. In the meanwhile, in the bull market, IPD is still significantly positive. Table
10 shows that the speculation spillover effect is stronger when the market is driven by
optimistic beliefs, which is consistent with the resale option theory.
Our investigation suggests that the speculation spillover effect between the warrants
market and the stock market is stronger when the underlying stock has a smaller float and
the market is optimistic in general. The findings are not affected by the information effect or
hedging but rather serve as evidence that the speculation spillover is essentially a result of
trading behavior due to increased heterogeneity among stock investors caused by warrant
trading.
V Conclusion
Behavioral biases have been found in both stock markets and derivatives markets. In
21
this paper, we demonstrate that the behavioral bias can be contagious across markets, where
speculation in the warrants market spreads to the underlying stock market. After the
introduction of warrants, the underlying stocks experience significant increases in their
trading activity. Furthermore, stock turnover is positively associated with warrant turnover
and the warrant bubble. This spillover effect is sustained when we consider the link between
two markets due to the information effect and hedging. In a robustness test with a sample
similar to that of Xiong and Yu (2010), the speculation spillover effect is strong, even though
information or hedging is not a relevant concern there.
We argue that the speculation spillover may be the result of increased behavioral biases
in stock trading introduced by the warrant bubble. Xiong and Yu (2010) demonstrate some
extreme cases where warrants were traded at significantly high prices despite having true
values closer to zero. We further show that China’s warrants are traded very speculatively
and the frenzied speculation in the warrants market creates some side effects for stock
traders. Information from the warrant trading, if there is any, is very difficult to interpret,
which may result in a higher heterogeneity of investor beliefs when investors trade stocks
with this information. Nevertheless, most investors in China’s stock market are not
sophisticated enough to understand the link between warrants and their underlying stocks. At
the same time, warrant trading may attract more attention of stock traders. Attention
combined with a lack of knowledge about warrants may create an investor base with a
significant divergence of opinions. According to past studies, these side effects contribute to
the increase of the resale option value of stocks (Harrison and Kreps (1978), Morris (1996),
Scheinkman and Xiong (2003), and Hong, Scheinkman and Xiong (2006)).
Our study provides a test of the resale option theory by examining the exogenous
influence of warrant speculations on stock trading. We test the incremental part of the resale
option value, if it exists, due to the increased heterogeneity caused by warrant trading, as
discussed above. We find that the speculation spillover is stronger when the underlying stock
has a small asset float or when the market is filled with pessimistic sentiment. These
findings are consistent with the resale option theory.
22
Our findings encourage more discussion on the design of financial derivatives in the
financial market. In a market dominated by individual investors and still in the early age of
development, a new financial instrument may not evolve as planned. It is not only the
structure of the financial product but also the potential users that will decide its fate. Our
study highlights the necessity of considering behavioral factors in the design of derivatives.
23
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This table compares the market of China and Hong in general. The table is constructed using the information in Hong Kong Stock Exchange Fact Book 2007, Shanghai Stock Exchange Fact Book 2007, and Shenzhen Stock Exchange Fact Book 2007. Under China (mainland), the data are the sum from Shanghai and Shenzhen stock exchanges. Hong Kong’s data have been converted from Hong Kong Dollar to RMB if applicable at the exchange rate of 1 RMB Yuan for 0.94 HK $. For both markets, we list the statistics for all securities, warrants, and the percentage of warrants as of all securities.
27
China (mainland) Hong Kong
All Securities Warrants Percentage All Securities Warrants Percentage
No. of Listings 1993 17 0.85% 5896 4512 76.53%
Tradable Market Capitalization (in Billion RMB Yuan) 11,418.79 22.17 0.19% 20,536.46 703.87 3.43%
Trading Volume (in Billion) 7,363.97 3,523.43 47.85% 22,913.22 - -
No. of Transactions (in Million) 2753.34 261.29 9.49% 148.31 1.01 0.68%
Trading Value (in Billion RMB Yuan) 56,308.14 7,782.76 13.82% 21,560.27 4,698.96 21.79%
Table 1 General information of China’s and Hong Kong’s market
Table 2 Sample distribution This table reports the sample distribution. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. Equity warrant is a standard warrant issued by a listed company. Covered warrant is a warrant that can be issued by investment banks. Panel A: The number of sample firms with warrant issue
Number of Sample Firms With Call Warrants Issue 23 With Put Warrants Issue 12 With Call and Put Warrants Issue 6 Total Number of Sample Firms 41
Panel B: The number of warrants.
Covered warrants Equity warrants Call Warrant 7 25 Put Warrant 11 7 Total Number of Warrants 18 32
28
Table 3 Summary statistics This table reports the descriptive statistics of the sample. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. We collect the variables of the warrants characteristics and the warranted stocks information on a daily basis except for the volatility. Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Turnover is the trading volume divided by the total tradable shares. Volatility is defined in two ways: the first one is the standard deviation of stock returns for the life of warrants; the second is the daily price range defined as (the highest price-the lowest price)/the closing price. Duration is the time left to maturity for warrants. (days/365) IPD is defined as log(warrant market price-warrant theoretical price), where the warrant theoretical price is calculated using the Black-Scholes model with the volatility as the standard deviation of stock returns in a 250-day trading period ending 10 days before the listing of a warrant. Mean, median, maximum, minimum, 10th percentile, 25th percentile, 75th percentile, and 90th percentile of variables are reported. Panel A reports the variables of the warranted stocks. Panel B reports the variables of the warrants. Panel A: Statistics of warranted stocks
Market Cap (Million Yuan) Turnover Volatility
(Standard deviation) Volatility
(Daily price range)Mean 21,452 0.024 0.035 0.049 Median 12,574 0.025 0.034 0.049 Max 113,434 0.050 0.041 0.062 Min 1,631 0.008 0.027 0.038 P10 5,171 0.014 0.030 0.043 P25 7,886 0.017 0.033 0.046 P75 24,385 0.028 0.037 0.051 P90 48,653 0.032 0.039 0.054
Panel B: Statistics of warrants
Duration (Year) IPD Turnover Volatility
(Standard deviation)Volatility
(Daily price range) Mean 1.3 1.316 0.654 0.086 0.069 Median 1.0 0.719 0.540 0.080 0.068 Max 2.0 6.077 1.689 0.185 0.119 Min 0.5 0.035 0.062 0.041 0.051 P10 1.0 0.116 0.242 0.052 0.055 P25 1.0 0.280 0.417 0.059 0.059 P75 2.0 1.625 0.829 0.106 0.076 P90 2.0 4.096 1.201 0.115 0.082
29
30
Table 4 Pre- and post-event comparison for turnover effects This table reports the difference of the turnover for the underlying stocks between pre- and post-listing of the warrants. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. For each warrant, we identify its listing date as the event date. Around the event date 0, we construct three pre-event windows (-45, -15), (-90, -30), and (-180, -30), and symmetrically three post-event windows: (15, 45), (30, 90), and (30, 180). Turnover is the trading volume divided by the A-shares outstanding. Adjusted turnover is defined as the turnover subtracted by the industry median. For each window, we report the mean. We also report the difference of means for two symmetric pre- and post-event windows. A t-test is used for reporting significance. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Panel A reports the comparison of the turnover in the full sample. Panel B reports the results in the sub-categories of the call and put warrants. Panel C reports the comparison of the turnover in the sub-categories of covered and non-covered warrants. Panel A: Stock turnover: full sample Adjusted Turnover Pre Event Post Event Difference (-45,-15)vs. (15,45) 0.0177 0.0272 0.0095*** (-90,-30)vs. (30,90) 0.0157 0.0250 0.0093*** (-180,-30)vs. (30,180) 0.0186 0.0261 0.0075***
Panel B: Stock turnover: call and put Adjusted Turnover Pre Event Post Event Difference With Call (-45,-15)vs. (15,45) 0.0203 0.0262 0.0058* (-90,-30)vs. (30,90) 0.0185 0.0263 0.0076** (-180,-30)vs. (30,180) 0.0237 0.0268 0.0028
With Put (-45,-15)vs. (15,45) 0.0143 0.0285 0.0141*** (-90,-30)vs. (30,90) 0.0120 0.0234 0.0114*** (-180,-30)vs. (30,180) 0.0118 0.0252 0.0134***
Panel C: Stock turnover: covered and non-covered Adjusted Turnover
Pre Event Post Event Difference Covered (-45,-15)vs. (15,45) 0.0186 0.0259 0.0073** (-90,-30)vs. (30,90) 0.0170 0.0257 0.0087*** (-180,-30)vs. (30,180) 0.0217 0.0265 0.0045
Non covered (-45,-15)vs. (15,45) 0.0160 0.0297 0.0137*** (-90,-30)vs. (30,90) 0.0132 0.0237 0.0104*** (-180,-30)vs. (30,180) 0.0123 0.0254 0.0131***
31
Table 5 Correlation This table reports the correlation of the variables of the warrants and the stocks. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. Warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. IPD is defined as log(warrant market price-warrant theoretical price), where the warrant theoretical price is calculated using the Black-Scholes model with the volatility as the standard deviation of stock returns in a 250-day trading period ending 10 days before the listing of a warrant. Unexpected IPD is the residual of the auto-regression of IPD with one-day lag. Warrant duration is the time left to maturity for warrants (days/365). Stock turnover is the trading volume divided by the total tradable shares. Δhedge ratio is the absolute value of the difference of hedge ratios between two adjacent days, where the hedge ratio is derived from the Black-Scholes model. Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. The variables are in daily basis. ***, **, and * indicate significance level at the 1%, 5%, and 10%, respectively.
Unexpected
Warrant Turnover
IPD Unexpected IPD ΔHedge Ratio Warrant
Duration Stock Market
Cap Stock Liquidity
Warrant Turnover 0.551*** 0.476*** 0.298*** 0.107*** -0.136*** 0.040*** 0.022* Unexpected Warrant Turnover 0.148*** 0.126*** 0.073*** -0.037*** 0.016 0.002 IPD 0.612*** -0.116*** -0.237*** 0.210*** -0.057*** Unexpected IPD -0.044*** -0.139*** 0.093*** -0.021* ΔHedge Ratio 0.125*** -0.242*** 0.342*** Warrant Duration -0.088*** 0.095*** Stock Market Cap -0.322***
32
Table 6 Multiple regression: Speculation spillover This table reports the results of the regression specifications. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. Stock turnover is the trading volume divided by the total tradable shares. As for the independent variables, warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. Covered dummy is set to be 1 if the stock has a covered warrant and 0 otherwise. Warrant duration is the time left to maturity for warrants (days/365). Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Stock liquidity is defined as the absolute daily stock return divided by the daily trading value in billions RMB. Market turnover is the total stock turnover of the market. The stock turnover and the market turnover have been multiplied by 100. Industry dummies are included. The variables are in daily basis. T-statistics of coefficients are reported in parenthesis. (1) (2) (3) (4)
Intercept 0.304 0.198 8.600 8.235 (5.483) (3.547) (17.623) (16.623)
Unexpected Warrant Turnover 0.385 0.402 (12.182) (13.266)
Unexpected IPD 0.347 0.189 (10.276) (5.619)
Covered Dummy -0.192 -0.204 (-5.149) (-5.405)
Warrant Duration 0.445 0.395 (13.681) (11.781)
Stock Market Cap -0.365 -0.350 (-17.380) (-16.453)
Stock Liquidity -7.153 -6.966 (-14.942) (-14.439)
Market Turnover 0.654 0.685 0.667 0.687 (62.766) (64.588) (64.746) (65.500)
Industry Dummy Yes Yes Yes Yes Adj. R2 0.382 0.380 0.431 0.422
33
Table 7 Multiple regression: Information and hedging This table reports the results of the regression specifications. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. Stock turnover is the trading volume divided by the total tradable shares. As for the independent variables, warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. Covered dummy is set to be 1 if the stock has a covered warrant and 0 otherwise. Warrant duration is the time left to maturity for warrants (days/365). Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Stock liquidity is defined as the absolute daily stock return divided by the daily trading value in billions RMB. Market turnover is the total stock turnover of the market.Δhedge ratio is the absolute value of the difference of hedge ratios between two adjacent days, where the hedge ratio is derived from the Black-Scholes model.. Put dummy is set to be 1 if the stock has a put warrant and 0 otherwise. Stock turnover and market turnover have been multiplied by 100. Industry dummies are included. The variables are in daily basis. T-statistics of coefficients are reported in parenthesis.
34
Information Hedging
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Intercept 0.308 11.858 11.968 11.547 -0.043 9.871 10.037 9.685 11.255 10.940 (5.455) (22.609) (23.094) (21.909) (-0.713) (19.637) (20.135) (19.169) (22.148) (21.226)
Put Dummy -0.249 -0.329 -0.321 -0.32 -0.368 -0.372 (-7.520) (-9.181) (-9.066) (-8.954) (-10.600) (-10.630)
ΔHedge Ratio 14.378 23.32 21.806 22.929 22.682 23.815 (13.013) (19.822) (18.586) (19.431) (19.420) (20.274)
Unexpected Warrant Turnover 0.415 0.352 0.345 (13.973) (11.826) (11.664)
Unexpected IPD 0.168 0.124 0.112 (5.077) (3.811) (3.467)
Covered Dummy -0.076 -0.072 -0.084 -0.241 -0.233 -0.241 -0.089 -0.096 (-1.905) (-1.841) (-2.109) (-6.618) (-6.445) (-6.611) (-2.327) (-2.473)
Warrant Duration 0.407 0.42 0.373 0.391 0.407 0.366 0.35 0.311 (12.434) (12.980) (11.174) (12.235) (12.831) (11.248) (10.955) (9.510)
Stock Market Cap -0.498 -0.501 -0.485 -0.42 -0.426 -0.413 -0.478 -0.466 (-22.235) (-22.652) (-21.551) (-19.611) (-20.033) (-19.150) (-22.045) (-21.203)
Stock Liquidity -16.752 -17.112 -16.549 -22.737 -22.635 -22.514 -23.702 -23.607 (-21.539) (-22.258) (-21.317) (-27.276) (-27.391) (-26.974) (-28.669) (-28.268)
Market Turnover 0.674 0.661 0.65 0.671 0.695 0.668 0.658 0.675 0.661 0.677
(63.890) (63.427) (62.954) (63.669) (65.451) (65.253) (64.623) (65.147) (65.368) (65.829) Industry Dummy Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Adj. R2 0.375 0.44 0.453 0.442 0.386 0.461 0.471 0.463 0.478 0.470
Table 8 Sample with deep-out-of-time put warrants This table reports the results of the regression specifications using a sample of deep-out-of-the-money put warrants. In this sample, we include only deep-out-of-the-mony put warrants that have a Black-Scholes value less than 0.05 pennies. Stock turnover is the trading volume divided by the total tradable shares. As for the independent variables, warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. Warrant close price is the daily closing price for a warrant. Covered dummy is set to be 1 if the stock has a covered warrant and 0 otherwise. Warrant duration is the time left to maturity for warrants (days/365). Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Stock liquidity is defined as the absolute daily stock return divided by the daily trading value in billions RMB. Market turnover is the total stock turnover of the market. Stock turnover and market turnover have been multiplied by 100. Industry dummies are included. The variables are in daily basis. T-statistics of coefficients are reported in parenthesis.
(1) (2)
Intercept 26.661 25.788 (17.200) (16.640)
Unexpected Warrant Turnover 0.099 (4.042)
Warrant Close Price 0.096
(2.004)
Covered Dummy 0.068 0.123 (0.704) (1.077)
Warrant Duration 1.327 0.834 (5.779) (3.948)
Stock Market Cap -1.055 -1.010 (-16.020) (-15.480)
Stock Liquidity -61.898 -60.458 (-11.500) (-11.180)
Market Turnover 0.217 0.207 (8.387) (7.954) Industry Dummy Yes Yes
Adj. R2 0.254 0.246
35
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Table 9 Multiple regression: Float shares This table reports the results of the regression specifications. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. Stock turnover is the trading volume divided by the total tradable shares. As for the independent variables, warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. Covered dummy is set to be 1 if the stock has a covered warrant and 0 otherwise. Δhedge ratio is the absolute value of the difference of hedge ratios between two adjacent days, where the hedge ratio is derived from the Black-Scholes model. Warrant duration is the time left to maturity for warrants (days/365). Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Stock liquidity is defined as the absolute daily stock return divided by the daily trading value in billions RMB. Float is the log of the number of the A-shares outstanding. Stock turnover and market turnover haven been multiplied by 100. The variables are in daily basis. T-statistics of coefficients are reported in parenthesis.
(1) (2) (3) (4)
Intercept 11.446 11.519 11.104 11.252 (22.294) (20.511 (21.333) (19.837)
Unexpected Warrant Turnover 2.435 2.442 (3.676) (3.685)
Unexpected Warrant Turnover * Float -0.101 -0.101
(-3.148) (-3.157)
Unexpected IPD 2.596 2.601
(4.061) (4.068)
Unexpected IPD * Float -0.119 -0.119
(-3.881) (-3.886)
Float -0.009 -0.019
(-0.320) (-0.658)
Put Dummy -0.361 -0.360 -0.362 -0.362 (-10.359) (-10.343) (-10.330) (-10.302)
ΔHedge Ratio 19.311 19.382 20.303 20.446 (18.335) (18.004) (19.177) (18.917)
Covered Dummy -0.083 -0.081 -0.084 -0.078 (-2.169) (-2.062) (-2.157) (-1.982)
Warrant Duration 0.369 0.369 0.333 0.332 (11.480) (11.473) (10.081) (10.059)
Stock Market Cap -0.485 -0.480 -0.472 -0.462 (-22.146) (-17.595) (-21.286) (-16.660)
Stock Liquidity -23.485 -23.521 -23.464 -23.537 (-27.745) (-27.541) (-27.453) (-27.309)
Market Turnover 0.659 0.658 0.677 0.676 (64.935) (63.050) (65.579) (63.761) Industry Dummies Yes Yes Yes Yes
Adj. R2 0.478 0.478 0.471 0.471
Table 10 Multiple regression: Bull/Bear Market This table reports the results of the regression specifications in bull and bear market. We collect the complete observations of 50 warrants that are listed in Shanghai Stock Exchange and Shenzhen Stock Exchange between August 2005 and June 2008. The 50 warrants are written on 41 firms. We use Oct. 16th 2007 as the cutting point and define the sample period before it as the bull market and the sample period after it as the bear market. Stock turnover is the trading volume divided by the total tradable shares. Warrant turnover is calculated as the trading volume divided by the outstanding warrants shares. Unexpected warrant turnover is the residual in the auto-regression of warrant turnover with one-day lag. Covered dummy, is set to be 1 if the stock has a covered warrant and 0 otherwise. Δhedge ratio is the absolute value of the difference of hedge ratios between two adjacent days, where the hedge ratio is derived from the Black-Scholes model. Warrant duration is the time left to maturity for warrants (days/365). Market Capitalization is the A-share market capitalization calculated as the stock price multiplied by the total tradable shares. Stock liquidity is defined as the absolute daily stock return divided by the daily trading value in billions RMB. Float is the log of the number of the A-shares outstanding. Stock turnover and market turnover haven been multiplied by 100. The variables are in daily basis. Bull-Bear column reports the difference of the coefficients from the bull market and the bear market regressions. T-statistics of coefficients are reported in parenthesis.
Bull Market Period Bear Market Period Bull - Bear Bull Market Period Bear Market Period Bull - Bear Intercept 13.917 21.727 13.524 21.829 (21.653) (23.700) (20.754) (23.656) Unexpected Warrant Turnover 0.372 0.250 0.122 (10.399) (5.682) (2.010) Unexpected IPD 0.103 -0.082 0.185 (3.048) (-0.947) (2.815) Put Dummy -0.363 -0.439 -0.365 -0.419 (-9.450) (-3.260) (-9.392) (-2.987) ΔHedge Ratio 20.224 24.035 21.264 25.170 (17.081) (11.828) (17.862) (12.356) Covered Dummy -0.174 2.345 -0.173 2.343 (-4.370) (14.760) (-4.317) (14.247) Warrant Duration 0.633 -0.379 0.585 -0.387 (16.181) (-5.545) (14.391) (-5.594) Stock Market Cap -0.607 -0.858 -0.593 -0.863 (-21.879) (-23.554) (-21.063) (-23.534) Stock Liquidity -25.027 -17.575 -24.891 -17.777 (-22.023) (-14.234) (-21.716) (-14.308) Market Turnover 0.736 0.806 0.754 0.813 (63.779) (18.369) (64.025) (18.399) Industry Dummies Yes Yes Yes Yes Adj. R2 0.537 0.479 0.529 0.472
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Figure 1 Averaged weekly stock turnover and warrant turnover
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Figure 2 Averaged daily stock turnover within warrant turnover group in each half year
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