Options Trading Activity and Firm Valuation
by
Richard Roll, Eduardo Schwartz, and Avanidhar Subrahmanyam
March 2, 2009
Abstract
We study the relation between options trading volume and the value of the underlying
firm. Options may have an effect on firm value because they help complete markets
(thus contributing to allocational efficiency) and stimulate informed trades (thereby
enhancing informational efficiency). However, these benefits are likely to manifest
themselves in active, rather than inactive, options markets. Supporting this observation,
we find that firms with more options trading have higher values of Tobin’s q, after
accounting for other determinants of value. This finding holds for all sample firms and
for the subset of firms with positive options volume. Corporate investment in firms with
greater options trading is more sensitive to stock prices. We also find that the effect of
options trading on firm valuation is stronger in stocks where the role of private
information is likely to be greater. These results indicate that options trading activity is
positively associated with firm values as well as information production.
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Contacts
Roll
Schwartz
1-310-825-6118
1-310-825-2873
1-310-206-8404
1-310-825-6384
rroll@anderson.ucla.edu
eschwart@anderson.ucla.edu
Anderson School
Anderson School
UCLA
UCLA
Los Angeles, CA 90095-1481 Los Angeles, CA 90095-1481
Subrahmanyam
1-310-825-5355
1-310-206-5455
asubrahm@anderson.ucla.edu
Anderson School
UCLA
Los Angeles, CA 90095-1481
We thank three anonymous referees, Yakov Amihud, Robert Battalio, Sreedhar Bharath,
Jennifer Carpenter, Zhi Da, John Doukas, Ned Elton, Steve Figlewski, Paul Gao, Marty
Gruber, Bruce Grundy, Kose John, Marcin Kacperczyk, Robert Mendenhall, M.P.
Narayanan, Paolo Pasquariello, Jonathan Paul, Lasse Pedersen, Amiyatosh Purnanandam,
Uday Rajan, Nejat Seyhun, Sophie Shive, Richard Stapleton, Kathy Yuan, and seminar
participants at Vienna University of Economics and Business Administration, New York
University, University of Melbourne, University of Michigan, and the University of
Notre Dame for valuable comments.
Options Trading Activity and Firm Valuation
Abstract
We study the relation between options trading volume and the value of the underlying
firm. Options may have an effect on firm value because they help complete markets
(thus contributing to allocational efficiency) and stimulate informed trades (thereby
enhancing informational efficiency). However, these benefits are likely to manifest
themselves in active, rather than inactive, options markets. Supporting this observation,
we find that firms with more options trading have higher values of Tobin’s q, after
accounting for other determinants of value. This finding holds for all sample firms and
for the subset of firms with positive options volume. Corporate investment in firms with
greater options trading is more sensitive to stock prices. We also find that the effect of
options trading on firm valuation is stronger in stocks where the role of private
information is likely to be greater. These results indicate that options trading activity is
positively associated with firm values as well as information production.
1. Introduction
Over the past few decades, options markets have experienced an exponential growth,
both in the number of underlying assets on which options are written, and in the volume
of trading. The question of how such contingent claims affect markets for the underlying
assets is an enduring one in financial economics.
More than thirty years ago Ross
(1976) argued that options written on existing assets can improve welfare by permitting
an expansion of the contingencies that are covered by traded securities. Thus, in the
absence of complete markets, simple options are powerful abettors of efficiency in
competitive equilibrium.
In addition to completing markets, options may also alter the incentives to trade
on private information about the underlying asset. For example, Cao (1999) argues that
agents with information about future contingencies should be able to trade more
effectively on their information in the presence of options, thus improving informational
efficiency. In addition, informed traders may prefer to trade options rather than stock,
because of increased opportunities for leverage (Back, 1992, Biais and Hillion, 1992).
Consistent with the preceding notions, Cao and Wei (2008) find evidence that
information asymmetry is greater for options than for the underlying stock, implying that
agents with information find the options market a more efficient venue for trading. This
finding is supported by Easley, O’Hara, and Srinivas (1998) and Chakravarty, Gulen, and
Mayhew (2004) who find that options order flows contain information about the future
direction of the underlying stock price.
These arguments together imply that
informational efficiency may be greater in the presence of actively traded options.
The enhanced informational efficiency induced by options may affect the
underlying asset by translating to higher market valuations. For example, if prices reveal
more information, then corporate resources may be allocated more efficiently, which
leads to increased firm values (Khanna, Bradley, and Slezak, 1994, Subrahmanyam and
Titman, 1999). In addition, there is a direct argument (Cao, 1999) that the informed
1
trading induced by derivatives makes prices reflect more information and thus reduces
the risk of investing in the underlying asset, which, in turn, tends to raise the asset’s price.
Thus, existing theory suggests that ceteris paribus, markets for claims in firms with
active options markets should be valued more highly.
The starting point of our paper is the recognition that the valuation benefit from
options to a firm should depend on options trading activity, over and beyond the presence
of an options market on the firm’s stock.
Thus, for example, due to the adage that
“liquidity-attracts-liquidity,” there may be multiple equilibria where some options
markets may attract considerable volume whereas others may remain thin and inactive
(Pagano, 1989).
In turn, the incremental benefit from listing should be related to
whether the market for the listed option has sufficient volume, because informed traders
would be more active in high-volume markets (Admati and Pfleiderer, 1988).
Consequently, the enhancement of informational efficiency should be higher in such
markets.
Further, any benefit to even uninformed traders from market completion
should depend on the level of options trading activity, because thin, inactive markets
would repel all traders, informed or uninformed.
Motivated by these observations, in
this paper, we empirically analyze the link between options trading activity and the
market value of the firms’ equity.
While our data analysis is inspired by arguments that point to a positive relation
between options trading and valuation, there are competing hypotheses. For example, if
options trading activity simply represents uninformed speculation and adds volatility to
prices then such activity may actually decrease market values.
Thus, our work can be
viewed as resolving the tension between these opposing arguments. To the best of our
knowledge, such an analysis of the relation between options trading activity and firm
valuation has not previously been undertaken.
For a large sample of firms during the 10-year period 1996 to 2005 we analyze
the effect of options trading volume on firm value after controlling for other variables
that may also affect firm value such as firm size, share turnover, return on assets, capital
2
expenditures, leverage and dividend payments. Following other studies (Lang and Stulz,
1992, Allayannis and Weston, 2001, and Carter, Rogers, and Simkins, 2006) we use a
measure of Tobin’s q as the valuation metric.
We find evidence that firms with greater levels of options trading have higher
valuations. This result is robust to the inclusion of all sample firms, or to the restricted
set of firms with positive options volume, and is present in every year of our sample
period.
Regression analysis suggests that the effect of options volume on q is
statistically significant and economically meaningful after accounting for a variety of
control variables, including firm size, industry membership, and trading activity in the
underlying stock.
We also perform specific tests to identify whether the effect of options activity on
valuations obtains by way of options’ effects on information production.
We uncover
evidence that firms with more options trading activity in a given period tend to have
greater sensitivity of corporate investment to stock price and improved financial
performance in the future after accounting for various controls, which accords with the
premise that options trading, by enhancing information flows, may lead to better
corporate resource allocation. In addition, our results indicate that the effect of options
trading on firm valuation is greater in stocks with low analyst following and high values
of PIN, the Easley, Hvidkjaer, and O’Hara (2002) measure of information asymmetry.
This suggests that the impact of options trading on information production is larger in
stocks where information asymmetries are greater and where investment analysis
produces comparatively less public information.
Previous studies (Brennan, Chordia, and Subrahmanyam, 1998 or Datar, Naik,
and Radcliffe, 1998) find that high trading activity in a firm’s stock implies a lower cost
of capital. Our finding of a positive contemporaneous relation between options trading
activity and firm valuation complements these studies and indicates that valuation effects
of trading may not be confined to trading in the own asset, but can extend to contingent
claims on the asset.
Thus, our results indicate that studies of the effect of trading
3
activity on asset pricing should be broadened to include trading activity in derivatives on
the assets.
The paper proceeds as follows. Section 2 reviews the literature and describes our
hypotheses. Section 3 describes the data. Section 4 presents the main empirical results,
Section 5 presents some robustness checks. Section 6 presents a further exploration of
the link between options trading and information production, and Section 7 concludes.
2. Literature Review and Economic Hypotheses
This paper lies at the intersection of the literatures on derivatives pricing, market
microstructure, and corporate finance.
Black and Scholes (1973) treat options as
securities that are redundant and can be replicated in continuous time by investments in
stocks and bonds. However, it is well-known that when markets are incomplete, options
cannot be replicated by simple securities such as stocks and bonds (see Ross, 1976,
Hakansson, 1982, and Detemple and Selden, 1991).
Another branch of the literature
shows that options cannot be dynamically replicated with stocks and bonds when the
dynamic process for the underlying stock involves features such as stochastic
discontinuities (see, for example, Naik and Lee, 1990, and Pan and Liu, 2003).
If options are not redundant, then their introduction may allow agents to expand
the set of contingencies available through trading and thus may be associated with a
positive price effect on the underlying stock.1 Indeed, Conrad (1989) documents an
upward effect on stock prices following an options listing using an event study approach.
However, Sorescu (2000) finds opposing results for a more recent sample period.
Danielsen and Sorescu (2001) rationalize Sorescu’s (2000) finding by suggesting that
options listing may be accompanied by a negative price impact because options alleviate
short-selling constraints and thus allow adverse information to be incorporated into stock
prices. However, in a careful study, Mayhew and Mihov (2005) provide evidence that
1
Baptista (2003) and Kahn and Krasa (1993) suggest that American options need not always lead to a
welfare enhancement.
4
the magnitude and sign of the estimated abnormal returns around options listing appears
to depend on the methodology used (such as the event window and the period used to
estimate the market model parameters).
In this paper, we complement previous studies on options listing effects by
proposing that the valuation benefit of options should depend on trading activity in
options.
Previous literature, both theoretical and empirical, has argued that options
increase the amount of private information conveyed by prices (see Biais and Hillion,
1994, Cao, 1999, Easley, O’Hara, and Srinivas, 1998, or Chakravarty, Gulen, and
Mayhew, 2004).2 Such increases in price efficiency may occur because informed agents
are able to cover more states when options markets are available.3
In the presence of
frictions, options may also allow informed agents to obtain leverage more readily.
While these arguments suggest that informed trading would be stimulated by the listing
of an option on a stock, agents with information need to camouflage their trades amongst
other traders to be effective (Glosten and Milgrom, 1985; Kyle, 1985). Would new
options markets always attract a large number of agents? Pagano (1989) sheds light on
this question by arguing that microstructure models have multiple equilibria where
“liquidity begets liquidity.” Thus, if agents conjecture that a new market will have little
volume they optimally desist from trading and this belief becomes self-fulfilling. On the
other hand if the conjecture is the opposite, then a market with large levels of trading is
sustainable. In the latter equilibrium, informed traders also are more active (Admati and
Pfleiderer, 1988, Chowdhry and Nanda, 1991, Pagano, 1989).4 This line of thinking
indicates that different options markets may have varying degrees of thinness, which also
implies different degrees of informational efficiency, with greater option volumes
implying greater price informativeness.
2
Jennings and Starks (1986) present evidence that options markets allow prices to adjust more quickly after
earnings announcements. Mendenhall and Fehrs (1999) argue that options trading increases the speed of
adjustment of prices to earnings before, rather than after the earnings announcement, by way of insider
trading. Figlewski and Webb (1993) argue that options, by effectively alleviating short-sale constraints
through put options and written calls, increase informational efficiency.
3
Note that more informed trading affects the costs of liquidity trading. But the valuation effects of such
costs are limited because they are a zero sum transfer from liquidity to informed traders.
4
Thus, Pagano (1989, p. 255) states that “trading volume and absorptive capacity of the market tend to
feed positively on each other: more speculators make for more active trade, and vice versa.”
5
What is the link between informational efficiency and firm valuation? A vast
literature examines this question. Fishman and Hagerty (1992), Khanna, Bradley, and
Slezak (1994), Dow and Gorton (1997), and Subrahmanyam and Titman (1999) all
conclude that if prices convey more information, corporate resources are allocated more
efficiently, and this leads to greater firm valuation.
If options stimulate informed
trading, then greater options activity could imply greater informed trading, and in turn,
enhanced firm values due to increased price efficiency.5 Further, note that even without
alluding to informed trading, options may have a pricing effect by completing markets
and thus enhance the welfare of traders wishing to cover more contingencies (Conrad,
1989). These traders may also be attracted to options with greater trading activity (and
lower trading costs), and thus may value claims in such firms more highly.
To sum up, our arguments may succinctly be described as follows:
1. If options listing has a welfare benefit, it is more likely to obtain if an option is
actively traded (a failed market would likely be unable to create a benefit).
2. If options have an informational benefit it is likely to be greater in more active
options because informed traders may migrate to more active markets and create
informational efficiency.
This phenomenon, in turn, can lead to improved
allocation of resources and greater valuations.
Thus, we suggest the inclusion of options trading activity in assessing the beneficial
effects of options on the underlying firms.6
Furthermore, in addition to empirically
analyzing the link between firm valuation and options trading, in the penultimate section
5
Alternatively, one could also argue that greater informational efficiency reduces the conditional risk of
investing in an asset (Cao, 1999), which would directly tend to make an asset more valuable. To see this
consider the extreme case where informed agents have perfectly precise information and the price reveals
all of their information. In this case the conditional risk of investing in the asset is zero and it is clearly
worth more to invest in this asset, ceteris paribus, relative to an asset where the price reflects the
information imprecisely. Testing this implication is difficult, however, because the trading process itself
could add volatility to prices (French and Roll, 1986), thus contaminating the risk reduction due to higher
informational efficiency.
6
Detemple and Jorion (1990), Hakansson (1982), and Sorescu (2000) make the observation that the
introduction of index options could reduce the welfare benefit from market completion afforded by
individual stock options to well-diversified investors. However, since firm-specific information (such as
that related to the firm’s product quality and competitive environment) is often relevant for corporate
investment (Subrahmanyam and Titman, 1999), the informational benefit of options is less likely to be
influenced by the presence of index options.
6
of the paper, we shed specific light on our proposed hypothesis that the effect of options
activity on firm valuation occurs by way of its impact on price informativeness.
While our specific focus in this paper is to test the hypothesis that options with
greater trading activity should be accompanied by higher firm valuations, it is worth
noting other possible hypotheses.
For example, if options lead to increased price
uncertainty due to more speculative trading by uninformed agents (De Long, Shleifer,
Summers, and Waldmann, 1990) and this effect dominates the potential positive effects
delineated above then the valuation effect of options could be negative. Our tests may
thus be viewed as an effort to distinguish between these competing hypotheses.
3. Data
OptionMetrics LLC provides data on options trading.
This database includes daily
numbers of contracts traded for each individual put and call option traded on U.S. listed
equities along with daily closing bid and asked prices.
This makes it possible to
approximate the total annual dollar options volume for each stock by first multiplying the
total trade in each option by the end-of-day quote midpoint for that option and then
aggregating this number annually across all trading days and all options listed on the
stock.7 The resulting annual options volume is then matched with data from Compustat
on Tobin’s q and with a constellation of control variables.8
Tobin’s q is computed as the sum of the market capitalization of the firm’s
common equity, the liquidation value of its preferred stock, and the book value of its debt
divided by the book value of the firm’s assets.9
While measurement of q necessarily
requires judgment, any imperfection in the estimate would likely bias against finding
7
We cannot calculate the dollar value of trades by multiplying each trade by the execution price because
intraday transactions prices are not available over the large sample period. Our method induces a slight
errors-in-variables problem, but this should be mitigated by annual averaging. In any case, the usual effect
of measurement error is to bias coefficients away from significance.
8
An annual observation interval is dictated by the necessity of using reliable accounting data from the
annual report.
9
This simplified estimate of q is adapted from Chung and Pruitt (1994). Using total firm q to preserves
comparability with the corporate finance literature, but results go through even if the market-to-book ratio
of the firm’s equity is used instead of q .
7
significant results. The control variables are as follows. A proxy for the firm’s leverage,
long-term debt to total assets, is intended to measure the likelihood of distress.10
Profitability, measured by return on assets (ROA), is net income divided by the book
value of assets. This variable is intended to capture the notion that more profitable firms
may have more favorable investment opportunities, leading to higher valuations. On the
other hand, high ROA may also signal that the firm is in a mature phase, and has limited
growth opportunities, so that the effect of ROA on q is an empirical issue.
Capital expenditures divided by sales is a direct measure of investment
opportunities actually undertaken.
Firms that invest more presumably have higher
growth opportunities and a higher q. A dummy variable for whether the firm pays a
dividend proxies for capital constraints (firms that pay dividends may have more free
cash flow, which may potentially be used to overinvest in marginal projects). We also
include firm size (market value of the firm’s shares) based on Peltzman (1977) who
argues that size may reflect greater efficiency because it may be an outcome of a firm’s
discovery and exploitation of a superior technology (see also Mueller, 1987).11 All these
controls have been used in previous literature, e.g., Allayannis and Weston (2001),
Carter, Rogers, and Simkins (2006). In addition, share turnover in the underlying stock
is included to control for liquidity effects arising from stock trading activity (Amihud and
Mendelson, 1986), which may spill over to options volume and contaminate inferences.
Table 1 gives the number of firms in each sample year. The number of firms with
non-missing Compustat data ranges from more than 6300 in 1996 to about 4000 in 2005.
The decrease is likely due to the downturn in the technology sector, which was
accompanied by financial distress, bankruptcy and eventual delisting. The number of
firms with positive options trading volume ranges from 1342 in 1996 to 1717 in 1998, its
peak year.
10
Inclusion of an additional measure of the short-term debt burden, based on the ratio of current liabilities
to current assets, does not alter any of the results substantively.
11
The market value of the firm’s shares proxies for size. However, using alternative proxies, such as the
number of employees or the book value of the firm’s assets leaves the central results qualitatively
unchanged.
8
Any firm with no options volume data in Options Metrics for a particular year is
assumed to have an options volume of zero in that year.
This suggests a natural
bifurcation of samples into one consisting of all firms, (with the majority having zero
options volume), and a second consisting only of firms with positive options volume.12
Table 2 presents summary statistics (over all firms and years) for Tobin’s q, the control
variables, and options volume. Panel A, covers all firms while Panel B includes firms
with positive options volume. The mean value of q for the whole sample is about 1.9.
The mean value of return on assets is negative, presumably because small (tech) firms did
not perform well during this period. Panel B shows that firms with positive options
volume have a higher Tobin’s q, both mean and median. Such firms are also larger and
more profitable on average than those without options volume.
Table 3 presents correlations among the variables (again, pooled over firms and
years). Again, Panel A is for the full sample while Panel B is for firms with positive
options volume. The correlation between Tobin’s q and options volume is positive for
both samples and reaches almost 18% for the subsample with positive options volume.
Tentatively, this positive correlation is consistent with our main premise that greater
options activity is associated with higher firm values. We will examine this relation in
greater detail in the next section.
With regard to the other correlations of Table 3, it can be seen that options
volume is positively correlated with firm size as well as share turnover, and this is
consistent with the intuitive notion that larger, more actively traded firms have greater
levels of options activity. Tobin’s q is negatively correlated with the return on assets,
which is counterintuitive, but may be because stocks with high current income are in the
“mature” phase of their life-cycle with fewer opportunities for future growth.
12
Overall,
We aggregate options volume across calls, puts, and times to maturity. While an analysis of volume
disaggregated by maturity and type of option is possible, there are no clear hypotheses. For example, it
may be conjectured that managers are more likely to act on positive signals that suggest investment as
opposed to negative signals that indicate divestment, since irreversibility often implies that divestment is
costly. But since calls and puts can be written or bought freely, and our data consists of unsigned volume
and not signed order imbalance, the sum of call and put volumes cannot be linked to bullish or bearish
sentiment. Similarly, while it may be that managers are more likely to react to long-term information
contained in long-maturity options, these options are also more illiquid, making them less attractive to
informed traders. Because of these confounding issues, we look at aggregated options volume.
9
the correlations of q and options activity with the other variables in Table 3 underscore
the need for controls in analyzing the relation between options activity and q. This
motivates the regressions to follow in the next section.
As a pre-amble to the main analysis, we document the results of portfolio sorts
that consider the relation of q with options volume. We take the subsample of firms with
positive options volume, and sort them into deciles by options volume each year. For
each decile, the average value of Tobin’s q across all years appears in Figure 1. As can
be seen, average q increases monotonically with options volume, supporting the positive
correlation between q and options trading activity documented in Table 3. Average q for
the highest options volume decile is more than double that for the lowest options volume
decile, and an unreported test indicates that this difference is statistically significant.
We next examine sorts by market capitalization and options volume to allow for
independent variation in size and options activity. Specifically, every year for the firms
with positive options volume, we form quintile portfolios first by size, and then by
options volume within each size quintile.
The average values of Tobin’s q for the
resulting 25 portfolios are listed in Table 4. It can be seen that Tobin’s q monotonically
increases across the options volume quintiles in each of the five size groups; whereas
there is no uniform monotonicity in q across the size quintiles though the general pattern
is that q tends to increase with size.
The differences in q across the extreme options
volume portfolios are economically meaningful in each case, Unreported tests indicate
that each of the five differences in q across the extreme options volume portfolios is
significant at 1% level.13
4. Regression Results
This section examines the determinants of Tobin’s q.
Since the arguments above are
cross-sectional in nature, the natural approach is to run year-by-year cross-sectional
13
Two-way sorts by stock trading activity (i.e., annual dollar value of shares traded, instead of size) and
options volume lead to results qualitatively identical to those in Table 4.
10
regressions and then test the significance of the time series means of the cross-sectional
coefficients.14 But the residuals of the cross-sectional regressions are likely to be serially
correlated due to autocorrelation in Tobin’s q, so simple t-statistics may be misleading.
To overcome this potential problem, t-statistics are corrected according to the procedure
of Newey and West (1987).15 Results for the full sample of firms and for the subsample
with positive options volume are reported in Tables 5 and 6, respectively.16
Both dividends and leverage have significantly negative impacts on valuation for
both samples, as postulated in the previous section. For the full sample, ROA also is
inversely related to q, indicating that high ROA signals firm maturity and relative paucity
of future growth options.
On the other hand, capital expenditures, presumably proxying
for future growth opportunities, have a positive impact on valuation in the full sample of
firms.
ROA and capital expenditures are not significant for the sample of firms with
positive options volume, suggesting that the role of these variables is more relevant in the
smaller firms, where growth options may be more relevant to valuation. We also find
that share turnover has a positive impact on valuation, consistent with the presence of a
liquidity premium in asset prices (Amihud and Mendelson, 1986). Size has a weak but
positive impact on Tobin’s q. In general, these results are consistent with the rationales
for the controls provided in the previous section.
14
There is no evidence of non-stationarity in the aggregate q. Thus, the linear trend in the cross-sectional
average value of q is insignificant, and the point estimates do not monotonically increase or decrease across
the years. In any case, results with linearly detrended values of q are substantively similar to those
reported.
15
As suggested by Newey and West (1994), the lag-length equals the integer portion of 4(T/100}2/9, where
T is the number of observations.
16
We report the results for the full sample and the subsample of firms with positive options volume
separately, which allows for different coefficients for the explanatory variables across the two samples.
This is reasonable if the firms without options listing tend to be small with different structural relationships
between q and the right-hand variables (for example, small, high growth firms may have weaker
relationships between q and past profitability because their q may largely be a result of future growth
options). However, we tried two alternative approaches. In the first, we included a dummy variable for
positive options volume within the full sample, and found the dummy to be positive and significant, while
the significance of the options volume was preserved. In the second, we performed a Tobit analysis for the
full sample, assuming that options volume was censored at zero. In this alternative analysis, the coefficient
of options volume remained significant.
11
The coefficient of options volume is positive and significant for both subsamples
indicating that options volume has an upward impact on firm valuation. 17 For all firms,
the magnitude of the coefficient implies that a one standard deviation move in options
volume implies a 16% higher q relative to its mean value. The effect for the subsample
of firms with positive options value is stronger: in this case, a one-standard deviation
move in options volume implies a q that is higher relative to its mean by 23%.18 Thus,
the effect of options trading on firm valuation is both statistically and economically
significant.
5. Robustness Checks
In this section, we report the results of several checks on the basic results.
The tests
consider skewness, panel regression, endogeneity issues, industry effects, and additional
explanatory variables.
A. Different Specification for Options Trading Activity
From Table 2, it may be seen that the distribution of options volume is skewed because
the mean is quite different from the median. The natural way to address this is to take
logarithms. But in doing so, we are precluded from including firms with zero options
volume.
Since we already have noted that our results obtain both including and
excluding firms with options volume, we address the skewness issue by using the
logarithm of options volume, and thus by definition, using only those firms with positive
levels of options trading activity. Results from this alternative specification (the analog
of Table 6) appear in Table 7. As can be seen, the coefficient of options volume remains
positive and strongly significant, while the other coefficients are largely unchanged
relative to those in Table 6.
17
In another specification for Table 5, we included both the options volume as well as a dummy for
whether options volume was non-zero, and found that both of these variables were significant. This
suggests that there is a baseline effect of non-zero options volume on q, as well as an additional effect
relating to the level of this positive volume.
18
Note that the coefficient on options volume is scaled upward by 104 in Tables 5 and 6.
12
The economic magnitude of the effect of options volume also remains largely
unchanged in Table 7 relative to the earlier tables. Indeed, straightforward calculations
show that the effect of a one standard deviation move in the logarithm of options volume
changes q by about 21% relative to its overall sample mean, which is very close to the
magnitudes discussed at the end of the previous section. From now on, we will use the
logarithmic transformation of options volume (and refer to it as just options volume for
brevity), though similar results are obtained using the untransformed variable as well.
B. Panel Regression
The earlier regressions reported average coefficients from annual cross-sectional
regressions, and thus did not use information contained in the time-series.
Indeed, we
view our economic hypothesis as indicating a cross-sectional relation between q and
options activity, not as a time-series phenomenon that relates year-to-year changes in q to
changes in options activity.
Specifically, q may respond sluggishly to time-series
changes in options activity due to irreversibility or rigidity in investment policies, thus
attenuating the time-series relation between q and options trading.19 Nonetheless, to
incorporate the time-series aspect, we now present results from a panel regression that
pools the time series and cross-sectional data. The Parks (1967) procedure (as described
in Kmenta, 1986) is adapted to control for serial correlation as well as for crosscorrelation in the error terms. This requires a balanced panel, so we use the 502 firms that
are present in every year of the sample. Details of the procedure are in the appendix.20
Results from the panel procedure appear in Table 8, where it can be verified that
the conclusions are mostly similar to those in Table 7. Thus q is negatively associated
with the dividend dummy and leverage, but positively associated with firm size.
However, the coefficient on stock turnover reverses sign, indicating that for the sample of
firms in Table 8, the expected positive effect of turnover on q does not obtain. While this
19
Supporting this argument, the grand cross-sectional correlation between annual changes in q and options
volume is a relatively modest 0.091 within the sample.
20
Since the panel procedure uses GLS, an R2 measure is not appropriate (Judge et al., 1988), and therefore
is omitted from all tables in this paper that report estimates from panel regressions.
13
finding requires further research, it may be related to the result that the pricing of stock
liquidity (which is related to stock trading activity) is stronger in smaller firms (Chordia,
Huh, and Subrahmanyam, 2008), whereas the firms in Table 8 are required to have been
present in the sample throughout the period, and thus are likely the larger firms. For our
purposes, the relevant result is that options volume continues to be positively and
significantly associated with q.21 The magnitude of the options volume coefficient,
however, decreases relative to Table 7.
Based on the sample means and standard
deviations of q and the options volume variable, the coefficient of options volume
indicates that a one standard deviation increase in options volume implies a 11% increase
in q relative to its mean, which is lower than the corresponding effect in Table 5, but still
economically significant. The decrease in the economic magnitude may reflect the fact
that the panel accounts for both cross-sectional and time-series effects.
As indicated
earlier, if q responds sluggishly to time-series changes in options activity due to some
inflexibility in corporate investment, then we would expect such an attenuation in the
coefficient.22
C. Endogeneity
The next issue to consider is endogeneity. One may, for example, argue that high q firms
may attract more attention and this may translate to greater options volume.
A
straightforward way to address this is to consider the relation between q and one-year
lagged options volume. Results from doing so appear in Table 9. As can be seen, the
significance of options volume is preserved in this alternative specification, even though,
understandably, the point estimate of the coefficient declines.
However, while this
approach of using lagged options volume addresses endogeneity to some degree, ideally,
one needs instruments for options volume that is inherently unrelated to q. But finding
21
As an alternative, we estimate a standard panel model with firm and year fixed effects to account for any
unobserved heterogeneity. The coefficient of options volume remains positive and significant with a tstatistic of 8.72 in this specification.
22
A balanced panel approach is required for the Parks procedure because the procedure requires the
estimation of first-order serial correlation for each cross-sectional observation across the same time-period
for all observations. Unbalanced panel approaches are possible when residuals are assumed to be serially
uncorrelated. We estimated an unbalanced panel regression under this assumption using the Fuller and
Battese (1974) procedure with both fixed and random effects and found that the options volume coefficient
remained significant in such a specification.
14
such an instrument is a difficult endeavor and inevitably involves an element of
subjectivity. In the analysis below, we consider two instruments in turn: moneyness (i.e.,
the average absolute difference between the stock’s market price and the option’s strike
price), and open interest in the stock’s listed options.
There are several reasons why options activity may be related to moneyness.
First, agents speculating on volatility would eschew deep in the money or out of the
money options because the vega of such options is close to zero. Moreover, informed
traders may be attracted to out of the money options because they provide the maximum
leverage, but uninformed traders may migrate to in the money options to avoid risky
positions.23 These arguments provide a link between absolute moneyness and options
volume, but do not specify an unambiguous direction, which remains an empirical issue.
There is no reason, however, that unsigned moneyness should be inherently related to q,
since exchanges periodically list new options with strike prices close to the recent market
price of the underlying stock. Thus, there does not appear to be a strong rationale for a
mechanical link between (unsigned) absolute moneyness and Tobin’s q.24 Given this
observation, we calculate the annual average of the daily absolute deviation of the
exercise price of each traded option from the closing price of the underlying stock (the
average absolute moneyness).25 The correlation of this variable with options volume
across the full sample is 0.247, suggesting that the instrument is indeed related to options
trading activity. 26
23
Pan and Poteshman (2006) document that volume from customers of discount brokers is slightly higher
in out of the money options.
24
It is possible, however, for moneyness to be related to volatility because highly volatile stocks may cause
exchanges to list options with more dispersed exercise prices. But, as mentioned in Section 5.E, volatility
is not a significant determinant of q in our sample, suggesting that the potential link between moneyness
and volatility does not affect our results.
25
For traded option k on stock j for day t, the absolute deviation is |ln(pricej,t/strikek)|. This is averaged
over all k and t within a year for each stock j. Options without trades are not included in the calculation of
the moneyness measure. Using a volume-weighted average annual moneyness measure for each stock j,
where each option’s moneyness is weighted by the proportion of total option volume for stock j contributed
by that option, yields substantively similar results.
26
While the moneyness variable is positively and significantly related to options volume for the overall
sample, this does not necessarily mean that volume tends to be higher in options that are away from the
money. It might also be induced if the options exchange lists a larger number of options, with different
exercise prices, on firms with more overall options trading. But regardless of the underlying reason, so
long as the instrument is well correlated with the explanatory variable (options volume) and does not
15
We compute a two-stage least-squares (2SLS) estimation of the regression in
Table 7. This procedure models q and options activity as being determined jointly as part
of a system of linear equations.
Based on the preceding arguments, moneyness is
included as a determinant of options activity but not q. Specifically, in our 2SLS system,
there are two equations.
In the first equation, q is modeled as a function of all of the
variables in Table 7. In the second equation, options volume is modeled as a function of
the average absolute moneyness and all of the other control variables for q in Table 7.
These variables are included for completeness and because they are intuitive
determinants of options volume. In particular, larger, more profitable firms may attract
more options traders, as can firms with high leverage and hence higher ex ante volatility.
Similarly non-dividend paying firms and firms that invest substantially may also be
viewed as growth-oriented, more speculative firms (and thus attract more options
volume). Inclusion of all of the controls makes the options equation under-identified, so
that its estimates cannot be reported.
But, the q equation is exactly identified (since
moneyness is excluded from this equation). Estimates of the equation for q appear in the
second and third columns of Table 10.
As can be seen, the coefficient for options
volume remains significant in this regression,27 suggesting that the main result survives
the consideration of reverse causality.
The qualitative aspects of the other variables in
the equation are unaltered relative to Table 7.
An alternative instrument for options volume is the total open interest in options
within a given year.
The level of q should not be inherently related to open interest,
which consists of open call as well as put contracts. Thus, high or low levels of q could
inherently depend on the dependent variable (Tobin’s q), the instrumental variable procedure is wellspecified.
27
Note that the coefficient of options volume in Table 10 is smaller than its value in Table 7. It is possible
for 2SLS coefficients to be larger or smaller in magnitude than the corresponding OLS ones; see, for
example, Beaver, McAnally, and Stinson (1997) or Irwin and Terviö (2002) for the relevant econometric
intuition on this issue. A discrepancy between the 2SLS and OLS coefficients can occur if, for example,
the right-hand variable (in this case options volume) is measured with error, or if the measurement error in
q is correlated with that in options activity. While the specific reason for this discrepancy is not the focus of
this paper, we find that the 2SLS coefficient of options volume is significant at the 5% level in each of the
ten years in the sample period. The consistent significance of the options volume coefficient supports the
notion that options volume affects q.
16
be associated with high or low call or put interest, but the sum of the two should not be
linked to q in any intrinsic way.
Using this argument, we use total open interest in place
of absolute moneyness as an instrument. The open interest variable is measured as the
average open interest across all options on a stock throughout the calendar year.
This
variable’s correlation with annual options volume is 0.365 across the entire sample,
which suggests that open interest indeed bears a relation with options trading activity in
the expected direction.
Results from the two-stage least-squares regression results using open interest as
the instrument are presented in the last two columns of Table 10.
options volume is 0.1385 with a t-statistic of 2.84.
The coefficient of
These numbers are close to the
corresponding ones in Table 7. Thus, this alternative instrument for options volume also
is consistent with the notion that there is a significant causality running from options
volume to q.
Having established this, for the remainder of the paper, we revert to the
single equation model of Table 7.28
D. Year-by-Year Regression Coefficients and Industry Controls
A potential concern is that the relation between Tobin’s q and options trading may be
driven by significant effects in only one or two years.
In order to obtain a more
complete picture of the effect of options trading on valuation, the second and third
columns of Table 11 report the annual regression coefficients that are used in computing
the averages reported in Table 7, together with their corresponding t-statistics. In every
year, the coefficient of options trading is positive and strongly significant. This provides
reassurance that the results are not driven by high coefficient magnitudes in one or two
years.29 Overall, these results and Figure 1 suggest that the results are not an artifact of
cross-sectional or time-series outliers.
28
Using system models for the q analyses in the remainder of the paper does not alter the results
substantively; though the magnitudes of some coefficients change somewhat. Full details are available
from the authors upon request.
29
We link q to options trading in our data by matching the relevant Compustat year used for the inputs to q
with the year for which options trading activity is calculated (Chen, Goldstein, and Jiang, 2007, in their
study of the link between corporate investment and price informativeness, also adopt this matching
17
There may be a concern that industry effects may be driving the results, especially
duing the height of the boom in technology stocks during the late 1990s. Furthermore, q
and options volume may vary in a correlated fashion across industries, even though
unambiguous a priori reasons for this correlation may be hard to discern.
To address
these issues, dummy variables for each of Fama and French’s (1997), forty-eight industry
groups are included as control variables in the regressions.30 The resulting year-by-year
coefficients of options volume are reported in the last two columns of Table 11. The
pattern of significance is not materially altered by inclusion of industry indicators,
indicating that the results survive even after accounting for industry effects.31
One of the interesting aspects of the coefficient patterns in Table 11 is that the
coefficients are substantially higher than the average towards the end of the 1990s.
While this pattern warrants further analysis in future research, we propose one
explanation: that information produced by the trading process is particularly valuable for
growth-oriented tech companies that boomed during this period. Therefore, the link
between options trading activity and firm valuation may be large for such companies,
which is manifested in the higher coefficients during the period where the representation
of tech stocks in the sample was particularly high.
procedure of linking Compustat variables to variables obtained from CRSP daily data and TAQ intradaily
transactions data). But fiscal years do not always coincide with calendar years, thus causing some
asynchronicity in the measurement of the regressors. To address this issue, we ran regressions restricting
the sample to only those firms whose fiscal years ended in December. The coefficient of options volume
remained significant in every year for this subsample as well, just as in Table 11. The overall Newey-West
t-statistic also remained significant and the coefficient did not change materially from that in Table 7. Full
details are available from the authors.
30
The industry dummy definitions follow Appendix A of Fama and French (1997). Their last-listed
classification, financial firms (SIC codes 6200-6299 and 6700-6799), is the base case.
31
We have not included industry dummies in the other regressions reported in the paper (consistent with
Allayannis and Weston, 2001), but have verified that inclusion of these dummies does not alter any of our
results in a material way.
18
E. Miscellaneous Robustness Checks
In other unreported regressions we employ alternative specifications using logarithms of
firm size and share turnover;32 again, the coefficient of options volume does not change
appreciably. Using share volume instead of share turnover and scaling options volume
by shares outstanding also have little impact on the significance of the options volume
coefficient.33
One major concern about the results is that options trading may proxy for stock
riskiness, which could potentially affect q.
We therefore include a measure of return
volatility, measured by the annual standard deviation of daily returns, in the regression
corresponding to the first two columns of Table 11.34 However, the return volatility
variable is not significant (its t-statistic was 1.42), which indicates that perhaps another
included variable, such as leverage, accounts for the effect of stock riskiness on q. Even
in the presence of return volatility, however, the options volume variable remains
significant with a coefficient of 0.098 and a t-statistic of 4.46.35
Finally, we include a
dummy variable for S&P 500 index membership, on the grounds that such stocks may be
have higher values of q due to either higher liquidity or excess demand created by index
funds (Shleifer, 1986). Including the variable does not alter the sign and significance of
32
The other variables in the regression are not constrained to be strictly positive, thus precluding us from
taking their logarithms.
33
Another issue is whether options volume is simply proxying for stock price runup (stocks that have gone
up would attract options volume and past returns may also be related to q). It is debatable whether past
return should be included as an explanatory variable for q over and above profitability measures such as
ROA. We find, however, that including the past year’s return in the equation for q does not alter the
significance of options volume. An additional issue is whether proxies for corporate governance should be
included as determinants of q. Again, this is debatable because profitability measures such as ROA should
capture the notion that good governance leads to greater profitability and thus higher valuations.
Nonetheless, we include the governance index of Gompers, Ishii, and Metrick (2003) in the annual as well
as the panel regressions of Tables 5 through 8 (since the governance index is not updated every year, we
use the most recent value of the index). We find that the significance of the options volume coefficient
remains virtually unchanged in this exercise.
34
The impact of return volatility is not affected by inclusion of the industry controls in Table 11.
35
We also include two other proxies for uncertainty surrounding a firm’s cash flows, namely, firm age and
a measure representing divergence of opinion. Age is simply the number of days from the firm’s initial
appearance on CRSP (CRSP variable BEGDAT) to the last trading day of the calendar year, and dispersion
of opinion is measured by the standard deviation of I/B/E/S analyst forecasts scaled by the market price
(the dispersion measure is calculated every month and averaged across the year for each stock). Inclusion
of these variables does not substantively alter the sign, significance, or magnitude of the options volume
coefficient.
19
the options volume coefficient. Full details of all these robustness checks are available
upon request.
6. Options Trading and Information Production: Further Analysis
In this section, we perform further empirical tests to identify the specific mechanism by
which options trading affects firm values. Note that if options trading activity stimulates
information production and beneficially influences corporate investment, then there
should be links between options trading and the firm’s financial performance as well as
the sensitivity of corporate investment to market prices. Further, the effect of options
trading on firm values should be greater in stocks with greater levels of information
asymmetry. In this section, we provide empirical evidence on these notions. The results
generally support the notion that options trading activity affects firm valuations by way
of its impact on price informativeness.
A. Options Trading and Firm Profitability
Better corporate investment decisions due to information conveyed by more active
options markets should translate to greater profitability. The effect may, however, be
spread out over a number of years, making its statistical detection difficult. Nonetheless,
in an effort to detect this effect, we regress return on assets (ROA -- our measure of
financial performance) on one-year lagged values of log option volume plus the other
controls in Table 9 (lagged ROA is included to account for serial dependence in the
variable).
Panel regressions using the Parks (1967) procedure to account for
autocorrelation are presented in Table 12.36
As can be seen, firms that paid dividends last year are more profitable, which is
consistent with intuition.
High leverage is associated with lower future profit,
suggesting that leverage may be associated with distress. ROA is serially persistent. The
36
Inferences from averages of year-by-year coefficients are not substantively different from the ones
presented.
20
relevant result for our purposes is that firms with greater levels of past options volume
tend to be more profitable in the future.
The economic magnitude of the effect is
appreciable; based on the sample statistics, a one-standard deviation move in options
volume increases ROA by 0.8%, which is substantial relative to ROA’s sample mean of
3.6%.
This result supports our proposition that options trading can lead to better
corporate resource allocation by increasing price efficiency.37
B. Options Trading and Investment Sensitivity to Stock Price
The degree to which managers obtain information from market prices to make investment
decisions can be captured by the sensitivity of corporate investment to market prices.
Several papers have theoretically and empirically analyzed this sensitivity; see, for
example, Dow and Gorton (1997), Subrahmanyam and Titman (1999), and, more
recently, Chen, Goldstein, and Jiang (2007).38 Managers might learn more from market
prices when options volume is greater, because options trading activity produces private
information. We now empirically test this conjecture.
We define corporate investment to be the sum of capital expenditure and R&D
expenses scaled by beginning-of-year book assets.
The main explanatory variable of
interest is the interaction of Tobin’s q with options volume.
To be consistent with
previous tables, the logarithm of this variable is used, though similar results obtain with
the unlogged version as well.
Tobin’s q itself is included to capture the baseline effect
of market valuation on investment. Both variables are lagged one year to address the
notion that investment decisions are made conditional on the values of these variables.
We also include the following control variables, as in Chen, Goldstein, and Jiang (2007).
First, minus the log of the previous year’s book assets is included to correct spurious
correlation that might be introduced by the error-prone common scaling variable that
37
Since options volume is significantly related to q, a potential concern with this result is simply that high q
firms are more profitable in the future. To address this, we include past year’s q in the regression. Doing
so preserves the significance of the lagged options trading variable.
38
Chen, Goldstein, and Jiang (CGS) (2007) analyze the relation between investment sensitivity to stock
price and measures of information asymmetry. We address the link between these measures and options
activity in the next subsection. Combining the CGS analysis with ours is problematic because the measure
of information asymmetry they use is not readily available for the entirety of our sample period.
21
appears on both sides of the regression. To account for the well-studied impact of cash
flow on investment (e.g., Fazzari, Hubbard, and Petersen, 1988), we include cash flow, as
measured by net income plus depreciation, amortization, and R&D expenses, scaled by
beginning-of-year book assets. To account for managerial market timing, (i.e., managers
invest more when their stock is overvalued and they expect lower future returns), we
include the following year’s return.39
Results from a panel regression appear in Table 13.
Similar conclusions are
obtained from the averages of year-by-year cross-sectional regressions. As can be seen,
the coefficient of Tobin’s q is positive, suggesting a positive sensitivity of investment to
stock price. The signs of the other control variables are consistent with information
conjectures, thus cash flow has a positive effect on investment, and managers appear to
invest more when stocks are overvalued and future returns are lower. The scaling control
(1/assets) has a positive coefficient, which suggests that it contains errors that are
introduced on both sides of the regression.
For our purposes, the central result is that the interaction of q with options volume
is strongly significant, indicating a greater sensitivity of investment to stock price when
options trading activity is high.
From the perspective of economic significance,
unreported calculations reveal that a one standard deviation increase in this interaction
increases corporate investment by 6.7% relative to its mean, which is a reasonably
substantive effect.
This supports the notion that options trading contributes to
information production, which managers use in making corporate investment decisions.
C. A Direct Measure of Information Asymmetry
One channel by which options trading improves firm valuation is by stimulating informed
trading but the extent of informed trading undoubtedly varies in the cross-section. The
39
In unreported regressions, we included the interaction of equity share volume with q, but found that this
variable was not significant. We also experimented with additional control variables, specifically those
used in Table 12, and found that the significance of the interaction of q with options was unaltered in these
alternative specifications.
22
effect of options trading on valuation may be particularly pronounced in stocks with
greater levels of informed trading. Computing reliable proxies for informed trading in
the options market presents challenges due to a dearth of good quality transactions data
for a large sample over a long period. However, informed agents may exploit private
information in both the stock and options market, and arbitrage forces link informed
trading in options and stocks. Thus, it seems sensible to investigate the well-known PIN
(probability of informed trading) measure as a proxy for information asymmetry in the
joint stock/options market system.
PIN is derived from a Bayesian model of
microstructure developed in Easley, Hvidkjaer, and O’Hara (2002) and estimates the
probability that any given order in a particular stock emanates from an informed trader.
Thus, PIN captures the extent of informed trading in the market for a stock. For stocks
with high PINs (as estimated from intraday stock transactions data), the effect of options
volume on valuation should be greater.
Soeren Hvidkjaer kindly provided annual PINs from 1996 through 2001.
Unfortunately, due to the larger volume of transactions data following 2001, it has not yet
been updated. Since the PIN ranges between zero and one, we logistically transform it
first, and then multiplicatively interact it with options volume. Using the PIN sample, we
then run regressions analogous to Table 7, including the interaction variable in addition to
all of the other variables in that table.
For brevity, instead of reporting all the regression coefficients, we report only the
yearly coefficients of options volume and the interaction variable in Table 14. The
results indicate that the options volume variable remains significant in every year, and the
interaction of the options volume with PIN is always positive and is significant at 5% (at
least) in five out of six years (in 1997-2001) and at 10% in the other year (1996). This is
suggestive evidence that the effect of options volume on q is stronger in stocks where
more information is produced by the trading process.
23
D. Security Analysts and Options Trading
It also is possible that options volume proxies for another measure of information
production, the extent of analyst following. Indeed, the role of analysts as producers of
private information is documented in Bhushan (1989), Brennan, Jegadeesh, and
Swaminathan (1993), and Mikhail, Walther, and Willis (2004).
Based on this
observation, the number of analysts following a company as of the end of the year (from
I/B/E/S) is directly included as another regressor for the full sample regression. It is not
significant in the analogs to Tables 6 or 7, whereas options volume remains significant.
As previously noted, options volume is influenced by uncertainty.
A forward-
looking measure of uncertainty is the dispersion of long-term growth forecasts by
security analysts, which is related to the collective imprecision of the information
possessed by analysts. Pastor and Veronesi (2003) show that uncertainty about future
growth rates can affect valuation as well. Thus, the issue is to ascertain whether options
volume is proxying for uncertainty in growth forecasts.
We therefore include the
standard deviation of analysts’ growth forecasts as of December of each year within the
regression of Tables 6 and 7. This reduces the sample size, since an analyst following of
at least two is required. Including this growth uncertainty variable, however, does not
materially alter the significance of the options volume coefficient, even though the
growth uncertainty variable is positive and marginally significant (at the 10% level),
consistent with Pastor and Veronesi (2003).
There may be an additional effect of analyst following on the results linking
valuation to options trading activity. Specifically, Easley, O’Hara, and Paperman (1998)
indicate that analysts are a source of publicly generated information for companies. If
this be the case, and options trading indeed increases information production, then
options activity may have a stronger role in enhancing informational efficiency in stocks
with low analyst following (where trading on private information may be more
important).
To address this issue, we divide the sample into three equal groups by
analyst following, labeling these groups (low to high analyst following) as 0, 1, and 2.
24
The indicator variable corresponding to the three groups is interacted with options
volume and included with the other variables reported upon in Table 7. Results from this
regression appear in Table 15. The coefficient of options volume remains positive and
significant but the coefficient of the interaction variable is negative and significant.40
This indicates that the impact of options volume on firm valuation is greater for stocks
with low analyst following. These results are consistent with options trading increasing
firm values to a greater extent when public information production by analysts is less
intense.41 Our analysis thus supports the dual views that options activity increases firm
values by way of its impact on information production, and that security analysts
substitute for private information trading by generating public information signals
(Easley, O’Hara, and Paperman, 1998).
Overall, the results provide good support for the hypothesis that options trading
activity is associated with increased firm valuation, and that at least part of this
phenomenon is linked to the increased information production in actively traded options
markets.
7. Conclusion
Options markets may increase market valuations by allowing agents to cover more
contingencies, and by stimulating more privately informed trading, which may enhance
the efficacy of resource allocation. But these benefits are more likely in active options
markets, because these are associated with easier and cheaper trading. Supporting this
notion, we find evidence that firm values increase with options trading volume. This
40
To preserve comparability with Table 7, we use the coefficient averages from year-by-year regressions to
draw inferences, but the conclusions are unchanged in a panel regression using the Parks (1967) procedure
(as in Table 8). Further, interacting options volume with the actual number of analysts, and dividing the
sample into two (as opposed to three) groups by analyst following, also has no material impact on the
results.
41
In terms of economic magnitudes, unreported calculations indicate that a one standard deviation increase
in options volume increases q by 28%, and a one standard deviation increase in the interaction variable
decreases q by 9%. The net effect of a one standard deviation move in each of these variables is about
19%, which is comparable to the magnitude in Table 7.
25
result survives the inclusion of a host of control variable and a variety of robustness
checks.
There is also evidence of a link between options trading activity and future firm
profitability. Corporate investment in firms with greater options trading is more sensitive
to stock prices. The results suggest that options trading can improve corporate resource
allocation by enhancing price efficiency.
The effect of options trading on firm valuation
is stronger in stocks where information asymmetry is likely to be greater, specifically,
stocks with higher values of PIN and “neglected” stocks with low levels of analyst
following. This supports the notion that options trading plays a relatively stronger role
in enhancing price efficiency when analysts collectively generate less public information.
A key point of our paper is that the valuation effect of options can depend on
option trading activity, over and beyond the listing of the option per se. It would be
interesting to consider whether this notion extends to other scenarios. For example,
certain countries have futures contracts on individual stocks, and the effect of trading
activity in such contracts could be ascertained. In addition, to further explore the link
between options trading and information production, the specific impact of options
trading on the adjustment of stock prices to corporate informational events such as
earnings announcements appears a worthwhile exercise.
26
References
Admati, A., and P. Pfleiderer, 1988, A theory of intraday patterns: Volume and price
variability, Review of Financial Studies 1, 3-40.
Allayannis, G., and J. Weston, 2001, The use of foreign currency derivatives and firm
market value, Review of Financial Studies 14, 243-276.
Amihud, Yakov, and Haim Mendelson, 1986, Asset pricing and the bid-ask spread,
Journal of Financial Economics 17, 223-249.
Back, K., 1992, Asymmetric information and options, Review of Financial Studies 6,
435-472.
Baptista, A., 2003, Spanning with American options, Journal of Economic Theory 110,
264-289.
Beaver, W., M. McAnally, and C. Stinson, 1997, The information content of earnings and
prices: A simultaneous equations approach, Journal of Accounting and Economics 23,
53-81.
Bhushan, R., 1989, Firm characteristics and analyst following, Journal of Accounting and
Economics, 11, 255-274.
Biais, B., and P. Hillion, 1994, Insider and Liquidity Trading in Stock and Options
Markets, Review of Financial Studies 7, 743-780.
Black, F., and M. Scholes, 1973, The pricing of options and corporate liabilities,
Journal of Political Economy 81, 637-654.
Brennan, M., T. Chordia, and A. Subrahmanyam, 1998, Alternative factor
specifications, security characteristics, and the cross-section of expected stock returns,
Journal of Financial Economics 49, 345-373.
Brennan, M., N. Jegadeesh, and B. Swaminathan, 1993, Investment analysis and the
adjustment of stock prices to common information, Review of Financial Studies 6, 799824.
Cao, H., 1999, The effect of derivative assets on information acquisition and price
behavior in a dynamic rational expectations model, Review of Financial Studies 12,
131-163.
27
Cao, M., and J. Wei, 2008, Commonality in liquidity: Evidence from the option
market, forthcoming, Journal of Financial Markets.
Carter, D., D. Rogers, and B. Simkins, 2006, Hedging and value in the U.S. airline
industry, Journal of Applied Corporate Finance 18, 21-33.
Chakravarty, S., H. Gulen, and S. Mayhew, 2004, Informed Trading in Stock and Option
Markets, Journal of Finance 59, 1235–1258.
Chen, Q., I. Goldstein, and W. Jiang, 2007, Price informativeness and information
sensitivity to stock price, Review of Financial Studies 20, 619-650.
Chordia, T., S. Huh, and A. Subrahmanyam, 2008, Theory-based illiquidity and asset
pricing, forthcoming, Review of Financial Studies.
Chowdhry, B., and V. Nanda, 1991, Multimarket trading and market liquidity, Review of
Financial Studies 4, 483-511.
Chung, K., and S. Pruitt, 1994, A simple approximation of Tobin’s q, Financial
Management 23, 70-74.
Conrad, J., 1989, The price effect of option introduction, Journal of Finance 44, 487-498.
Danielsen, B., and S. Sorescu, 2001, Why do option introductions depress stock prices?
An empirical study of diminishing short-sale constraints, working paper, Texas A&M
University.
Datar, V., N. Naik, and R. Radcliffe, 1998, Liquidity and stock returns: An alternative
test, Journal of Financial Markets 1, 203-219.
De Long, B., A. Shleifer, L. Summers, and R. Waldmann, 1990, Noise trader risk in
financial markets, Journal of Political Economy 98, 703-738.
Detemple, J., and P. Jorion, 1990, Option listing and stock returns: An empirical analysis,
Journal of Banking and Finance 14, 781–801.
Detemple, J., and L. Selden, 1991, A general equilibrium analysis of option and stock
market interactions, International Economic Review 32, 279-303.
Dow, J., and G. Gorton, 1997, Stock market efficiency and economic efficiency: Is
there a connection?, Journal of Finance 52, 1087-1129.
Easley, D., S. Hvidkjaer, and M. O’Hara, 2002, Is information-based risk a determinant
of asset returns?, Journal of Finance 57, 2185-2221.
28
Easley, D., M. O’Hara, and J. Paperman, 1998, Financial analysts and information-based
trade, Journal of Financial Markets 1, 175-201.
Easley, D., M. O’Hara, and P. Srinivas, 1998, Option volume and stock prices: Evidence
on where informed traders trade, Journal of Finance 53 431-465.
Fama, E., and K. French, 1997, Industry costs of equity, Journal of Financial
Economics 43, 153-193.
Fazzari, S., G. Hubbard, and B. Petersen, 1988, Finance constraints and corporate
investment, Brookings Papers on Economic Activity 1, 141–195.
Figlewski, S., and G. Webb, 1993, Options, short sales, and market completeness,
Journal of Finance 48, 761-777.
Fishman, M., and K. Hagerty, 1992, Insider trading and the efficiency of stock prices,
RAND Journal of Economics 23, 106-122.
French, K. and R. Roll, 1986, Stock return variances: The arrival of information and the
reaction of traders Journal of Financial Economics 17, 5-26.
Fuller, W., and G. Battese, 1974, Estimation of linear models with crossed-error
structure, Journal of Econometrics 2, 67-78.
Glosten, L., and P. Milgrom, 1985, Bid, ask and transaction prices in a specialist market
with heterogeneously informed traders, Journal of Financial Economics 14, 71-100
Gompers, P., J. Ishii, and A. Metrick, 2003, Corporate governance and equity prices,
Quarterly Journal of Economics 118, 107-155.
Hanka, G., 1998, Debt and the terms of employment, Journal of Financial Economics 48,
245-282.
Jennings, R., and L. Starks, 1986, Earnings announcements, stock price adjustments, and
the existence of option markets, Journal of Finance 41, 107-125.
Jensen, M., 1986, Agency costs of free cash flow, corporate finance, and takeovers.,
American Economic Review 76, 323–329.
Judge, G., W. Griffiths, R. Hill, and T. Lee, 1988, The Theory and Practice of
Econometrics, John Wiley and Sons, New York, NY.
Kahn, C., and S. Krasa, 1993, Non-existence and inefficiency of equilibria with
American options, Economic Theory 3, 169-176.
29
Khanna, N., S. Slezak, and M. Bradley, 1994, Insider trading, outside search, and
resource allocation: why firms and society may disagree on insider trading restrictions,
Review of Financial Studies 7, 575-608.
Kmenta, J., 1986, Elements of Econometrics (2nd Edition), MacMillan, New York.
Kyle, A., 1985, Continuous auctions and insider trading, Econometrica 53, 1315-1335.
Hakansson, N., 1982, Changes in the financial market: Welfare and price effects and the
basic theorems of value conservation, Journal of Finance 37, 977-1004.
Irwin, D, and M. Terviö, 2002, Does trade raise income? Evidence from the twentieth
century, Journal of International Economics 58, 1–18.
Lang, L., and R. Stulz, 1994, Tobin’s q, corporate diversification, and firm
performance, Journal of Political Economy 102, 1248-1280.
Mayhew, S., and V. Mihov, 2005, Short sale constraints, overvaluation, and the
introduction of options, working paper, U.S. Securities and Exchange Commission.
Mendenhall, R., and D. Fehrs, 1999, Option listing and the stock-price response to
earnings announcements, Journal of Accounting and Economics 27, 57-87.
Mikhail, M., B. Walther, and R. Willis, 2004, Do security analysts exhibit persistent
differences in stock picking ability?, Journal of Financial Economics 74, 67-91.
Mueller, D., 1987, The Corporation: Growth, Diversification, and Mergers, Harwood:
Chur, Switzerland.
Naik, V., and M. Lee, 1990, General equilibrium pricing of options on the market
portfolio with discontinuous returns, Review of Financial Studies 3, 493-521.
Newey, W., and K. West, 1987, A simple positive semi-definite, heteroskedasticity and
autocorrelation consistent covariance matrix, Econometrica 55, 703-708.
Newey, W., and K. West, 1994, Automatic lag selection in covariance matrix
estimation, Review of Economic Studies 61, 631-653.
Pagano, M., 1989, Trading volume and asset liquidity, Quarterly Journal of Economics
104, 255-274.
Pan, J., and J. Liu, 2003, Dynamic derivative strategies, Journal of Financial Economics
69, 401-430.
Pan, J., and A. Poteshman, 2006, The information in options volume for future stock
prices, Review of Financial Studies 19, 871-908.
30
Parks, R., 1967, Efficient estimation of a system of regression equations when
disturbances are both serially correlated and contemporaneously correlated, Journal of
the American Statistical Association 62, 500-509.
Pastor, L., and P. Veronesi, 2003, Stock valuation and learning about profitability,
Journal of Finance 58, 1749–1789.
Peltzman, S., 1977, The gains and losses from industrial concentration, Journal of Law
and Economics 20, 229-263.
Ross, S., 1976, Options and efficiency, Quarterly Journal of Economics 90, 75-89.
Shleifer, A., 1986, Do demand curves for stocks slope down?, Journal of Finance 41,
579-590.
Skinner, D., 1990, Option markets and the information content of accounting earnings
releases, Journal of Accounting and Economics 13, 191-211.
Sorescu, S., 2000, The effect of options on stock prices: 1973 to 1995, Journal of
Finance 55, 487–514.
Subrahmanyam, A., and S. Titman, 1999, The going-public decision and the
development of financial markets, Journal of Finance 54, 1045-1082.
31
Appendix: The Parks (1967) Procedure
This appendix describes details of the panel procedure used in Table 8. Consider a
balanced panel regression:
Yit=βk Xitk +eit
where i denotes the cross-sectional observation (the firm), k the k’th dependent variable,
and t the time indicator.
The error terms e are contemporaneously correlated and serially dependent:
E(eit2)=σii, E(eit,ejt)=σij,
and
eit=ρi ei,t-1+uit,.
Further, uit is an error term with the following assumed properties:
E(uit)=0,
E(uit, ujt)=Cij,
E(ei,t-1,ujt)=0,
and
E(uitujt′)=0 for t≠t′.
The procedure involves first using the OLS residuals to estimate the autoregression
parameters for each firm.
Denote these as ρ̂ i and construct the usual transformed
variables Yit – ρ̂ i Yi,t-1, Xitk – ρ̂ i Xi,t-1,k and eit – ρ̂ i ei,t-1 to replace of the original Yit, Xitk
and eit. OLS with the resulting transformed data provides a new set of residuals. These
second stage residuals have a contemporaneous covariance matrix with elements Cij.
Finally, the estimated covariance matrix is used to form a GLS estimator for the vector
with elements βk. It is shown in Parks (1967) that this method results in consistent and
efficient coefficient estimates.
32
Table 1
Number of firms with non-missing data.
This table contains the sample size of firms each year. The second column lists the total
number of firms with available data for the dependent variable (Tobin’s q) and the
control variables. The third column lists the number of firms with positive options
volume. Firms with no data on options trading activity are assumed to have options
volume of zero.
Year All firms
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
6366
6430
6157
5874
5633
5150
4883
4653
4603
4064
33
Positive
options
volume
1342
1575
1717
1686
1638
1503
1597
1565
1705
1655
Table 2
Summary statistics
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend.
Panel A: All firms
Variable
Mean
Median
Tobin’s q
Options volume
Size
Share turnover
ROA
CapX
LTD
DivDum
1.915
1877
2.197
1.533
-0.063
0.566
0.183
0.319
1.151
0
1.885
0.949
0.026
0.040
0.114
0
Standard
Deviation
3.364
23434
12.61
2.636
0.553
25.02
0.269
0.466
Panel B: Firms with positive options volume
Variable
Mean
Tobin’s q
2.250
Options volume 6487
Size
5.239
Share Turnover 2.241
ROA
-0.0072
CapX
0.2631
LTD
0.1852
DivDum
0.3911
34
Standard
Deviation
1.450
2.929
394
43223
1.025 19.92
1.601
2.468
0.0406 0.2947
0.0489 6.1213
0.1348 0.2075
0
0.4880
Median
Table 3
Correlation matrix
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend.
Panel A: All firms
Optvol
Size
Stkturn
ROA
CapX
LTD
DivDum
Tobin’s
q
0.0915
0.0628
0.1055
-0.1175
0.0100
-0.0464
-0.0960
Optvol
Size
Stkturn
ROA
CapX
LTD
0.4136
0.0902
0.0156
-0.0013
-0.0154
0.0146
-0.0099
0.0401
-0.0030
-0.0100
0.1497
-0.0786
-0.0015
-0.0555
-0.1331
-0.0102
-0.0806
0.1475
0.0152
-0.0125
0.0824
Panel B: Firms with positive options volume
Optvol
Size
Stkturn
ROA
CapX
LTD
DivDum
Tobin’s
q
0.1798
0.1057
0.1514
-0.0500
0.0155
-0.1350
-0.1639
Optvol
Size
Stkturn
ROA
CapX
LTD
0.4679
0.1375
0.0261
-0.0028
-0.0393
0.0040
-0.0787
0.0734
-0.0068
-0.0340
0.1823
-0.0613
0.0045
-0.0976
-0.2945
-0.0200
-0.0744
0.1781
0.0125
-0.0240
0.0661
35
Table 4
Average Tobin’s q for portfolios sorted by size and options volume
This table presents the mean value of Tobin’s q for portfolios sorted annually first by
market capitalization (Size), then by options volume. The time-period is 1996 to 2005.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets.
Options volume
quintile
1
2
3
4
5
1
1.382
1.456
1.714
2.008
2.202
36
Size quintile
2
3
1.548
1.770
1.603
1.840
1.931
2.151
2.382
2.782
2.764
3.130
4
1.596
1.792
2.316
2.858
3.370
5
1.569
2.278
2.490
3.038
4.283
Table 5
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear cross-sectional regressions from 1996 through 2005 for Tobin’s q as the
dependent variable, using the full sample of firms with available data.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend. The
coefficients of size and options volume are multiplied by 102 and 104, respectively.
Variable
Coefficient
t-statistic
Optvol
0.1297
4.83
Size
0.9875
2.18
Stkturn
0.1259
3.55
ROA
-0.8672
-3.01
CapX
0.0125
2.81
LTD
-1.0970
-2.73
Divdum
-0.4326
-4.88
2
Average adjusted R =8.55%
Average number of firms: 5381
37
Table 6
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear cross-sectional regressions from 1996 through 2005 for Tobin’s q as the
dependent variable, using only those firms with positive options volume.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend. The
coefficients of size and options volume are multiplied by 102 and 104, respectively.
Variable
Coefficient
t-statistic
Optvol
0.1188
3.38
Size
0.7017
2.09
Stkturn
0.1437
2.75
ROA
-0.5756
-1.25
CapX
0.0632
1.78
LTD
-1.631
-4.31
Divdum
-0.7293
-5.31
2
Average adjusted R =12.05%
Avg no. of firms: 1557
38
Table 7
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear cross-sectional regressions from 1996 through 2005 for Tobin’s q as the
dependent variable, using the logarithm of options volume.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend. The
coefficient of size is multiplied by 102.
Variable
Coefficient
t-statistic
Ln(Optvol)
0.1978
3.72
Size
0.8288
2.70
Stkturn
0.0873
2.35
ROA
-0.6761
-1.43
CapX
0.0569
1.66
LTD
-1.638
-4.47
Divdum
-0.7923
-5.57
Average adjusted R2=12.61%
Average number of firms: 1557
39
Table 8
Panel estimation for the period 1996 to 2005 with Tobin’s q as the dependent
variable.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), Stkturn is the annual share turnover in the underlying stock, ROA is
the return on assets defined as net income divided by the book value of assets, CapX is
capital expenditures divided by sales, LTD is long-term debt divided by book value of
assets, and DivDum is an indicator variable for whether the firm pays a dividend. The
Parks (1967) procedure is used to account for autocorrelation, using a balanced panel of
502 firms present in every year of the sample. The coefficient of size is multiplied by
102.
Variable
Ln(Optvol)
Size
Stkturn
ROA
CapX
LTD
Divdum
Panel Estimates
Coefficient
t-statistic
0.1097
12.98
2.786
26.57
-0.0857
-7.48
-0.0573
-0.22
0.3299
1.03
-0.6712
-2.97
-0.9649
-16.07
40
Table 9
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear cross-sectional regressions from 1997 through 2005 for Tobin’s q as the
dependent variable, using lagged options volume.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Lag(Optvol)
is the one-year lagged natural logarithm of annual options volume (in ten thousands of
dollars), Size is market capitalization (in billions of dollars), Stkturn is the annual share
turnover in the underlying stock, ROA is the return on assets defined as net income
divided by the book value of assets, CapX is capital expenditures divided by sales, LTD
is long-term debt divided by book value of assets, and DivDum is an indicator variable
for whether the firm pays a dividend. The coefficient of size is multiplied by 102.
Variable
Coefficient
t-statistic
Lag(Optvol)
0.0879
5.56
Size
1.381
2.60
Stkturn
0.1779
2.06
ROA
-0.0912
-0.30
CapX
0.0717
1.74
LTD
-0.9991
-4.80
Divdum
-0.8275
-5.27
2
Average adjusted R =10.19%
Average number of firms: 1359
41
Table 10
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear two-stage least-squares cross-sectional regressions from 1996 through 2005 for
Tobin’s q as the dependent variable, using only those firms with positive options
volume and using annual average absolute moneyness and open interest as
instruments for options volume.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets,
2SLS(Optvol) is the two-stage least squares estimate of the logarithm of annual options
volume (in ten thousands of dollars) using, in turn, the average absolute deviations from
even-moneyness and open interest as instruments to identify options volume, Size is
market capitalization (in billions of dollars), Stkturn is the annual share turnover in the
underlying stock, ROA is the return on assets defined as net income divided by the book
value of assets, CapX is capital expenditures divided by sales, LTD is long-term debt
divided by book value of assets, and DivDum is an indicator variable for whether the firm
pays a dividend. The coefficient of size is multiplied by 102.
Variable
2SLS(optvol)
Size
Stkturn
ROA
CapX
LTD
Divdum
Moneyness as instrument
Open interest as instrument
Coefficient
t-statistic
Coefficient
t-statistic
0.1882
2.71
0.1385
2.84
0.9429
3.23
1.118
2.91
0.1225
2.95
0.1367
2.63
-0.6452
-1.39
-0.6277
-1.35
0.0574
1.73
0.0586
1.72
-1.658
-4.41
-1.608
-4.47
-0.7430
-5.49
-0.7415
-5.78
2
Average adjusted R =11.60% Average adjusted R2=11.53%
Average number of firms: 1557
42
Table 11
Year-by-year coefficients and t-statistics for the logarithm of options volume from
annual cross-sectional regressions from 1996 through 2005 with Tobin’s q as the
dependent variable, without and with industry dummies.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets. The
explanatory variables are the logarithm of optvol, i.e., the annual options volume, Size:
market capitalization, Stkturn: the annual share turnover in the underlying stock, ROA:
the return on assets defined as net income divided by the book value of assets, CapX:
capital expenditures divided by sales, LTD: long-term debt divided by book value of
assets, and DivDum, which is an indicator variable for whether the firm pays a dividend.
The last two columns report the results when the 48 industry dummies of Fama and
French (1997) are included in the regression.
Without industry controls
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Coefficient
0.1452
0.1788
0.2236
0.5553
0.2820
0.1524
0.0898
0.0873
0.1123
0.1518
t-statistic
4.06
5.52
6.28
8.41
9.01
6.05
4.92
4.80
5.87
7.98
43
With Fama and French
(1997) industry controls
Coefficient
t-statistic
0.1351
3.79
0.1659
5.18
0.2029
5.73
0.5025
7.49
0.2405
7.54
0.1410
5.68
0.0885
5.03
0.0835
4.80
0.1085
5.87
0.1433
7.68
Table 12
Panel estimation for the period 1997 to 2005 with return on assets as the dependent
variable and explanatory variables lagged one year.
ROA is the return on assets defined as net income divided by the book value of assets,
Optvol is the annual options volume (in ten thousands of dollars), Size is market
capitalization (in billions of dollars), Stkturn is the annual share turnover in the
underlying stock, CapX is capital expenditures divided by sales, LTD is long-term debt
divided by book value of assets, and DivDum is an indicator variable for whether the firm
pays a dividend. The Parks (1967) procedure is used to account for autocorrelation, using
a balanced panel of 502 firms present in every year of the sample. The coefficient of size
is multiplied by 102.
Panel Estimates
One-year
lagged
variables
Ln(Optvol)
Size
Stkturn
ROA
CapX
LTD
Divdum
Coefficient
0.0042
0.0041
-0.0019
0.4283
0.0411
-0.1135
0.0456
44
t-statistic
12.35
0.74
-4.63
9.32
1.65
-5.98
14.45
Table 13
Panel estimation for the period 1997 to 2005 with corporate investment as the
dependent variable.
The dependent variable is corporate investment, defined as the sum of capital
expenditures and R&D expenses scaled by beginning-of-year book assets. This is
modeled as a function of the following variables. Tobin’s q is defined as the market
capitalization of common stock plus liquidation value of preferred shares plus book value
of long-term debt divided by total assets. The variable Ln(Optvol*q) is the log of the
interaction of Tobin’s q with options volume. Both these variables are lagged one period.
The log of the inverse of book assets (InvAssets) in the previous year is included to offset
any correlation induced by the common scaling variable in both the left-hand and the
preceding right-hand variables. The “Return” variable is simply the one-year leading
annual return. Cash flow is measured by net income plus depreciation, amortization, and
R&D expenses, scaled by beginning-of-year book assets. The Parks (1967) procedure is
used to account for autocorrelation, using a balanced panel of 295 firms present in every
year of the sample. All coefficients are multiplied by 100.
Panel Estimates
Explanatory
variables
Tobin’s q
Ln(Optvol*q)
InvAssets
Return
Cash flow
Coefficient
t-statistic
0.4168
0.1793
0.4436
-0.0604
2.805
8.29
8.33
6.32
-2.20
8.35
45
Table 14
Year-by-year coefficients and t-statistics for the logarithm of options volume
(LOVOL) and the logistic transformation of PIN multiplied with LOVOL from
annual cross-sectional regressions from 1996 through 2001 with Tobin’s q as the
dependent variable.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets. The
explanatory variables are the logarithm of the annual options volume (LOVOL), the
interaction of LOVOL with PINL, where PINL is the logistic transform of PIN, the
Easley, Hvidkjaer, and O’Hara (2002) probability of informed trading measure. Other
control variables are included but their coefficients are not reported. These controls are
Size: market capitalization, Stkturn: the annual share turnover in the underlying stock,
ROA: the return on assets defined as net income divided by the book value of assets,
CapX: capital expenditures divided by sales, LTD: long-term debt divided by book value
of assets, and DivDum, which is an indicator variable for whether the firm pays a
dividend.
Year
1996
1997
1998
1999
2000
2001
LOVOL
Coefficient
t-statistic
0.2297
2.82
0.4388
5.14
0.2948
4.95
0.5390
7.29
0.3795
4.03
0.3227
3.02
46
LOVOL*PINL
Coefficient
t-statistic
0.0645
1.77
0.1334
3.81
0.0650
2.66
0.1563
5.31
0.1150
2.95
0.0907
2.31
Table 15
Time-series coefficient averages and Newey-West corrected t-statistics for year-byyear cross-sectional regressions from 1996 through 2005 with Tobin’s q as the
dependent variable, and with analysts following interacted with options volume.
Tobin’s q is defined as the market capitalization of common stock plus liquidation value
of preferred shares plus book value of long-term debt divided by total assets, Optvol is
the annual options volume (in ten thousands of dollars), Size is market capitalization (in
billions of dollars), ANALYS is a variable that takes on the values 0, 1, or 2 for three
equal portfolios sorted by low to high analyst following, Stkturn is the annual share
turnover in the underlying stock, ROA is the return on assets defined as net income
divided by the book value of assets, CapX is capital expenditures divided by sales, LTD
is long-term debt divided by book value of assets, and DivDum is an indicator variable
for whether the firm pays a dividend. The coefficient of size is multiplied by 102.
Variable
Ln(Optvol)
Ln(Optvol)*ANALYS
Size
Stkturn
ROA
CapX
LTD
Divdum
Coefficient
0.2573
-0.0293
0.9940
0.0183
-0.6138
0.0565
-1.5869
-0.7511
47
t-statistic
4.23
-3.78
2.96
2.38
-1.37
1.67
-4.55
-5.61
Figure 1. Average Tobin’s q and Options Volume
Firms with positive options volume during 1996-2005 are sorted into ten deciles by
options volume. The mean value of Tobin’s q over all sample years within each decile is
depicted below.
Figure 1: Tobin's q vs. options volume decile
4
3.5
Tobin's q
3
2.5
2
1.5
1
0.5
0
1
2
3
4
5
6
Options volume decile
48
7
8
9
10