The Market Value of Corporate Votes: Theory and
Evidence from Option Prices
Avner Kalay, Oǧuzhan Karakaş, and Shagun Pant∗
January 2011
ABSTRACT
This paper quantifies the market value of the right to vote as the difference in the
prices of the stock and the corresponding synthetic stock. Votes are found to have
positive value that increases in the time to expiration of the options used to construct
the synthetic stocks. Consistent with the theory, the value of vote increases around
special meetings, with a larger increase for meetings with a high-ranking agenda, and
where the proposal discussed has (ex-post) close votes. The value of the vote increases
around M&A events and periods of hedge fund activism. We show that the value of
the vote is not bounded by exogenous arbitrage activity - to the contrary- the value of
the vote is an important ingredient in the cost of the put call arbitrage activity. We
estimate the mean annualized value of a voting right to be 1.58% of the underlying
stock price.
∗
Kalay is with the University of Utah and Tel-Aviv University, Karakaş is with Boston College, and
Pant is with Texas A&M University. This paper combines two earlier papers: “The Market Value of
the Vote: A Contingent Claims Approach” by Kalay and Pant and “Another Option for Determining the
Value of Corporate Votes” by Karakaş. We thank seminar participants at the 2010 WFA, 2009 NFA,
2009 Banff Frontiers in Finance Conference, 2009 Drexel Corporate Governance Conference, 2009 NYUPenn Law and Finance Conference, 2008 FMA Doctoral Consortium, Arizona State University, Bilkent
University, Boston College, Boston University, Columbia University, EMLYON, Erasmus University, Harvard
Business School, Imperial College, INSEAD, London Business School, MIT, NYU, Rutgers University,
Stanford University, Tel Aviv University, Texas A&M University, Tilburg University, UC Berkeley, UCLA,
University of Alberta, University of Florida, University of Iowa, University of Pennsylvania, University of
Utah, Washington University in St. Louis, Yale University, and conference held in the honor of Haim Levy
for helpful comments. We also thank Viral Acharya, Yakov Amihud, Shmuel Baruch, Hank Bessembinder,
Jennifer Carpenter, Francesca Cornelli, Julian Franks, Denis Gromb, Joel Hasbrouck, Michael Lemmon,
Stewart Myers, Hélène Rey, Henri Servaes and Paolo Volpin for their helpful comments. Conversations
with Nihat Aktaş, Sirio Aramonte, Yasuhiro Arikawa, Ramin Baghai, Süleyman Başak, Morten Bennedsen,
Mikhail Chernov, Alexander Dyck, Daniel Ferreira, Marc Gabarro, Francisco Gomes, Jungsuk Han, Brandon
Julio, Eugene Kandel, Samuli Knüpfer, Xi Li, Lars Lochstoer, Michelle Lowry, Pascal Maenhout, Massimo
Massa, Narayan Naik, Anna Pavlova, Joël Peress, Urs Peyer, Ludovic Phalippou, Astrid Schornick, Lucie
Tepla, Theo Vermaelen, Vikrant Vig, Russ Wermers and Robert Whitelaw contributed greatly to this paper.
Financial supports from Marie Curie Early Stage Research Training Host Fellowship and from London
Business School’s Centre for Corporate Governance under ESRC contract number R060230004 are gratefully
acknowledged by Karakaş.
Electronic copy available at: http://ssrn.com/abstract=1747952
The estimation of the market value of the right to vote1 embedded in common stocks
has been a topic of continual interest to financial economists. However, the separation of
the market value of the vote from the ownership of the cash flows generated by the firm is
not trivial.2 In this paper we propose, develop, and test a new methodology to measure the
market value of the vote. We quantify the value of the vote as the difference in the price
of the stock and the price of the corresponding synthetic stock that is constructed using
options.
Evidence on the market value of the vote thus far has been focused on two methods
of estimation. The first method computes the market value of the vote by observing the
difference between the prices of multiple classes of stocks having identical cash flow rights
and differential voting rights.3 Studies that employ this method, find that the shares with
superior voting rights trade at a premium implying a positive market value to the right to
vote. As Table I reveals, there is considerable variation across countries and time periods in
the documented value of the vote. It varies from a low of 2% of the value of the share for 39
firms listed for trade in the US to a high of 81.5% of the value of the share for 96 firms traded
in Italy. By construction, however, application of this method of estimation is restricted to
firms listed on exchanges as having dual class of shares resulting in small samples (typically
less than 100). Moreover, the two classes usually differ in their liquidity thereby complicating
the extraction of the value of the vote from their price differences. More importantly, these
samples are potentially subject to selection biases – firms issuing dual classes of shares are
likely to have their reasons to do so, and stockholders buying the shares with the inferior
1
All through the paper we use the term “vote” and “right to vote” interchangeably.
2
See Adams and Ferreira (2008) and Burkart and Lee (2008) for surveys of empirical and theoretical work
on disproportional ownership and corporate control.
3
See, for example, Levy (1982), Lease, McConnell, and Mikkelson (1983), Rydqvist (1996), Zingales
(1994), Zingales (1995), Nenova (2003), and Karakaş (2010). Hauser and Lauterbach (2004) examine
compensation paid to owners of superior voting rights during a process of unifications of dual classes of
shares and find a positive value to the vote. Table I provides a quick summary of these studies.
1
Electronic copy available at: http://ssrn.com/abstract=1747952
voting rights are likely to value the right to vote the least (see, for example, DeAngelo and
DeAngelo (1985) and Smart and Zutter (2003)).
The second method focuses on privately negotiated block sales and measures the value
of control as the difference between the price per share at which a block trades and the
price per share prevailing in the market right after the block sale.4 The price paid for the
controlling block consists of the ownership of the future cash flows that the block generates
and the value of the private benefits of control. The difference between the price per share
paid by the controlling blockholder and the market price per share right after the block trade
is used as a measure of the value of control. Dyck and Zingales (2004) find an average control
value of 14% with estimates ranging from −4% in Japan to 65% in Brazil.5 This approach
is unable to measure the value of control when the controlling block is not transferred. The
other limitations are the potential selection bias and the small sample size.
Our technique of estimating the market value of the vote uses the existence of derivative
markets. The derivative market enables the construction of synthetic stocks. An investor
that buys a call option, sells a put option with the same strike price and time to expiration,
and, invests in a risk free asset an amount equal to the present value of the strike price, creates
a synthetic stock.6 These synthetic stocks replicate the cash flows that the stockholder is
entitled to, but, do not give the holder the right to vote.7 Thus, we quantify the value of
the vote as the difference in the price of the stock and the price of the synthetic stock. The
advantages of our technique are three fold. First, it enables the estimation of the market
4
See, for example, Barclay and Holderness (1989) and Dyck and Zingales (2004). Table I provides a quick
summary of these studies.
5
An exception to the above mentioned methods is the study by Christoffersen, Geczy, Musto, and Reed
(2007) that uses a proprietary database from a custodian bank and quantifies the market value of the vote
as the incremental cost of borrowing stock around the record date. They conclude that the vote sells for
zero. In contrast, using a larger data set, Aggarwal, Saffi, and Sturgess (2010) find positive lending fees,
especially when the supply of shares are restricted.
6
This argument implicitly assumes that the options are European style.
7
An adjustment needs to be made for the payments of cash dividends during the life of the options.
2
value of the vote for all stocks that have options traded on them. Thus it allows for the
quantification of the market value of the vote for a large number of stocks. Second, the
trading of options on the stock of a firm is primarily an exogenous event that is not under
the control of the shareholders of the firm. Hence, the sample of stocks used does not suffer
as much from selection bias issues. Third, we can estimate the value of voting right attached
to a stock at any time, as long as the stock has call and put option pairs of same maturity
and strike price traded.
To begin with, let us consider European style options. At option expiration, the price of
the synthetic stock and the stock converges. An investor that holds a synthetic stock forgoes
the voting right only during the life of the synthetic stock. This means that the difference
in the price of the stock and the synthetic stock gives a measure of the right to vote during
the life of the synthetic stock. As a result, our measure gives us the market value of the
vote during the life of the options used to construct the synthetic stock. Consequently, we
expect the market value of the vote to be an increasing function of the time to maturity of
the options used to construct the synthetic stock.
Our experiment compares prices of synthetic stocks and stocks of US equities. As is well
known, the options on equities in the US are American style. The possibility of early exercise
has important implications on the estimation of the market value of the vote. First, one has
to compute the early exercise premium embedded in the prices of American style calls and
puts to compute the price of the synthetic stock. Second, the expected life of a synthetic
stock constructed with American style options is almost always less than the official time
to expiration, T .8 Hence, the difference in the price of the stock and the synthetic stock
quantifies the market value of the vote during the expected life of the synthetic stock.
8
The owner of the synthetic stock owns a call option and writes a put option on the underlying stock.
She can buy the stock by voluntarily early exercising her call option, or by being forced to buy the stock
from the holder of the put option she sold. From that point on she owns a stock with the associated voting
right.
3
Furthermore, when the call option used to construct the synthetic stock is very deep in
the money and close to expiration the value lost by its early exercise is small. Thus, prior to
an important voting event or the completion of an M&A activity, the holders of a deep in the
money call option can optimally exercise. For these option holders the loss due to forgone
time value is minimal. In general, the lower the time value of the option, the more likely
are the call option holders to exercise in an attempt to capture the value of the vote. This
means that call options can be exercised early even when the underlying pays no dividends.
The early exercise premium in the price of the call option due to the drop in the value of
the vote introduces a downward estimation bias in our measure. At the same time, biases
are also introduced in the computation of the early exercise premium of the put option due
to the change in the vote component.9 We conduct simulations to quantify these biases and
find that estimation biases are minimized for synthetic stocks that are constructed with close
to the money options.
Another way to interpret the method is that the voting rights are akin to a dividend.
Applying this insight, one can deduce a lower bound for the value of the vote from putcall parity bounds for American options. Even though we adopt the direct measure of
value of voting rights as the main framework for our tests, we compare our results to those
obtained using the lower bound approach. In general, we observe that the main results are
qualitatively the same with both methods. This finding suggests that the model dependency
of our computation of the early exercise premium is not critical for our results.10
9
We present these concepts more formally in Section I.
10
Two other works that also look at the put-call parity to compute the value of the vote have been recently
brought to our attention. Hodges (1993) in an independent PhD dissertation proposes the construction
of synthetic stocks to compute the value of the vote. This study ignores the early exercise premium in
constructing the synthetic stock. Additionally, the results are frequently statistically insignificant. In an
independent undergraduate honors thesis, Dixit (2003) uses synthetic stocks to value voting rights for the
HP-Compaq merger and finds a voting premium of 0.4%. However, while constructing synthetic stocks the
early exercise premium is ignored. The author fails to recognize the biases in the estimation. Finally, the
effect of the time to maturity of the options used to construct the synthetic stock on the market value of the
vote is not recognized.
4
Our estimation focuses on three instances where voting rights would be expected to
increase in value: shareholder meetings, episodes of hedge fund activism, and mergers and
acquisitions. In our empirical analysis, we use the IvyDB OptionMetrics database. Synthetic
stocks are constructed from pairs of call and put options on the same underlying stock with
90 days or less to expiration during the period 1996 through 2007. The sample covers 4, 768
firms. Consistent with the theory we find that our measure (the difference between the
price of the stock and the synthetic stock) is an increasing function of the official time to
expiration of the options used to construct it. When options with no more than 10 days
to expiration are used to construct the synthetic stock, we find the value of the vote to be
0.06% of the price of the stock. Constructing synthetic stocks with options having between
81 to 90 days to expiration, we find a significantly larger market value of the vote at 0.26%
of the price of the stock. As expected, the market value of the vote for the next 81 to 90
days is dramatically larger than the market value of the vote for less than 10 days.
Using close to the money options with maturity around 38 days, we document the value
of the vote for the average firm in our sample at 0.164%. This translates into an annualized
voting premium of 1.58%. The voting premium varies from a low of 0.11% in 2004 to a high
of 0.21% in 2001. Interestingly, the pattern that we document in the voting premium across
time bears some resemblance to the contemporaneous intensity of merger activity.
The voting premium calculated from dual class firms is (conceptually) closest to our
measure of the value of voting rights. To compare the two measures, we intersect the dual
class firms compiled by Gompers, Ishii, and Metrick (2010) with our sample. A total of 39
firms are in both samples. 27 matched through their inferior voting shares and 12 matched
through their superior voting shares. For the set of 12 dual class firms that have options
traded on the superior class of shares, we find the average dual class premium to be 7.0%,
whereas the average annualized option premium is 6.7%. The simple coefficient of correlation
between these two different measures of value of voting rights is significantly positive (0.22
at p < 0.0001). For the set of 27 dual class firms that have options traded on the inferior
5
class of shares, we find the average dual class premium to be 3.8%, whereas the average
annualized option premium is 1.2%. The simple coefficient of correlation between these two
different measures of value of voting rights is small and not significant (0.005 at p = 0.727).
These results are interesting and in agreement with economic theory. Where the options
are traded on the inferior class of shares, our measure captures the smaller residual voting
rights. While our estimate of the market value of the vote where options are traded on the
superior class of shares, is as expected, significantly larger and correlated with the dual class
measure.
The market value of the vote displays time series variation, and in particular, it should
increase around voting events that significantly alter the cash flows of the firm. At the same
time our measure should also exhibit cross-sectional variation based on the characteristics of
the events. We test these hypotheses by examining the variation of the average market value
of the vote around shareholder meetings, specifically annual and special meetings. Data on
record dates and meeting dates for firms from 1997 to 2007 is obtained from ISS. We find
that for annual meetings there is very little variation in the value of the vote. However, there
is a substantial increase in the value of the vote around special meetings. The value of the
vote starts to increase several days prior to the record date. We also observe a drop in the
value of the vote after the record date. For a subset of the meetings where data is available,
we find that the change in the value of vote is higher for special meetings, for meetings with
a high-ranking agenda, and if the proposal discussed has (ex-post) close votes. These results
are in line with the hypothesis that the more likely the meetings are to be contentious, the
higher the value of voting rights.
What if the difference between the price of the stock and the synthetic stock is wide can arbitrageurs profit from this? Can they put an upper bound on the possible difference?
Theory suggests that the answer is No. If the synthetic stock is significantly lower than the
stock, arbitrage activity to profit from the gap requires a short position in the stock and
long in the synthetic stock. But around special voting events, shareholders are expected
6
to require substantial compensation for lending their stocks. Thus, the importance of the
vote determines the effective transaction costs of the put-call parity arbitrage. We present
evidence that supports this proposition. First, we divide the firms in our sample into groups
based on market size, and find no relationship between firm size and the voting premium.
Transaction costs associated with trading options written on stocks of large firms should be
lower and short selling less costly - yet the gap between the stock and the synthetic stock
we document is not smaller. Next, the data on shareholder meetings is divided into groups
based on the trading volume of the underlying asset. We find no relationship between the
increase in the voting premium around meetings and the liquidity of the underlying. We also
divide the meetings into groups based on the volume of the options used to construct the
synthetic stock. Again, we find no relationship between the increase in the voting premium
and the volume in the option market. We also use relative short interest (RSI) as a proxy
for short sale constraints as suggested by Boehme, Danielsen, and Sorescu (2006). RSI is
the percentage of shares that are held short for each firm. Boehme, Danielsen, and Sorescu
(2006) show that RSI is highly correlated with equity lending fees. We find that even
after controlling for RSI our results remain unchanged. All of the evidence suggests that
our measure is indeed picking up the value of the vote and is not just a manifestation of
decreased liquidity or high short-sale constraints.
Second part of our empirical analysis focus on hedge fund activism.
Compared to
traditional investors, hedge funds use more sophisticated financial products (e.g., options,
equity swaps, etc.) and more aggressive tactics. Klein and Zur (2009) find that activist
hedge funds achieve their goals by posing a credible threat of engaging the target into a
proxy solicitation contest. For this reason, hedge fund activism provides an ideal setting to
study the value of voting rights. We use Brav, Jiang, Partnoy, and Thomas (2008)’s sample
of US firms targeted by activist hedge funds between 1990 and the first half of 2008.11 For
each target, the data set includes the date of engagement and detailed information about
the engagement such as type or hostility of the engagement. Of the 1,066 sample firms, 424
11
We are grateful to Brav et al. for sharing their data with us.
7
have the needed options and financial data in the intersection of OptionMetrics and CRSP
databases. Out of these 118 are classified as hostile. We find that the value of the vote
increases after the announcement of the hedge fund activism. The increase in the value of
the vote is higher for hostile engagement. We also control for the volume of the underlying
stock and the option volume and find that our results remain unchanged.
Third part of our empirical analysis is on M&A activities. A significant fraction of the
special meetings are centered on M&A activity. To investigate the time series behavior of
the value of the vote around M&A events we obtain data from SDC Platinum. Our data
consists of M&A activity from 1996 to 2005. We keep only those deals for which the target
has options traded and where a successful deal would have resulted in the acquirer owning
at least a 50% stake in the target. The resulting sample consists of 1, 525 M&A events.
We estimate the price of the synthetic stock on the target for every day starting from 200
trading days before the announcement to up to 200 trading days after the completion of
the deal. The completion date is either the date the deal is effective or it is the date the
deal is withdrawn. We find a significant jump in the value of the vote on the announcement
date of the M&A activity. While the average value of the vote during days −20 to −1 is
slightly negative, it jumps to 0.22% during days 0 to 19. We observe a significant drop in
the value of the vote right after the merger completion date.12 While the drop is large for
deals that were effective, the deals that are withdrawn do not exhibit a drop in the value
of the vote. In summary, the time series variation documented around special meetings,
12
The documented drop in the market value of the vote at the completion of the M&A deal indicates
that it can be optimal to exercise deep in the money call options prior to the official expiration, even if the
underlying stock pays no dividends. Holders of deep in the money call options can capture the value of
the vote by exercising their American style options prior to the drop in the value of the vote. In this case
early exercise of call options can be optimal even in the absence of dividends. In other words, dividend like
behavior of the value of voting rights might make early exercise of call options optimal. This study is the
first to point out that early exercise of call options can be optimal even in the absence of dividends on the
underlying. At the same time some put option holders will find it optimal to delay exercise until after the
drop in the vote.
8
hedge fund activism, and M&A activity lend further support to our proposed measure of the
market value of the vote.13
Our measure of the market value of the vote seems to be a good estimate of the private
benefits of control. In a related paper, Kalay and Pant (2010) model shareholders’ choice of
voting/cash flows mix in the presence of derivative market around control contests. In their
model, where shareholders are risk neutral and markets are frictionless, the optimal use of
synthetic stocks enables extraction of the entire private benefits of control from the winning
team. In such a case, at the time of the control contest, the difference between the prices
of the stock and the synthetic stock quantifies precisely the per share private benefits of
control. The actual estimate of the market value of the vote is unlikely to capture the entire
private benefits of control. The idealized conditions for the extraction of the entire private
benefits of control are unrealistic. Yet, Ehling, Kalay, and Pant (2010) present evidence
indicating that firms with a larger percentage gap between the prices of their stock and their
synthetic stocks exhibit a higher propensity to buy insurance. This is consistent with the
agency rationale for corporate purchase of insurance - managers are buying insurance to
protect their rents. More importantly, the evidence indicates that our measure of the private
benefits of control, while partial, works fairly well in the cross section.
The rest of the paper is organized as follows.
Section I outlines the method and
testable hypotheses. Section II describes the data and documents the value of voting rights.
We present an empirical analysis of the market value of voting rights around shareholder
13
Our theory may help explain some of the irrational exercise patterns documented in the literature. For
instance Poteshman and Serbin (2003) document irrational early exercises of call options. It also helps to
explain some (the estimated gap between the stock and the synthetic stock could also contain non-voting
related costs of short selling) of the asymmetric violation of the put call parity documented in the literature.
Klemkosky and Resnick (1979) document violations in the put call parity relationship for a sample of fifteen
stocks during the first year of put trading on the CBOE. Fifty eight percent of the violations occur because
the price of the stock was higher than the price of the synthetic stock. Ofek, Richardson, and Whitelaw
(2004) find that 65% of put call parity violations are such that the price of the stock is higher than the
synthetic stock. Both of these findings can be explained by a positive market value of the vote. Battalio and
Schultz (2006) use intraday option data for a small sample of stocks and find symmetric violations.
9
meetings in Section III, for activist hedge fund targets in Section IV, and around mergers
and acquisitions in Section V. Section VI concludes.
I. Market Value of the Vote: Put-Call Parity Revisited
The put-call parity relationship (see Stoll (1969)) for European style options on non-dividend
paying stocks is stated as:
S + p = c + P V (X),
(1)
where c is the price of the call option with strike X and time to expiration T , p is the
price of the put option with strike X and time to expiration T , and, P V (X) is the present
value of investing in a bond with face value X that matures at time T . Investors can design
a synthetic long position in the stock by buying a call option with strike X and time to
maturity T , writing a put option with strike X and time to maturity T , and, investing in a
bond with face value X for time T . Similarly, investors can design a synthetic short position
in the underlying stock.
Ŝ(T ) = c − p + P V (X),
(2)
where Ŝ(T ) represents a position in the synthetic stock. These synthetic stocks replicate
the cash flows of the underlying stock, but, do not give the investors voting rights, i.e., the
owner of the synthetic stock is not entitled to vote. Hence an adjustment to the put-call
parity must be made that reflects the right to vote which is enjoyed only by the owner of
the stock. The modified put-call parity relationship is now stated as:
S + p = c + P V (X) + P V (V oteT ),
10
(3)
where P V (V oteT ) reflects the market value of the vote prior to option expiration.14 In other
words, the synthetic stock is a function of T , or the time to expiration of the options that
are used to construct it. At option expiration the price of the synthetic stock and stock
converge. Hence, the difference in the price of the stock and the synthetic stock gives the
market value of the vote in the next T days.
P V (V oteT ) = S − Ŝ(T ).
(4)
A. American Style Options
When the options are American style, the option holder has the right to exercise the options
prior to maturity. The put-call parity adjusted for the early exercise premium and for
dividends is stated as:
S = C − EEPcall − P + EEPput + P V (X) + P V (div) + P V (V oteT ).
(5)
The EEPcall in the above equations quantifies the value of the right to exercise the call
option anytime prior to option expiration. It is well known that American call options might
be exercised early if there is a large enough dividend prior to the expiration of the option.
Since historical dividend information is readily available, it is easy to calculate the part of
the EEPcall due to dividends. However, if the vote component of the underlying stock is
expected to decrease prior to option expiration (this could be the case if for instance there
is an important voting event that takes place prior to option expiration after which the vote
component of the stock is expected to decline) then it could be the case that early exercise
of call options is optimal even if the underlying stock pays no dividends. Since, we do not
have the vote component of the stock, we are unable to adjust for the early exercise premium
of the call option due to the vote. This introduces a bias in the estimation of the vote. In
14
Note that if voting rights are valuable (e.g., during a takeover contest), a voting right is akin to a
dividend right. Therefore one may also interpret P V (V oteT ) as the present value of a voting right dividend.
11
addition to initiating early exercise of the call options, the vote component also introduces
biases in the estimation of the early exercise premium of the put. Next, we study these
biases in detail.
A.1. Exercise Behavior of the Call
For simplicity let us consider that the underlying stock does not pay any dividends. If the
vote component of the stock is expected to decrease prior to option expiration, then it could
be optimal for call option holders to exercise their options prior to the drop in the value of
the vote. In this case, the only way an option holder can realize the value of the vote is
by exercising the call option on or before the last cum-vote day15 . The option holder will
exercise only if the expected drop in the value of the vote is large enough relative to the time
value of the option on the ex-vote day.
In order to calculate the value of the vote in the next T days, we need to construct
the synthetic stock which requires an accurate quantification of the EEPcall . However, to
calculate the EEPcall accurately we need to know the expected drop (if any) in the value of
the vote. If the EEPcall which is attributed to the drop in the value of the vote is ignored,
we will overestimate the value of the synthetic stock and hence underestimate the value
of the vote. The downward bias in the measurement of the value of the vote (due to the
inability to measure the EEPcall attributed to the drop in the value of the vote) will be
a function of the moneyness of the call option used to construct the synthetic stock. Call
options that are out of the money will have a lower probability of early exercise than options
that are at the money or in the money. As options get more in the money the value of
the EEPcall due to the vote will be higher. Hence, the difference in the price of the stock
and the synthetic stock will be a function of the moneyness of the options used to construct
the synthetic stock. More formally, let v be the expected drop in the value of the vote.
Consider two call options with the same time to maturity and strike prices X1 and X2 where
15
Cum-date is three trading days before the record date.
12
vote
X1 < X2 . Also, we denote the early exercise premium due to the vote as EEPcall
. The
early exercise premium of these options is a function of (a) the probability that this option
will be in the money on the last cum-day and (b) the probability that it will be optimal to
exercise early, given that the option is in the money on the last cum-day. The probability
of a call option being in the money on the last cum-day decreases with increasing strike
price, i.e., options with lower strike prices have a higher probability of being in the money
on the last cum-day. This implies that there is a strictly higher probability that the option
with strike X1 will be in the money on the last cum-day. Additionally, we know that the
time value of in the money call options is an increasing function of the strike price, i.e.,
conditional on two options being in the money the option with a lower strike price will have
a lower time value. This is equivalent to T V (X1 ) < T V (X2 ), where T V (X) is the time value
of a call option with strike X. Shareholders will exercise the call option early on a stock
paying no dividends if S − X > S − v − X + T V (X). This is equivalent to v > T V (X).
Since T V (X1 ) < T V (X2 ), this implies that if both the options are in the money on the last
cum-day there is a strictly higher probability that the option with the lower strike X1 will
be exercised early. The preceding analysis implies that call options with a lower strike price
vote
have a higher probability of being exercised early. Thus the EEPcall
will be higher for the
vote
option with a lower strike price, i.e., the EEPcall
is a decreasing function of the strike price.
vote
Since we are unable to measure the EEPcall
the synthetic stock is now constructed as:
Ŝ(T ) = C − P + EEPput + P V (X).
(6)
Let us assume for now that we are able to accurately estimate the EEPput . In this case, for
American options the difference between the price of the stock and the price of the synthetic
stock then is the value of the right to vote less the early exercise premium of the call due
to the expected drop (if any) in the vote component of the underlying stock:
vote
S − Ŝ(T ) = P V (V oteT ) − EEPcall
.
13
(7)
Since we are not able to account for the early exercise premium in the call option due to the
vote
vote, this introduces a downward bias in the estimation of the vote. Since EEPcall
is an
increasing function of the moneyness (which is quantified as ln(S/X)) of the call option, the
downward bias also increases with increasing moneyness. As the call option is more in the
money, the downward bias in the estimation of the vote due to the early exercise premium
of the call increases. The drop in the value of the vote triggers early exercise of call options
that have smaller strike prices.
A.2. Exercise Behavior of the Put
The drop in the value of the vote introduces an exact opposite reaction in put option holders.
Put option holders may find it optimal to delay exercising their options until after the drop
in the value of the vote. The put option holder can capture the vote by exercising the put
option right after the drop in the value of the vote. Delaying exercise is optimal only if the
drop in the value of the vote is large relative to the interest rate.
The probability of the delay in exercise due to the vote will depend on the strike price of
the put option. Put options that are in the money and have a high strike price, i.e. are more
in the money will have a smaller likelihood of delay in exercise. Delaying exercise of the put
option until after the ex-vote day results in a loss of the interest rate on the strike price.
However, delaying exercise means that the option holder gains the present value of the vote
and also retains the right to decide whether or not to exercise in the future. The question
of delay in exercise only arises for those options that would have been exercised prior to the
ex-vote day in a world where there is no drop in the value of the vote. Let us say that in a
world where there is no drop in the value of the vote, the put option is optimally exercised
on day t. The ex-vote day is denoted as tv . Delay in exercise will occur when two conditions
are satisfied, a) the options would have been exercised prior to the ex-vote day in a world
where there is no drop in the value of the vote, i.e. t < tv , and b) the present value of the
vote is higher than the lost interest due to early exercise.
14
The probability that a put option would have been exercised prior to the ex-vote day
in a world where there is no vote dividend depends on the strike price of the put option.
Put options with a higher strike price, i.e. those that are more in the money have a higher
probability of t < tv . However, the lost interest due to delay in exercise will be higher for
the put options with a higher strike price. As a result, given that t < tv , the option with the
smaller strike price has a higher probability of delay in exercise due to the vote. In options
where the vote induces a delay in exercise, the right to exercise is not as valuable as in a
world where there is no vote. This means that when we estimate the early exercise premium,
we will over estimate the early exercise premium and hence under estimate the vote for these
particular options.
A.3. Simulations
As explained above, the bias in the early exercise premium of the call introduces a downward
bias in the estimation of the vote. Additionally, the downward bias is an increasing function
of the moneyness. The bias in the value of the vote introduced due to the delay in exercise of
the put options also introduces a downward bias. In addition to the biases due to the change
in exercise behavior of the call and put options, there are other estimation errors that are
introduced as a result of ignoring the vote component in the computation of the early exercise
premium of the put. We explain this in detail in Appendix B. We conduct simulations to
better understand how these biases vary with different strike prices and different expected
ex-vote days. The aim of this experiment is to find the level of moneyness that results in the
least biased estimates of the value of the vote. The details of the simulation are described
in Appendix B and results are reported in Table II. We find that the bias in the estimation
of the vote is minimized when the options are close to the money. For options that are
close to the money, there is a downward bias introduced due to the inability to estimate
the early exercise premium in the call due to the vote. However, at the same time this is
precisely where the early exercise premium of the put options is underestimated slightly. As
15
a result the two biases partially cancel each other out. Although, we still measure the vote
with a downward bias, the bias is minimized substantially for close to the money options.
An additional advantage of using close to the money options is increased liquidity. These
options have higher volumes and lower spreads, that helps minimize issues related to nonsynchronous trading in the option and equity markets.
A.4. Lower Bound for the Value of Voting Rights
Applying the insight that the voting rights are akin to a dividend, one can easily deduce the
following lower bound for the value of voting rights from put-call parity bounds for American
options (see Hull (2002)):
P V (V oteT ) ≥ S − X − C + P − P V (div).
(8)
Even though we adopt the direct measure of value of voting rights described in the
previous sections as the main framework for our tests, we consider the lower bound for the
value of voting rights as a complementary approach. The lower bound approach implicitly
assumes that the lower bound for the value of voting rights has similar properties to the
value of voting rights itself. While the lower bound measure is more difficult to interpret
as it is mostly negative,16 it has the advantage of not being model dependent and being
less difficult to compute. In general, the main results are qualitatively the same with both
methods. This suggests that the downward bias from ignoring the component of the early
exercise premium due to voting events does not play a major role. The findings also suggest
that the model dependency of the main framework for the calculation of the early exercise
premium is not critical for our results. Please see Appendix D for more detailed discussion
and comparison of results.
16
Note that in the absence of value of voting rights, the bound should always be less than or equal to zero
due to no arbitrage.
16
B. Testable Hypotheses
The difference between the price of the stock and the price of the synthetic stock (constructed
as illustrated above) provides a measure (possibly downward biased) of the value to vote in
the next T days. This leads to the following testable empirical implications.
1. If control rights have value then the difference in the price of the stock and the synthetic
stock should be non-negative.
2. If control rights have value then the difference in the price of the stock and the synthetic
stock should be a non decreasing function of the time to maturity.
3. If control rights have value then the difference in the price of the stock and the synthetic
stock should increase when having the right to vote is valuable. We look at three
scenarios where the right to vote is expected to be important - shareholder meetings,
hedge fund activism, and mergers and acquisitions.
II. Value of the Vote
A. Data
We combine data from several sources.
To construct synthetic stocks we use data on
options from the IvyDB OptionMetrics database. This gives us end of day data on options.
OptionMetrics gives us Bid and Ask quotes, option volume, and open interest for calls and
puts traded on the stocks. We use data for options with 90 days or less to expiration on
stocks from 1996 through 2007. We form option pairs that are used to construct the synthetic
stock. An option pair consists of a call option on the underlying stock matched with a put
option with the same strike price X and time to maturity T . We discard option pairs where
the quotes for either the call or the put option are locked or crossed. We keep only those
17
option pairs for which the volume for both the call and put is greater than zero and the
implied volatility (calculated using the Binomial option pricing model) for the call and put
is defined. Next, we match the data with CRSP to get information on distributions and
the corresponding ex-dates. Since the options are all American style we compute the Early
Exercise Premium for the put and the call using the Binomial option pricing model.17 This
information enables us to construct the synthetic stock using the following equation:
div
div
Ŝ(T ) = C − EEPcall
− P + EEPput
+ P V (X) + P V (div),
(9)
where C and P are the mid-points of the closing bid and ask quotes for the call and put
options respectively. Finally, the difference between the closing price of the stock and the
synthetic stock normalized by the price of the stock is calculated as the normalized value of
the right to vote in the next T days, V oteTnorm :
V oteTnorm = (S − Ŝ(T ))/S.
(10)
We refer to this data set as the option universe. The option universe is used to test the
variation of V oteTnorm with the time to maturity T and to quantify the value of the vote for
an average firm in our sample.
B. Value of the Vote in the Next T Days
The owner of the synthetic stock is entitled to all the cash flows that would accrue to the
owner of the stock but does not have the right to vote. At first glance it seems natural to
conclude that the difference in the price of the stock and the price of the synthetic stock
should provide a measure of the market value of the vote that is embedded in the stock.
However, the synthetic stock is a function of T , or the time to maturity of the options
17
See Appendix A for details.
18
that are used to construct the synthetic stock. At option expiration (or exercise) the price
of the synthetic stock and stock converge. Hence, the difference in the price of the stock
and the synthetic stock gives the value of the right to vote during the expected life of the
synthetic stock. A natural experiment is then to construct synthetic stocks with varying T
and characterize the market value of the vote as a function of T . We would expect to see a
non-decreasing relation between S − Ŝ(T ) and T .
In order to test this hypothesis, we first sort the synthetic stocks into three bins of 0 to
30 days to maturity, 31 to 60 days to maturity, and, 61 to 90 days to maturity. We find
support for our hypothesis. The average market value of the vote is 0.09% for the 0 to 30
days bin, 0.14% for the 31 to 60 days bin, and, 0.22% for the 61 to 90 days bin. Panel A and
Panel B of Table III show the relationship between the value of the vote and T for 30 day
bins and 10 day bins respectively. We also look at the variation of the value of the vote with
T at daily intervals. The results are in Figure 1. The figure plots the average normalized
value of the vote for synthetic stocks with 2 days, 3 days,....., and, 89 days to maturity. It
also plots the standard errors around the average. We find that the general trend in the data
supports our hypothesis that the normalized difference between the stock and the synthetic
stock measures the value of the right to vote in the next T days. The average value of the
vote for options with 2 days to maturity is 0.04% and for options with 89 days to maturity
is 0.28%.
The evidence so far establishes that the estimated market value of the vote is a function
of the expected life of the synthetic stock. We find that the market value of the vote increases
as the time to expiration of the options increases.18
18
The evidence documented here is for the average stock and hence is estimated at the portfolio level. Yet,
because the ex-ante probability of a voting event is a non-decreasing function of the time period, the market
value of the vote should also be non-decreasing function of the time period for each stock. Using the lower
bound approach to value the voting rights, we also find that the value of a voting right increases with the
time to maturity of the option pair.
19
C. Value of the Vote for Firms
As explained in Section I, the biases in the estimation of the vote are minimized when the
options used are close to the money. Next, we calculate the market value of the vote for
the firms in our sample. For each firm, we keep options that have moneyness between 0.1
and -0.1. Moneyness is defined as ln(S/X). Using these options, we calculate the value of
the vote for each firm. We keep only those firms that have at least 10 observations in a
given year. The average value for each firm in each year is first computed. These firm year
averages are then used to estimate the mean value of the vote for each firm. The value of the
vote is then averaged across firms to get the average value of the vote in our sample. The
results are reported in Panel A of Table IV. The time to maturity of the options used ranges
from around 17 days to 58 days. On average the time to maturity of the options is 38 days.
We estimate the average value of the right to vote in the next 38 days to be 0.164% of the
market value of the firm. This corresponds to an annualized value of 1.58%. In other words
the market value of the vote during the next year is quantified at 1.58% in our sample.
Next, we look at the voting premium of the average firm across time. The average voting
premium for each firm in each year is calculated. The average voting premium for a year is
then computed by averaging across the firms in each year. We find variation in the voting
premium from 1996 through 2007. As shown in Panel B of Table IV, the voting premium
increases from 1997 through 2001. The premium is 0.13% in 1997 and increases to 0.21%
in the 2001. It drops after that and is at 0.11% in 2004. It increases again to 0.16% in
2005. Interestingly, the variation in the voting premium through years has a resemblance to
the intensity of merger activity during this time period. Merger intensity increased steadily
from 1996 through 2000, peaking in the year 2000. This merger wave ended with the market
crash in 2001. The next merger wave started in 2004.
The firms in our sample are divided into 10 groups based on the market value of the
firm. The average value of the vote is computed for each of these 10 groups. If transaction
costs were driving our results, we would expect to see the highest premium for the smallest
20
firms and the lowest premium for the largest firms. As is evident in Table V, we find no
relationship between the size of the firm and our estimate of the value of the vote. The
estimate of the vote for the smallest firms in our sample is 0.12%, and the estimate for the
largest firms is 0.15%. Recall that the voting premium for the average firm in the entire
sample is 0.16%.
D. Dual Class Firms
The voting premium calculated from dual class firms is (conceptually) closest to our measure
of the value of voting rights. Indeed, our method can be interpreted as synthesizing an inferior
voting share. Technically there are two important differences between the two measures.
First, the time to maturity is finite in our method, whereas it is infinite in dual class firms.
Therefore, the value of voting rights would be expected to be higher in the latter method.
Second, our method generates a synthetic non-voting share as the inferior voting share
whereas in dual class firms the inferior voting shares usually have some voting rights. We
address this issue by adjusting the voting premium using the relative voting rights of different
class of shares following Zingales (1995).
To compare the two measures, we intersect the dual class firms compiled by Gompers,
Ishii, and Metrick (2010) with our sample. A total of 39 firms are in both samples. 27
matched through their inferior voting shares and 12 matched through their superior voting
shares. For each of these companies we calculate the voting premium as follows (Zingales
(1995)):
V PZ ≡
PS − PI
PI − rPS
(11)
where PS and PI are the prices of superior and inferior voting shares; and r is the relative
number of votes of an inferior voting share versus a superior voting one.
21
In order to compare our measure in a meaningful way with the dual class firms we first
annualize our measure.19 Our measure of the annual normalized voting rights (AV oteTnorm )
can be thought in line with the voting premium calculation where PS is the underlying
stock, PI is the synthetically generated non-voting share and hence r is zero. However, as
we normalize the value of voting rights by dividing it with the price of the underlying stock,
the denominator in our measure is the superior voting share rather than the inferior one
as in Zingales (1995). Therefore, to make our measure comparable to the voting premium
calculated above, we apply the following transformation:
V PO ≡
1
−1
1 − AV oteTnorm
(12)
Here V PO stands for the annualized voting premium inferred using options. For the
set of 12 dual class firms that have options traded on the superior class of shares, we find
the average V PZ to be 7.0%, whereas the average V PO is 6.7%. The simple coefficient of
correlation between these two different measures of value of voting rights is significantly
positive (0.22 at p < 0.0001). Regressing V PO on V PZ with firm clustered errors, we find
that V PO is positively correlated with V PZ . The coefficient for V PZ is 0.39 (p value 0.029).
For the set of 27 dual class firms that have options traded on the inferior class of shares,
we find the average V PZ to be 3.8%, whereas the average V PO is 1.2%. The simple coefficient
of correlation between these two different measures of value of voting rights is small and not
significant (0.005 at p = 0.727). Regressing V PO on V PZ with firm clustered errors, we
find that V PO is positively correlated with V PZ . The coefficient for V PZ is again small and
insignificant at 0.01 (p value 0.775).
These results are interesting and in agreement with economic theory. For dual class firms
where the options are traded on the inferior class of shares, our measure is only able to capture
any residual voting rights that the shareholders of the inferior class are entitled to. As such,
19
See Appendix C for the details of the annualization of the value of voting rights.
22
we do not expect any correlation between our measure and that of the traditional dual class
measures in these firms. At the same time, dual class firms where options are traded on the
superior class of shares should exhibit positive correlation between our measure of the value
of the vote and the voting premium inferred using traditional dual class measures.
III. Shareholder Meetings
The value of the right to vote can be expected to display time series variation. In particular,
when the probability of a voting event is high and the voting event is expected to significantly
affect future cash flows, the value of the vote component embedded in the stock should be
more pronounced. We test this hypothesis by looking at the time series and cross-sectional
variation in the average value of the vote around shareholder meetings.
A. Annual Meetings and Special Meetings
Data on shareholder meetings is obtained from ISS. The data covers meetings from 1998 to
2007. In addition to the meeting date and the record date for the meeting, we also know
whether the meeting is an “Annual” meeting or a “Special” meeting. We have a total of
14,501 meetings. 13,521 meetings are annual and 980 are special. For the annual meetings
the average number of days between the record date and the meeting date are 53, and for
the special meetings the average number of days between the record date and the meeting
date are 43.
Our main hypothesis is that the value of voting rights should increase prior to (as and
when information about an upcoming voting event becomes available) and leading to the
record date. Information about the record date of the meeting is widely available at least
20 days prior to the record date. Federal law (Reg. 240.14c7(a)(3)) states that firms are
required to notify brokers, dealers, and similar entities about upcoming record dates at least
23
20 trading days in advance (Christoffersen, Geczy, Musto, and Reed (2007)). We test this
hypothesis by looking at the time series variation in the average value of the vote around
annual and special meetings. For each of the days in the event window (80 days before the
cum-date and 80 days after the cum-date) we select a unique option pair to characterize the
time series variation in the value of the vote. For each of the days in the event window and
the control window, we select a unique option pair for each meeting. The option that has the
smallest moneyness, highest volume, and the least time to maturity is selected. We select
options that are close to the money to minimize biases in our estimation. Selecting options
with high volume and small time to maturity ensures that our results do not suffer from stale
prices and also enables us to study the time series variation in V oteTnorm while controlling for
T . This is essential since we have documented above that V oteTnorm varies with T . Figure 2
tracks the weekly time series variation of the vote around the cum-date of special and annual
meetings. We find that for annual meetings there is very little variation in the value of the
vote. However, special meetings exhibit an increase in the value of the vote prior to the
voting event.20 The value of vote increases several weeks prior to the cum-date. This is
expected since the value of the vote should be reflected in the price of the underlying as soon
as the possibility of a voting event is known. We also find that the value of the vote drops
after the cum-date. Since the record date establishes ownership and the right to vote on
the meeting date, we might expect the value of the vote to drop sharply after the cum-date.
However, we find that the value of the vote settles back to its original level over the next
few weeks. Uncertainty about the event is not resolved until the meeting occurs. While it is
true that the record date establishes ownership of the voting rights, the shareholders have
still not voted. The record date is not binding and can be changed by the management. As
such there is a strictly positive probability that the record date might move. Figure 3 tracks
the weekly time series variation of the vote around the meeting date of special and annual
meetings. The peak in the value of the vote occurs around 8 weeks prior to the meeting
20
We also find that the lower bound of the value of voting rights spikes up around the record date for
special meetings but stays relatively flat for annual meetings.
24
date. The value of the vote then starts to drop and settles to its original level prior to the
meeting date.
We also test our hypothesis by constructing a 20 trading day long window (4 weeks) prior
to the cum-date. This is labeled as the event window. Our control window is a 20 trading
day long window two quarters prior to the cum-date.21 We regress our measure of the value
of the vote on a dummy variable that takes the value 1 for the event window and the value 0
for the control window. Results are reported in Regression 1 of Table VI. We find no increase
in the value of the vote during the event window. As is expected, most of the meetings in
our sample are annual meetings. There are a total of 14,501 meetings in our sample, out of
these only 980 meetings are special. Next, we separate out the special meetings from our
sample and run the regression only on the subset of special meetings. Results are reported
in Regression 2 of Table VI. We find a significant and positive increase in our measure for
special meetings. The value of the vote more than doubles when compared to the control
window. This is consistent with theory since we expect the value of the vote to be higher
for special meetings.
We investigate the effect of liquidity on our measure in two different ways. First, we
divide the special meetings into 10 groups based on the volume of the options used to
construct the synthetic stock. Results are in Regression 3 of Table VI. Option Volume Rank
takes the value 0 through 9, with 0 corresponding to the group with the lowest volume and 9
corresponding to the group with the highest volume. We find no relationship between option
volume and the increase in our measure during the event window. The coefficient on the
event window remains the unchanged both in magnitude as well as significance. We repeat
this methodology and divide the special meetings into 10 groups based on the volume of the
underlying. Again, the increase in the value of the vote during the event window remains
unchanged after controlling for the volume of the underlying stock (Regression 4, Table VI).
21
Results are not sensitive to the particular event and control windows chosen.
25
B. Meeting Characteristics
For a subset of the meetings, we also have data on the description of the proposals,
the proponent of the proposals (e.g., shareholders, management), the voting requirement
(e.g., majority, supramajority), the vote’s outcome (e.g., percentage of votes for, against,
abstained, withheld), the ISS recommendation and the management recommendation.22 We
classify each proposal according to its content (e.g., antitakeover-related, directors related).
We also rank its agenda according to the possibility of a control event (the higher the
possibility, the higher the ranking). For instance, antitakeover-related proposals have the
highest ranking (rank=1) whereas the proposals about environmental and social issues have
the lowest ranking (rank=5).
Table VII reports the classification categories and their
rankings.23 Since usually several proposals are considered in a given meeting, we classify
the meeting according to the highest-ranking proposal.
We hypothesize that in addition to special meetings, meetings that have high-ranking
proposals (e.g., antitakeover-related), meetings with conflicts among different parties (e.g.,
ISS and management recommendations conflict), meetings with close votes, and meetings
with shareholder proposals24 should exhibit higher increases in the value of the vote. We
measure the closeness of a vote with the absolute value of the difference between the
percentage vote required for the proposal to be accepted and that actually cast in its favor.
To test our hypotheses we regress the difference in the value of the vote between the event
window and the control window for each meeting on different characteristics of the meeting.
More precisely, the dependent variable is the value of the voting right of a firm averaged for
each shareholder meeting during the event window (20 trading days prior to the cum-date)
22
See Maug and Rydqvist (2009) for a detailed description of the database.
23
We classify the proposals following the categories in the RiskMetrics’ Voting Analytics website. The
cases which do not fit into any of the categories in Voting Analytics are classified as “Other”.
24
Shareholder proposals are important mechanisms for shareholder activism (see, e.g., Gillan and Starks
(2007)). However, literature finds small effects of shareholder activism (see, e.g., Karpoff (2001) and Bebchuk
(2007)) as opposed to the recent hedge fund activism, which we examine in Section IV.
26
minus the value of the voting right averaged over the control window (20 trading days two
quarters prior to the cum-date).
Table VIII reports the results of the regression. “Meeting Dummy” takes the value 1
if the meeting is a special meeting and 0 if it is an annual meeting. “Agenda Dummy”
takes the value 1 if the meeting has an agenda with rank 1 (e.g., antitakeover-related) and 0
otherwise.25 “Closeness” is the absolute difference between the percentage vote required to
accept the proposal and that actually cast in its favor.26 “ISS-Management Conflict Dummy”
takes the value 1 if the ISS recommendation for the proposal conflicts with management’s.
Shareholder proposal takes the value 1 if the proponent of the proposal is a shareholder.
The results suggest that the value of voting rights increases during the event window for
special meetings, for meetings with a high-ranking agenda, and if the proposal discussed
has (ex-post) close votes. The coefficients of other variables also have the correct sign but
are not significant. Overall, these results are consistent with the hypothesis that the more
contentious the meetings, the higher the value of voting rights.
One issue with the independent variables is that they are correlated. For instance, the
meeting’s agenda likely affects the closeness of the vote. Therefore when put together in the
regression, some of these variables lose significance. In this framework, meeting type and
closeness of the votes seem to be the strongest independent variables.27
C. Further Analysis
In this section, we check the robustness of the findings. We also compare our measure of the
value of voting rights to the other measures in the literature.
25
The majority of the cases are clustered at proposals with rank 1 or 2. Therefore, we create the agenda
dummy and pool the proposals with ranking less than or equal to 2.
26
Note that Closeness is a forward-looking measure.
27
The replication of the same analysis with the lower bound approach yields qualitatively the same results.
27
C.1. Equity Lending
Equity lending has been used for vote trading as illustrated by Christoffersen, Geczy, Musto,
and Reed (2007). Therefore, one can infer the value of voting rights from equity lending fees
and compare it to our measure of the value of voting rights.28 For this comparison, we obtain
equity lending data (value-weighted and equal-weighted equity lending fee, total value of the
lendable share supply, and the total value of shares lent) for a subsample of firms from Data
Explorers, which is a global information company tracking all securities financing related
information.29 The data cover a year around the record dates (about three quarters before
and one quarter after the record dates).
We construct the subsample by first selecting the 100 stocks with the high and 100 stocks
with the low values of voting rights inferred from option prices around the record dates. Since
the equity lending data is available from 2005 onwards, we choose among the stocks with
record dates after mid-2005. Of these 200 stocks, 175 have the needed equity lending data
and out of these, 87 are among the 100 with the high values of voting rights (“high value
sample”) and 88 are among the 100 with the low value of voting rights (“low value sample”).
The average equity lending fee around the record date (specifically, [-3,3] trading weeks)
is 0.13% (5.02%) per year for the low (high) value sample.30 The corresponding annualized
value of voting rights measured with the option prices is 0.13% (5.40%) for low (high) value
sample.
We calculate the change in the equity lending fees and the change in the value of voting
rights around the record date ([-3,3] trading weeks) compared to a quarter before the record
date ([-18,-13] trading weeks). The simple correlation between these two change measures is
significantly positive (0.44 at p=0.000), and is mostly driven by the high value sample. The
28
See, e.g., Saffi and Sigurdsson (2010) for a detailed description of cross-country equity lending data.
29
We would like to thank Pedro Saffi for helping us with the equity lending data.
30
All equity lending fees reported are value-weighted figures. Results are similar for equal-weighted fees.
28
frequency of the equity lending data is weekly before 2007, and daily from 2007 onwards.
However, our measure of the value of voting rights is computed on a daily basis for the whole
period. This causes non-synchronicity of the two measures during 2005 and 2006 and biases
the correlation downwards.
We find that the lending supply and shares lent increase towards the record date for both
high and low value samples. Loan utilization rates (shares lent divided by lending supply)
for high value (low value) sample before and around record date are 59% and 68% (21% and
23%), respectively. The increase in the loan utilization rate is significant only for the high
value sample. These results imply that the lending market hosts a vote market when votes
matter. The results are also in line with Christoffersen, Geczy, Musto, and Reed (2007)
who find that loan volumes spike around record dates over 1998-1999. In a recent article,
Aggarwal, Saffi, and Sturgess (2010) analyze the equity lending market in US around the
time of proxy voting over 2005-2009. They find that towards the record date, on average,
there is a significant reduction in the supply of shares lent and an increase in the demand
for shares to borrow. They find that this behavior, in contrast to Christoffersen, Geczy,
Musto, and Reed (2007), leads to higher lending fees, especially in cases where the supply
restrictions are higher.31 These results are consistent with the view that the increase in the
value of voting rights would also be reflected in the equity lending markets.
C.2. Exogenous Transaction Costs
Arbitrage activity cannot put an upper bound on the market value of the vote. If the
synthetic stock is significantly lower than the stock, arbitrage activity to profit from the gap
requires a short position in the stock and long in the synthetic stock. But around special
voting events, shareholders will require substantial compensation for lending their stocks.
31
One possible reason that these two papers reach opposite conclusions might be due to different data sets.
The Aggarwal, Saffi, and Sturgess (2010) paper uses a dataset over 2005-2009 and the data is provided by 125
large custodians and 32 prime brokers in the securities lending industry. The data set used by Christoffersen,
Geczy, Musto, and Reed (2007) spans only one year (1998-1999) and it is provided by only one large lending
agent.
29
Thus, the importance of the vote determines the effective transaction costs of the put-call
parity arbitrage.
Put-call parity might be violated due to reasons other than voting issues.
Ofek,
Richardson, and Whitelaw (2004) show that short-sale constraints are linked to these
violations. As we argued above, the short-sale constraints would automatically be affected
if the value of voting rights increase. However, there might still be non-voting related issues
affecting short-sale constraints. In order to control for these, we use relative short interest
(RSI) as a proxy for short sale constraints as suggested by Boehme, Danielsen, and Sorescu
(2006). RSI is the percentage of shares that are held short for each firm. Boehme, Danielsen,
and Sorescu (2006) show that RSI is highly correlated with equity lending fees.
We obtain the RSI data from COMPUSTAT by dividing the short interest with the
number of common shares outstanding. Note that short interest data is monthly and the
figures reflect the positions held on the 15th business day of each month. Following Boehme,
Danielsen, and Sorescu (2006), we drop cases where the the number of short interest data
are missing.
After matching with the RSI data we are left with 5,012 meetings. Table IX reports
results of regressions that control for the relative short interest. The dependent variable
is the value of the voting right of a firm averaged for each shareholder meeting during the
event window (20 trading days prior to the cum-date) minus the value of the voting right
averaged over the control window (20 trading days, two quarters prior to the cum-date).
As is evident in Table IX, we find that even after controlling for RSI, both the magnitude
and the significance of the meeting dummy, agenda dummy and closeness variables remain
unchanged. This suggests that our measure is not influenced by non-control related shorting
difficulties.
30
IV. Activist Hedge Fund Targeting
In this section, we study the value of voting rights in firms targeted by activist hedge funds.32
Compared to traditional investors, hedge funds use more sophisticated financial products
(e.g., options, equity swaps, etc.) and more aggressive tactics (see Agarwal and Naik (2005)’s
and Brav, Jiang, and Kim (2009) surveys). Klein and Zur (2009) find that activist hedge
funds achieve their goals by posing a credible threat of engaging the target into a proxy
solicitation contest. For this reason, hedge fund activism provides an ideal setting to study
the value of voting rights.
We use Brav, Jiang, Partnoy, and Thomas (2008)’s sample of US firms targeted by
activist hedge funds between 1990 and the first half of 2008.33 For each target, the data
set includes the date of engagement and detailed information about the engagement such as
type or hostility of the engagement (see Brav, Jiang, Partnoy, and Thomas (2008) for more
details).
Of the 1,066 sample firms, 424 have the needed options and financial data in the
intersection of OptionMetrics and CRSP databases. Therefore the final treatment sample
(“target sample”) consists of 424 firms. Out of these 118 are classified as hostile.34 For each
of the targets we compute our measure of the value of the vote during the event window and
a control window. The event window is a 16 week window following the announcement of
the hedge fund activism. The control window is a 16 week window, two quarters prior to
the announcement of the activism. Table X presents results of the regression of the value
of the vote on the hedge fund activism dummy. The hedge fund activism dummy takes the
value 1 during the event window and the value 0 during the control window. We find a
significant and positive increase in our measure of the value of the vote during the event
32
See, e.g., Brav, Jiang, Partnoy, and Thomas (2008) and Klein and Zur (2009) for hedge fund activism
in the US, and Becht, Franks, and Grant (2009) for hedge fund activism in Europe.
33
We are grateful to Brav et al. for sharing their data with us.
34
Please see Brav, Jiang, Partnoy, and Thomas (2008) for a detailed explanation of the classification.
31
window. We also investigate the effect of liquidity on our measure in two different ways.
First, we divide the targets into 10 groups based on the volume of the options used to
construct the synthetic stock. Results are in Regression 2 of Table X. Option Volume Rank
takes the value 0 through 9, with 0 corresponding to the group with the lowest volume and
9 corresponding to the group with the highest volume. We find no relationship between
option volume and the increase in our measure during the event window. The coefficient
on the activism dummy remains unchanged both in magnitude as well as significance. We
repeat this methodology and divide the targets into 10 groups based on the volume of the
underlying. Again, the increase in the value of the vote during the event window remains
unchanged after controlling for the volume of the underlying stock (Regression 3, Table X).
Activism that is hostile in nature can be expected to have a higher increase in the value
of the vote. We test this hypothesis by dividing our sample into hostile and non-hostile
targets. We find that the increase in the value of the vote is higher for hostile targets. While
the increase in the value of the vote is still positive for non-hostile targets, the magnitude
is considerably smaller and the significance is reduced when compared to hostile targets
(Regressions 4 and 5 of Table X).
We also repeat our tests with a set of matched control firms. We construct a control
sample by matching each target firm with a non-target control firm in the intersection of
the CRSP and OptionMetrics databases having the same three-digit Standard Industrial
Classification (SIC) Code and with market capitalization closest (in absolute terms) to that
of the target firm at the end of 2000.35 The matching algorithm also makes sure that the
control firm has data available for the entire period the target firm covers.
Table XI shows the results of regressing the difference in the value of the vote between the
target firm and the control firm on the activism dummy. We find a significant and positive
increase in the difference during the event window. The coefficient on the activism dummy
35
We arbitrarily choose the year 2000 as a cutoff to be able to match the firms with a control group. If
matching in 2000 is not possible, it is done at the end of the earliest possible year after 2000. For a very few
firms that could not match with three-digit SIC Code, we match them with two- or one-digit SIC code.
32
is positive and highly significant for hostile targets. For non-hostile targets the coefficient is
small and not significant. This again confirms our results that the value of the vote increases
substantially for hostile targets. Regressions 4 and 5 look at the difference in the value
of the vote between the target and the control firms before and after activism for hostile
and non-hostile targets. The hostile targeting dummy takes the value 1 for hostile targets.
We find that before activism there is no difference between the hostile and the non-hostile
targets. However, after activism there is a significant difference between the hostile and the
non-hostile targets. The hostile targeting dummy is positive and significant after activism.
V. Mergers and Acquisitions
Control contests are arguably the most important events in the life cycle of a firm. The value
of the voting right component embedded in the common stock must exhibit large increases
during merger and acquisition events. To test this hypothesis we observe the time series
of the voting premium for targets around the announcement dates and completion dates of
M&A events.
Our sample consists of M&A deals where if successful, the acquirer would own at least a
50% stake in the target firm. We plot the value of the vote during 200 trading days before
the announcement date and up to 200 trading days after the completion date. The value of
the vote exhibits a significant and large jump on the announcement date (Figure 4). The
value continues to remain high after the announcement date. We note that as we move
further away from the announcement date the value of the vote continues to increase. The
sample consists of deals that have still not been completed on a particular day, i.e. as
we move further away from the announcement date the sample consists of deals that took
longer to complete. The value of the vote remains high prior to the completion date and
drops around the completion date. The drop however is not as large as the increase around
the announcement date. The completion date consists of both the deal effective date and
33
the deal withdrawn date. For deals where a merger was involved and was effective the firm
would cease to exist after the effective date. Hence the sample of synthetic stocks after the
completion date consists of deals that were either withdrawn or that were effective but did
not consist of a 100% acquisition (we include all deals where at least 50% of the target firm
is sought) of the target firm.
Table XII presents the regression analysis around the announcement dates for the deals.
The announcement dummy takes the value 1 after the announcement of the acquisition. We
find a significant and large increase in the value of the vote after the announcement of the
deal. Regression 2 looks only at the deals that were effective and Regression 3 looks only at
the deals that were withdrawn. We find that the increase in the value of the vote is more
than double for the effective deals. Table XIII presents the regression analysis around the
completion dates for the deals. We find a substantial decrease in the value of the vote at
the completion of the deal. Regression 2 looks only at the deals that were effective and
Regression 3 looks only at the deals that were withdrawn. We find that while there is a large
drop in the value of the vote for the effective deals, the deals that are withdrawn do not see
any change in the value of the vote.
Figure 6 plots the call and put option open interest and volume around the deal
announcement date.
All the four measures exhibit an increase in values around the
announcement date. As documented above, the value of the vote also increases around the
deal announcement date. This is interesting since this further assures us that the difference
between the stock and the synthetic stock is not a manifestation of reduced liquidity.
VI. Conclusions
This paper employs a new approach to estimate the market value of the right to vote
embedded in the stock price.
The difference between the prices of the stock and the
synthetic stock quantifies the market value of the right to vote during the expected life
34
of the synthetic stock. Holders of synthetic stocks with more time to expiration forgo the
right to vote in longer periods. The estimation of the synthetic stocks uses American style
options. The possibility of early exercise imbedded in American style options has important
implications on the estimation of the market value of the vote - the expected life of a synthetic
stock constructed with American style options is almost always less than the official time to
expiration. Hence, the difference in the price of the stock and the synthetic stock quantifies
the market value of the vote during the expected life of the synthetic stock.
The possibility for early exercise further complicates the analysis. Prior to an important
voting event or the completion of an M&A activity, the holders of a deep in the money call
option can optimally exercise. For these option holders the loss due to forgone time value is
minimal. Thus the price of an in the money American style call option contains a fraction of
the value of the vote, introducing a downward bias in our measure. At the same time, biases
are also introduced in the computation of the early exercise premium of the put option due
to the change in the vote component. We conduct simulations to quantify these biases and
find that estimation biases are minimized for synthetic stocks that are constructed with close
to the money options.
Using close to the money options with maturity around 38 days, we document the value
of the vote for the average firm in our sample at 0.164%. This translates into an annualized
voting premium of 1.58%. The voting premium varies from a low of 0.11% in 2004 to a high
of 0.21% in 2001. Consistent with the theory we document a positive correlation between
the market value of the vote and the expected life of the synthetic stock. Theory suggests
that important voting events that have significant effect on the firm’s cash flows should be
associated with an increase in the value of the right to vote. We examine the variation of
the average market value of the vote around shareholder meetings, specifically annual and
special meetings. Data on record dates and meeting dates for firms from 1997 to 2007 is
obtained from ISS. We find that for annual meetings there is very little variation in the value
of the vote. However, there is a substantial increase in the value of the vote around special
35
meetings. The value of the vote starts to increase several days prior to the record date.
We also observe a drop in the value of the vote after the record date. For a subset of the
meetings where data is available, we find that the change in the value of vote is higher for
special meetings, for meetings with a high-ranking agenda, and if the proposal discussed has
(ex-post) close votes.
Time series variation in the value of vote is further investigated around periods of intense
hedge fund activism. We use Brav, Jiang, Partnoy, and Thomas (2008)’s sample of US firms
targeted by activist hedge funds between 1990 and the first half of 2008. We find that value
of the vote increases after the announcement of the hedge fund activism. The increase in
the value of the vote is higher for hostile engagement. Controlling for the volume of the
underlying stock and the option does not change our results.
Finally, time series variation in the value of vote is explored around M&A events. In fact
a significant fraction of the special meetings are centered on M&A activity. To investigate
the time series behavior of the value of the vote around M&A events we estimate the price
of the synthetic stock on the target for every day starting from 200 trading days before the
announcement to up to 200 trading days after the completion of the deal. The completion
date is either the date the deal is effective or it is the date the deal is withdrawn. We find a
significant increase in the value of the vote on the announcement date of the M&A activity.
The average value of the vote during days −20 to −1 is slightly negative, possibly due to
insider trading of the firm’s derivatives. The value increases sharply to 0.22% during days 0
to 19. We observe a significant drop in the value of the vote right after the merger completion
date. In general, the time series variation documented around special meetings, hedge fund
activism, and M&A activity lend further support to our proposed measure of the market
value of the vote.
A potential arbitrage activity stemming from a positive value of vote would require buying
the synthetic stock and shorting the stock. Yet precisely when the gap is large stockholders
would require a larger premium to lend their stock to the arbitrageur. In other words, the
36
market value of the vote is not bounded by an exogenous level of transaction costs - to
the contrary - it is an important ingredient in the cost of put call parity arbitrage. We
present evidence that supports this proposition. We find no relationship between firm size
and the voting premium, though typical transaction costs associated with trading options
written on stocks of large firms should be lower. We find no relationship between the increase
in the voting premium around meetings and the liquidity of the underlying. We also find
no relationship between the increase in the voting premium and the volume in the option
market. The evidence suggests that our measure is indeed picking up the value of the vote
and is not just a manifestation of decreased liquidity or high short-sale constraints.
We examine the sensitivity of our results to the choice of model used to compute the
early exercise premium. One can view the voting rights as a dividend not paid to the owners
of the synthetic stock. Applying this insight, it is possible to deduce a lower bound for the
value of the vote from put-call parity bounds for American options. We compare our results
to those obtained using the lower bound approach. In general, we observe that the main
results are qualitatively the same with both methods. This finding suggests that the model
dependency of our computation of the early exercise premium is not critical for our results.
37
Appendix
A. Early Exercise Premium
The early exercise premium for put options and call options with dividends is calculated
using the Binomial option pricing model. We use the Cox, Ross, and Rubinstein (1979)
method to generate the lattice. This implies that the up and down factors for the lattice are
generated using the following equations:
u = eσ
√
d = e−σ
∆t
√
∆t
(13)
(14)
The inputs to the algorithm are the volatility, time to expiration, strike price, price
of the underlying stock, risk free rate, array of dividends and ex-dates if applicable. We
get the implied volatility, time to expiration, strike price and price of the underlying from
the OptionMetrics database. OptionMetrics also provides risk free rate data for certain
maturities. We interpolate the risk free rate data to get the risk free rate for the exact
maturity of the option being considered. Data on dividends and ex-dates is obtained from
CRSP.
We calculate the early exercise premium for the put options and the call options using
1000 steps. Over the course of each step the security price is assumed to move either “up”
or “down”. The size of this move is a function of the up and down factors that are in turn
determined by the implied volatility and the size of the step. In order to determine the
early exercise premium we start at the current security price S0 and build a “tree” of all the
possible security prices at the end of each sub-period, under the assumption that the security
price can move only either up or down. Next, the option is priced at each node at expiration
38
by setting the option expiration value equal to the exercise value: C = max(S i − X, 0)
and P = max(X − S i , 0), where X is the strike price, and S i is the projected price at
expiration at node i. The option price at the beginning of each sub-period is determined
by the option prices at the end of the sub-period. At each node we determine whether
early exercise is optimal or not. Working backwards we estimate the price of the American
option. In a similar fashion we determine the price of the equivalent European option (the
only difference being that early exercise is not an option until the very end of the tree). The
difference between the price of the American option and the European option gives us the
early exercise premium.
B. Bias in the Estimation of the Vote
As explained in Section I A, the inability to measure the early exercise premium of the call
due to the vote, introduces a downward bias in the estimation of the vote. Additionally, the
downward bias is a decreasing function of the strike price. The bias in the value of the vote
introduced due to the delay in exercise of the put options also introduces a downward bias
for synthetic stocks where the put options are in the money.
In order to construct the synthetic stock, we estimate the early exercise premium of the
put. The early exercise premium of the put is estimated using the implied volatility that
is computed from the observed market price of the American put. While computing the
implied volatility, and then the early exercise premium, the value of the vote is ignored.
This introduces biases in the computation of the early exercise premium of the put, EEPput .
est
act
The estimated premium, EEPput
, can be lower or higher than the actual premium, EEPput
.
As a result, this can introduce either an upward or a downward bias in the estimation of the
vote.
Ignoring the expected drop in the value of the vote while estimating the early exercise
premium leads to a bias. The bias enters in several different ways and depends on the
39
est
expected ex-vote day. The first step in calculating EEPput
is to get an implied volatility
using the observed American put price in the market. The American put price that is
observed in the market correctly accounts for the vote. Since the expected drop in the value
of the vote reduces the price of the stock, this increases the payoff of the put, if it is exercised
after the drop. While estimating the implied volatility we do not account for the vote. This
makes the put price seem a lot more expensive given the true volatility of the underlying.
Thus the implied volatility estimated using the observed put price is higher than the actual
implied volatility. As a result we use a higher implied volatility to compute the equivalent
European put. However, while computing the equivalent European put we once again ignore
the vote. This essentially means that we do not account for the drop in the value of the vote
that would occur on the ex-vote day. The drop effectively increases the payoff for the put
at expiration. Since we do not account for the drop, the put that we estimate need not be
higher than the actual put, even though the implied volatility used is higher than the true
implied volatility. In addition as discussed earlier, there is a third dimension to the bias the drop in the value of the vote can also delay exercise of the put option. If the ex-vote
day is close enough such that it is optimal for put option holders to delay exercise in order
to get a higher payoff, then the early exercise component of the put price is not as high as
it would have been if there was no drop in the value of the vote. As a result, the bias that
is introduced in the computation of the early exercise premium can go in either direction.
We conduct simulations to better understand how the biases vary with the strike price of
the synthetic stock. The aim of our experiments is to identify the strike price that minimizes
these biases. The Binomial option pricing model with a 1000 steps is used to conduct the
simulations. The true price process and the true call and put option prices are first simulated
using the tree. The following parameters are used, price of the underlying stock S = $100,
interest rate r = 5%, time to maturity of the options T = 35 days, and the value of the
vote v = 0.5. Simulations are run for all possible ex-vote days. The ex-vote days range from
1 through 34. Using simulations we obtain the true American prices for the call and put
options, and the true early exercise premiums for the options.
40
Once we have the true price process, we then estimate the early exercise premium for the
put. The estimation procedure ignores the value of the vote. Once we have the estimated
early exercise premium of the put, we then construct the synthetic stock. Note that the
synthetic stock does not account for the early exercise premium of the call due to the vote.
Then we calculate our estimate of the vote, V oteest . The error in the estimation is quantified
as V oteerror = (V oteactual − V oteest )/V oteactual . The absolute of V oteerror is computed as
the absolute error in the estimation of the vote. For each strike price we run simulations for
all possible ex-vote days. The mean of the absolute errors across different ex-vote days for
a given strike price is computed. These simulations are conducted for different strike prices.
The strike price varies from $70 through $140. This corresponds to moneyness levels ranging
from 0.36 through -0.34, where moneyness is defined as ln(S/X). Simulations are repeated
for different volatilities of the underlying ranging from 0.1 through 0.5. Results are reported
in Table II.
C. Annualized Vote Values
To better assess the economic significance of the results, we estimate the annualized value of
voting rights. For this, we first calculate a hypothetical voting right dividend yield using the
estimated value of the vote. Here we assume that this yield is constant until the maturity of
the options as the expected maturity of the synthetic non-voting share is not known. This
biases the estimated value of voting rights downwards. Then assuming this voting right
dividend yield remains constant over a year, we estimate the annualized value of a voting
right. Below are the details of the procedure:
In the analysis at the paper, we normalize the value of a voting right with the underlying
stock price (V oteTnorm = (S − Ŝ(T ))/S). Assuming a constant voting right dividend yield
41
(denoted dy ) over the time to maturity (T) of the options, the value of a voting right can be
expressed as:
S − Ŝ(T ) = S − Se−dy T .
(15)
Therefore the voting right dividend yield is:
dy = −
ln(1 − V oteTnorm )
.
T
(16)
We estimate the annualized normalized value of vote as following:
T
AV oteTnorm = 1 − e−dy 365 = 1 − eln(1−V otenorm )
365
T
= 1 − (1 − V oteTnorm )
365
T
.
(17)
D. Lower Bound Approach
As explained in Section A.4, the lower bound approach for the value of voting rights is a
complementary approach to the direct approach. While the lower bound approach is more
difficult to interpret since it is mostly negative, it has the advantage that it is not model
dependent. The approach implicitly assumes that the lower bound of the value of voting
rights has similar properties to the value of voting rights itself.
The measure is normalized by closing stock price of the underlying stock. The empirical
evidence indicates that the lower bound is negative for 88% of the option pairs.36 For these
cases, the lower bound of the voting rights is inferred to be zero as it cannot be negative
theoretically. Although this biases the measure of voting rights upwards, it is useful for
interpretation and the bias does not seem to be critical in results. Using the methodology
36
If the value of vote is not valuable, then 100% of the time the lower bound of the value of voting rights
should be less than or equal to zero. Since the observed value of vote is on average small it is not surprising
that the lower bound is positive at 12% of times.
42
described at Appendix C, the estimated mean value of voting right is 1.23% of the stock
price over a year around record dates.
Focusing only on cases with non-negative lower bounds (12% of the option pairs), the
empirical evidence indicates that the value of a voting right increases as the time to maturity
of the option pairs used increases. This result is consistent with the finding that the value of
voting rights increases with the time to maturity of the options documented using the direct
approach.
When the analysis is focused around the record date, the evidence shows that the lower
bound for the value of voting rights spikes at the record date for special meetings and stays
flat for annual meetings. In the cross-sectional analysis, the lower bound measure is higher
around record date if the proposal discussed in the meeting is about anti takeover, mergers &
reorganizations, capitalization or maximizing value issues rather than about compensation,
directors related, miscellaneous/routine, environmental/social and other issues. The lower
bound for the value of votes is also significantly higher for proposals that result in a close
vote, as measured by the wedge between the percentage vote required for the proposal to pass
and that actually cast in its favor, as well as for proposals where the ISS recommendation
conflicts with that of management. These results are in line with the hypothesis that the
fiercer the control contest, the higher the value of voting rights. These results are consistent
with the findings using the direct approach.
Overall, these findings suggest that the main results of the paper are robust to different
approaches for estimating the value of voting rights. The findings also suggest that the
model dependency of the main framework for the calculation of the early exercise premium
is not critical for our results.
43
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Experience, Review of Financial Studies 7, 125–148.
Zingales, Luigi, 1995, What Determines the Value of Corporate Votes?, Quarterly Journal
of Economics 110, 1047–1073.
47
Table I. Value of the Vote: Summary of the Literature.
The table reports a brief summary of the empirical literature that quantifies the value of the voting right.
The value of the vote is expressed as a percentage of the market value of the firm.
Panel A: Studies that are based on dual class shares
Study
Country
Period
n
Value of the vote
Levy (1982)
Israel
1974-1980
25
45.5%
Lease et. al. (1983)
US
1948-1978
30
5.4%
Horner (1988)
Switzerland
1973-1983
45
20.0%
Megginson (1990)
UK
1955-1982
152
13.3%
Zingales (1994)
Italy
1987-1990
96
81.5%
Zingales (1995)
US
1984-1990
94
10.5%
Smith and Amoako-Adu (1995)
Canada
1981-1992
96
10.4%
Rydqvist (1996)
Sweden
1983-1990
65
12.0%
Chung and Kim (1999)
South Korea
1992-1993
119
10.0%
a
Nenova (2003)
US
1997
39
2.0%
Hauser and Lauterbach (2004)
Israel
1990-2000
84
10.0%
Panel B: Studies that are based on block sales
Study
Barclay and Holderness (1989)
Dyck and Zingales (2004)b
Country
US
US
Period
1978-1982
1990-2000
n
63
46
Value of the vote
20.0%
1.0%
a
Nenova (2003) conducts a cross country analysis of 661 dual class firms across 18 countries and finds
average voting premia that vary from -5% in Finland to 36.5% in Mexico.
b
Dyck and Zingales (2004) use a sample of 393 control transactions across 39 countries from 1990 to 2000
and find an average control value of 14%, with estimates ranging from -4% in Japan to 65% in Brazil.
48
Table II. Simulated Biases in Estimating the Value of the Vote.
The table reports the average estimation error in the value of the vote as a function of the moneyness of
the synthetic stock and the volatility of the underlying process. The error in estimation is calculated using
simulations of the true price process and simulations of the estimation procedure. The binomial option
pricing model with 1000 steps is used to conduct the simulations. The following parameters are used, price
of the underlying stock S = $100, interest rate r = 5%, time to maturity of the options T = 35 days, and
the value of the vote v = 0.5. Simulations are run for ex-vote days ranging from 1 through 34. The error
in the vote estimation is calculated as V oteerror = (V oteactual − V oteestimated )/V oteactual . The mean of
the absolute errors across the ex-days, for a given level of moneyness and volatility of the underlying are
reported in Panel A. Panel B reports the corresponding signed errors.
Panel A: Average Absolute Error in the Estimation of the Value of the Vote
Volatility
0.1
0.2
0.3
0.4
0.5
Panel
Moneyness
-0.34
-0.26
-0.18
-0.10
0.00
49.63% 45.92% 40.05% 34.40% 13.99%
45.61% 40.34% 40.82% 20.90% 10.97%
45.59% 39.79% 28.63% 10.15% 9.58%
44.94% 33.40% 16.43% 7.09%
8.67%
36.64% 21.58% 10.84% 5.99%
8.02%
B: Average Signed Error in the Estimation of
Volatility
0.1
0.2
0.3
0.4
0.5
-0.34
12.75%
8.74%
8.79%
10.41%
11.09%
-0.26
8.14%
2.56%
3.32%
6.58%
7.83%
-0.18
0.56%
1.93%
1.66%
5.04%
5.71%
Moneyness
-0.10
0.00
-8.95% 12.00%
-1.59% 10.17%
3.53%
9.10%
4.35%
8.35%
4.51%
7.79%
49
0.11
0.22
9.22% 61.67%
45.29% 61.63%
30.41% 58.47%
22.44% 47.09%
17.89% 36.60%
the Value of the
0.36
66.46%
66.46%
66.44%
65.53%
60.55%
Vote
0.11
9.22%
45.29%
30.41%
22.44%
17.89%
0.36
66.46%
66.46%
66.44%
65.53%
60.55%
0.22
61.67%
61.63%
58.47%
47.09%
36.60%
0.35
normalized value of the vote in %
0.3
0.25
0.2
0.15
0.1
0.05
0
10
20
30
40
50
Time to Maturity
60
70
80
Figure 1. Value of the Vote as a Function of T : This figure characterizes the normalized
value of the vote as a function of time T . The value of the right to vote in the next T
days is calculated as the difference between the price of the stock and the price of the
synthetic stock, P V (V oteT ) = S − Ŝ(T ). The synthetic stock is constructed as Ŝ(T ) =
C − EEPcall − P + EEPput + P V (X) + P V (div), where C is the price of the call option with
strike X and T days to maturity, P is the price of the put option with strike X and T days
to maturity, P V (X) is the present value of investing in a bond with face value X, P V (div)
is the present value of the dividend stream prior to option expiration, EEPcall is the early
exercise premium of the call option, and EEPput is the early exercise premium of the put
option. The early exercise premiums for the call and put options are calculated using the
Binomial option pricing model with 1000 steps.
50
Table III. Market Value of the Vote in the Next T Days.
The table reports the normalized market value of the vote in the next T days, V oteTnorm , for stocks that have
exchange traded options during the time period 1996 through 2007. V oteTnorm is the value of the voting right
in the next T days, P V (V oteT ), normalized by the price of the stock. The confidence intervals reported are
based on robust and clustered errors.
Panel A: Groups of 30 days
V oteTnorm in %
T
(Days)
0 to 30
31 to 60
61 to 90
Lower CI
(95%)
0.0930
0.1403
0.2222
Mean
0.0935
0.1408
0.2233
Upper CI
(95%)
0.0940
0.1414
0.2243
Panel B: Groups of 10 days
V oteTnorm in %
T
(Days)
0 to 10
11 to 20
21 to 30
31 to 40
41 to 50
51 to 60
61 to 70
71 to 80
81 to 90
Lower CI
(95%)
0.0599
0.0890
0.1093
0.1145
0.1434
0.1693
0.1833
0.2180
0.2597
Mean
0.0607
0.0898
0.1101
0.1154
0.1444
0.1704
0.1851
0.2197
0.2616
51
Upper CI
(95%)
0.0616
0.0906
0.1109
0.1162
0.1455
0.1714
0.1868
0.2215
0.2636
Table IV. Market Value of the Vote for Firms.
The table reports the normalized market value of the vote in the next T days, V oteTnorm , for firms that have
exchange traded options during the time period 1996 through 2007. Only options with moneyness between
-0.1 and 0.1 are used. The average value for each firm in each year is first computed. The firm year averages
are then averaged across years to get an average vote for each firm. Panel A reports results for the average
firm. Panel B documents the value of the vote for the average firm across years 1996 through 2007.
Panel A: The Average Firm - 1996 to 2007
N
Mean
4768
0.16%
Year
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
N
1,179
1,524
1,645
1,738
1,869
1,705
1,627
1,680
1,945
2,057
2,767
3,082
Lower CI
Upper CI
0.15%
0.18%
Panel B: Vote across years
Vote Mean
0.14%
0.13%
0.17%
0.15%
0.17%
0.21%
0.16%
0.11%
0.11%
0.16%
0.11%
0.14%
Lower CI
0.12%
0.12%
0.15%
0.13%
0.14%
0.19%
0.14%
0.10%
0.10%
0.14%
0.09%
0.12%
52
Min
Max
-3.2%
11.6%
Upper CI
0.16%
0.15%
0.19%
0.18%
0.19%
0.23%
0.17%
0.12%
0.12%
0.17%
0.12%
0.16%
Table V. Value of the Vote for Firms - Size Sorts.
The table reports the normalized market value of the vote in the next T days, V oteTnorm , for firms that have
exchange traded options during the time period 1996 through 2007. Only options with moneyness between
-0.1 and 0.1 are used. The average value for each firm in each year is first computed. The firm year averages
are then averaged across years to get an average vote for each firm.
Size sorts
Size in $Million
177.76
317.68
464.28
636.00
849.68
1,186.51
1,727.72
2,705.64
5,152.95
26,945.81
Vote Mean
0.12%
0.18%
0.18%
0.16%
0.15%
0.14%
0.18%
0.16%
0.16%
0.15%
Std Error
0.02%
0.02%
0.02%
0.02%
0.02%
0.01%
0.02%
0.01%
0.01%
0.00%
53
Min
-1.13%
-0.74%
-1.21%
-0.82%
-0.55%
-0.27%
-0.82%
-0.83%
-0.14%
-0.01%
Max
3.36%
5.70%
3.65%
4.65%
5.97%
2.33%
4.93%
4.84%
1.04%
0.63%
0.3
Annual meetings
Special meetings
normalized value of the vote in %
0.25
0.2
0.15
0.1
0.05
0
-15
-10
-5
0
5
number of trading weeks from cum-date
10
15
Figure 2. Value of the Vote around Voting Events: This figure characterizes the
time series variation of the normalized market value of the vote around annual and special
meetings during the time period 1998 through 2007. The value of the vote is calculated as
the difference between the price of the stock and the price of the synthetic stock normalized
by the price of the stock. The synthetic stock is constructed as Ŝ(T ) = C − EEPcall − P +
EEPput +P V (X)+P V (div), where C is the price of the call option with strike X and T days
to maturity, P is the price of the put option with strike X and T days to maturity, P V (X)
is the present value of investing in a bond with face value X, P V (div) is the present value of
the dividend stream prior to option expiration, EEPcall is the early exercise premium of the
call option, and EEPput is the early exercise premium of the put option. The early exercise
premiums for the call and put options are calculated using the Binomial option pricing model
with 1000 steps. The figure plots the average value of the vote for 16 trading weeks prior
to the cum-date and 16 trading weeks after the cum-date for special meetings and annual
meetings.
54
0.3
Annual meetings
Special meetings
normalized value of the vote in %
0.25
0.2
0.15
0.1
0.05
0
-20
-15
-10
-5
0
number of trading weeks from meeting date
5
Figure 3. Value of the Vote around Voting Events: Meeting Date Centered:
This figure characterizes the time series variation of the normalized market value of the
vote around annual and special meetings during the time period 1998 through 2007. Week 0
corresponds to the meeting date. The value of the vote is calculated as the difference between
the price of the stock and the price of the synthetic stock normalized by the price of the stock.
The synthetic stock is constructed as Ŝ(T ) = C −EEPcall −P +EEPput +P V (X)+P V (div),
where C is the price of the call option with strike X and T days to maturity, P is the price of
the put option with strike X and T days to maturity, P V (X) is the present value of investing
in a bond with face value X, P V (div) is the present value of the dividend stream prior to
option expiration, EEPcall is the early exercise premium of the call option, and EEPput is
the early exercise premium of the put option. The early exercise premiums for the call and
put options are calculated using the Binomial option pricing model with 1000 steps.
55
Table VI. Value of Vote around Shareholder Meetings.
The table reports regressions of the value of the vote during the event window and the control window. The
event window is a 20 trading day long window (4 weeks) prior to the cum-date. The control window is a
20 trading day long window two quarters prior to the cum-date. The dummy variable Record Date takes
the value 1 for the event window, and 0 for the control window. Regression 1 uses all the meetings in the
sample, whereas Regression 2 only uses the special meetings. Regressions 3 and 4 also control for the option
volume and stock volume. The t-stats are reported in parentheses. The errors are clustered and robust.
Value of Vote
Record Date
[Event:1, Control:0]
−1−
−2−
−3−
−4−
.002
.113
.113
.114
(0.38)
(5.31)
(5.32)
(5.44)
Option Volume Rank
-.003
[High Volume:9, Low:0]
(-0.69)
Stock Volume Rank
-.003
[High Volume:9, Low:0]
Constant
Obs
Special Meetings in Obs
(-0.93)
.112
.092
.103
.106
(27.4)
(7.54)
(4.82)
(4.90)
14,501
980
980
980
980
980
980
980
56
Table VII. Classification and Ranking of Proposals.
Rank
M anagement P roposals
Shareholder P roposals
1
Antitakeover-Related
Mergers & Reorganizations
Capitalization
Antitakeover-Related
Maximize Value
2
Compensation
Directors Related
Executive Compensation
Directors Related
3
Routine/Miscellaneous
Miscellaneous
4
Other
Other
5
Environmental & Social
57
Table VIII. Characteristics of Shareholder Meetings.
The table reports regressions of the change in the value of the vote between the event window and the control
window. The event window is a 20 trading day long window (4 weeks) prior to the cum-date. The control
window is a 20 trading day long window two quarters prior to the cum-date.
Change in the Value of the Vote
−1−
Meeting Dummy
[Special:1, Annual:0]
Agenda Dummy
[High Ranking:1, Low:0]
−2−
−3−
−4−
−6−
−7−
−8−
.074
.054
.059
.074
(3.65)
(2.81)
(2.84)
(3.66)
.039
.027
.005
(3.61)
(2.35)
(0.43)
Closeness
[|Vote Required-Vote Cast For|]
ISS-Management Conflict
-.054
-.047
-.035
(-4.35)
(-3.69)
(-2.48)
7,919
336
Yes
7,919
336
Yes
.018
[Conflict:1, Agree:0]
(1.34)
Shareholder Proposal
.023
[Shareholder:1, Management:0]
Obs
Special Meetings in Obs
Firm Dummy
−5−
(1.22)
7,919 7,919
336
336
Yes
Yes
58
7,919 7,919
336
336
Yes
Yes
7,919 7,919
336
336
Yes
Yes
Table IX. Change in the Value of the Vote: Controlling for Relative Short
Interest (RSI).
The table reports regressions of the difference in the value of the vote between the event window and the
control window. The event window is a 20 trading day long window (4 weeks) prior to the cum-date. The
control window is a 20 trading day long window two quarters prior to the cum-date. RSI is the percentage
of shares that are held short for each firm.
Change in the Value of the Vote
−1−
Meeting Dummy
[Special:1, Annual:0]
−2−
.101
.101
(2.82)
(2.83)
Agenda Dummy
[High Ranking:1, Low:0]
−3−
−4−
.020
.020
(1.52)
(1.50)
Closeness
[|Vote Required-Vote Cast For|]
Relative Short Interest (RSI)
Obs
Special Meetings in Obs
Firm Dummy
5,012
193
Yes
59
−5−
−6−
-.041
-.040
(-2.66)
(-2.63)
-0.196
-0.164
-0.155
(-0.95)
(-1.18)
(-1.12)
5,012
193
Yes
5,012
193
Yes
5,012
193
Yes
5,012
193
Yes
5,012
193
Yes
Table X. Hedge Fund Activism.
The table reports regressions of the value of the vote during the event window and the control window. The
event window is a 16 week window starting at the announcement of the activism. The control window is 16
week window two quarters prior to the announcement date. Regression 1 presents the results for the entire
sample. Regression 2 controls for the option volume rank, and Regression 3 controls for the stock volume
rank. Regressions 4 and 5 present results for the non-hostile and hostile events respectively.
Value of Vote
Hedge Fund Activism
[After:1, Before:0]
−1−
−2−
−3−
−4−
−5−
.071
.065
.071
.060
.094
(2.26)
(2.23)
(2.35)
(1.61)
(1.97)
Option Volume Rank
.013
[High Volume:9, Low:0]
(1.69)
Stock Volume Rank
.000
[High Volume:9, Low:0]
Constant
Obs
Hostile Targets in Obs
(0.04)
.113
.056
.112
.116
.105
(6.78)
(1.71)
(3.84)
(6.20)
(5.13)
424
118
424
118
424
118
306
0
118
118
60
Table XI. Hedge Fund Activism: Controlling for Matching Firms.
The table reports regressions of the difference in the value of the vote between the target firm and the
matched firm. The event window is a 16 week window starting at the announcement of the activism. The
control window is 16 week window two quarters prior to the announcement date. Regression 1 presents
the results for the entire sample. Regressions 2 and 3 analyze non-hostile and hostile events respectively.
Regression 4 looks at the entire sample during the control window. Regression 5 looks at the entire sample
during the event window.
Difference in Value of Vote Between Target and Matching Firms
−1−
Hedge Fund Activism
[After:1, Before:0]
−2−
−3−
.046
.012
.084
(1.67)
(0.49)
(2.09)
Hostile Targeting
[Hostile:1, Non-Hostile:0]
Constant
Obs
Hostile Targets in Obs
Hedge Fund Activism
−4−
−5−
.002
.073
(0.11)
(2.24)
.030
.030
.032
.030
.042
(1.40)
(1.20)
(1.41)
(1.20)
(1.94)
424
118
306
0
118
118
424
118
Before
424
118
After
61
0.8
0.7
normalized value of the vote in %
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-20
-15
-10
-5
0
5
10
Groups of 10 trading days relative to announcement date
15
20
Figure 4. Value of the Vote around Merger and Acquisition Announcements:
This figure characterizes the time series variation of the normalized market value of the vote
around merger and acquisition announcements. The value of the vote is averaged over groups
of 10 trading days. The value of the right to vote in the next T days is calculated as the
difference between the price of the stock and the price of the synthetic stock, P V (V oteT ) =
S − Ŝ(T ). The synthetic stock is constructed as Ŝ(T ) = C − EEPcall − P + EEPput +
P V (X) + P V (div), where C is the price of the call option with strike X and T days to
maturity, P is the price of the put option with strike X and T days to maturity, P V (X) is
the present value of investing in a bond with face value X, P V (div) is the present value of
the dividend stream prior to option expiration, EEPcall is the early exercise premium of the
call option, and EEPput is the early exercise premium of the put option. The early exercise
premiums for the call and put options are calculated using the Binomial option pricing model
with 1000 steps.
62
0.5
normalized value of the vote in %
0.4
0.3
0.2
0.1
0
-10
-5
0
5
Groups of 10 trading days relative to completion date
10
Figure 5. Value of the Vote around Merger and Acquisition Completion Dates:
This figure characterizes the time series variation of the normalized market value of the
vote around merger and acquisition completion dates. The value of the vote is averaged over
groups of 10 trading days. The value of the right to vote in the next T days is calculated as the
difference between the price of the stock and the price of the synthetic stock, P V (V oteT ) =
S − Ŝ(T ). The synthetic stock is constructed as Ŝ(T ) = C − EEPcall − P + EEPput +
P V (X) + P V (div), where C is the price of the call option with strike X and T days to
maturity, P is the price of the put option with strike X and T days to maturity, P V (X) is
the present value of investing in a bond with face value X, P V (div) is the present value of
the dividend stream prior to option expiration, EEPcall is the early exercise premium of the
call option, and EEPput is the early exercise premium of the put option. The early exercise
premiums for the call and put options are calculated using the Binomial option pricing model
with 1000 steps.
63
Table XII. Merger and Acquisition Announcements.
The table reports regressions of the value of the vote before and after the announcement of the merger and
acquisition event. The after window is a 16 week window starting at the announcement of the deal. The
before window is a 16 week window prior to the announcement date. Regression 1 presents the results for
the entire sample. Regressions 2 and 3 present results for the effective and withdrawn deals respectively.
Value of Vote
Announcement
[After:1, Before:0]
Constant
Obs
Withdrawn Deals in Obs
64
−1−
.216
−2−
.242
−3−
.105
(6.78)
(6.40)
(2.40)
.042
.044
.036
(3.18)
(3.00)
(1.22)
1,261
243
1,018
0
243
243
Table XIII. Merger and Acquisition Completions.
The table reports regressions of the value of the vote before and after the completion of the merger and
acquisition event. The after window is a 16 week window starting at the completion of the deal. The before
window is a 16 week window prior to the completion date. Regression 1 presents the results for the entire
sample. Regressions 2 and 3 present results for the effective and withdrawn deals respectively.
Value of Vote
Completion
[After:1, Before:0]
Constant
Obs
Withdrawn Deals in Obs
65
−1−
-.174
−2−
-.267
−3−
.016
(-3.98)
(-4.48)
(0.44)
.339
.381
.176
(8.82)
(8.01)
(6.10)
1,261
243
1,018
0
243
243
8000
7000
Call Open Interest
Call Volume
Put Open Interest
Put Volume
6000
5000
4000
3000
2000
1000
0
-20
-15
-10
-5
groups of 10 trading days relative to announcement date
0
5
Figure 6. Option Volume and Open Interest around Merger and Acquisition
Announcement Dates: This figure characterizes the time series variation of the Volume
and Open Interest of options around merger and acquisition announcement dates. The
variables are averaged over groups of 10 trading days.
66