the market value of corporate votes: theory and evidence from option prices

THE JOURNAL OF FINANCE • VOL. LXIX, NO. 3 • JUNE 2014

The Market Value of Corporate Votes: Theory andEvidence from Option Prices

AVNER KALAY, OGUZHAN KARAKAS, and SHAGUN PANT∗

ABSTRACT

This paper proposes a new method using option prices to estimate the market valueof the shareholder voting rights associated with a stock. The method consists ofsynthesizing a nonvoting share using put-call parity, and comparing its price to thatof the underlying stock. Empirically, we find this measure of the value of voting rightsto be positive and increasing in the time to expiration of synthetic stocks. The measurealso increases around special shareholder meetings, periods of hedge fund activism,and M&A events. The method is likely useful in studies of corporate control and alsohas asset pricing implications.

∗Avner Kalay is Maurice and Gertrude Deutch Chaired Professor at Tel Aviv University andFrancis A. Madsen Professor at the University of Utah, Oguzhan Karakas is Assistant Professor atBoston College, and Shagun Pant is Assistant Professor at the University of Iowa. This paper com-bines two earlier papers: “The Market Value of the Vote: A Contingent Claims Approach” by Kalayand Pant and “Another Option for Determining the Value of Corporate Votes” by Karakas. Wethank seminar participants at the 2011 Southwind Conference, 2010 WFA, 2009 NFA, 2009 BanffFrontiers in Finance Conference, 2009 Drexel Corporate Governance Conference, 2009 NYU-PennLaw and Finance Conference, 2008 FMA Doctoral Consortium, Arizona State University, BilkentUniversity, Boston College, Boston University, Columbia University, EMLYON, Erasmus Uni-versity, George Mason University, Harvard Business School, Imperial College, INSEAD, LondonBusiness School, MIT, NYU, Rutgers University, Stanford University, Tel Aviv University, TexasA&M University, Tilburg University, UC Berkeley, UCLA, University of Alberta, University ofFlorida, University of Iowa, University of Pennsylvania, University of Utah, Washington Univer-sity in St. Louis, Yale University, and a conference held in the honor of Haim Levy for helpfulcomments. We also thank Viral Acharya, Yakov Amihud, Shmuel Baruch, Hank Bessembinder,Jennifer Carpenter, David Chapman, Francesca Cornelli, Julian Franks, Denis Gromb, Joel Has-brouck, Clifford Holderness, Edith Hotchkiss, Michael Lemmon, Alan Marcus, Stewart Myers,Jeffrey Pontiff, Helene Rey, Henri Servaes, Philip E. Strahan, Jerome Taillard, Hassan Tehranian,Ashish Tiwari, Paolo Volpin, the Editor (Campbell Harvey), an Associate Editor, the referees, andan advisor for their helpful comments. Conversations with Nihat Aktas, Sirio Aramonte, YasuhiroArikawa, Ramin Baghai, Suleyman Basak, Morten Bennedsen, Mikhail Chernov, Alexander Dyck,Daniel Ferreira, Marc Gabarro, Francisco Gomes, Jungsuk Han, Brandon Julio, Eugene Kan-del, Samuli Knupfer, Xi Li, Lars Lochstoer, Michelle Lowry, Pascal Maenhout, Massimo Massa,Narayan Naik, Anna Pavlova, Joel Peress, Urs Peyer, Ludovic Phalippou, Astrid Schornick, LucieTepla, Theo Vermaelen, Vikrant Vig, Russ Wermers, and Robert Whitelaw contributed greatly tothis paper. Financial support from Marie Curie Early Stage Research Training Host Fellowshipand from London Business School’s Centre for Corporate Governance under ESRC contract numberR060230004 are gratefully acknowledged by Karakas.

DOI: 10.1111/jofi.12132

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SINCE THE SEMINAL WORK of Berle and Means (1932), it has been widely heldthat one of the most important contractual rights that shareholders have isthe right to vote in corporate elections. Within this framework, starting withGrossman and Hart (1988) and Harris and Raviv (1988), a vast literatureanalyzes security voting design and points to the importance of shareholdervoting rights. Separating the value of voting rights from that of cash flowrights, however, is not trivial.1 In this paper, we propose, develop, and testa new method to measure the market value of shareholder voting rights.2

We estimate the value of voting rights as the difference between the price ofthe stock and the price of the equivalent nonvoting synthetic stock that isconstructed using options.

Extant studies of the value of voting rights use three estimation methods.The first method computes the voting premium as the price difference betweenmultiple classes of stock with differential voting rights.3 Studies that employthis method find that shares with superior voting rights trade at a premium,implying a positive value to the right to vote. However, this method is restrictedto cases in which firms have dual-class shares and both classes of shares aretraded. This restriction results in very small data samples (typically below 100).Further, even if both classes of shares are traded, one might be less liquid thanthe other. More importantly, these samples are potentially subject to selectionbiases (see, for example, DeAngelo and DeAngelo (1985) and Smart and Zutter(2003)).

The second method focuses on privately negotiated sales of controlling blocksand measures the value of control as the difference between the price per shareat which a block trades and the stock price right after the block sale.4 The valueof control is generally found to be positive under this method as well. Withthis approach, finding reliable data is more difficult. Moreover, measuring thevalue of control is not possible if the controlling block is not transferred. Otherlimitations are the small sample size and potential selection biases.

The third method quantifies the value of the vote as the incremental costof borrowing stock (implied by the equity lending fee) around the record datesrelated to shareholder meetings. Using a proprietary database from a custo-dian bank, Christoffersen et al. (2007) conclude that the vote sells for zero.5

1 See Adams and Ferreira (2008) and Burkart and Lee (2008) for surveys of empirical andtheoretical work on optimal security voting design and the value of voting rights.

2 Throughout the text, we use the terms “the value of voting rights,” “the value of the vote,” “thevoting premium,” and “the value of the right to vote” interchangeably to refer to the market valueof shareholder voting rights.

3 See, for example, Lease, McConnell, and Mikkelson (1983), Levy (1983), Zingales (1994, 1995),Rydqvist (1996), Nenova (2003), Hauser and Lauterbach (2004), and Karakas (2010). Table Iprovides a quick summary of these studies.

4 See, for example, Barclay and Holderness (1989) and Dyck and Zingales (2004). Table I providesa quick summary of these studies.

5 Christoffersen et al. (2007) take the difference between the prices of loans on record dates andloans on surrounding dates (10 trading days before and after) to infer the value of the vote. Ananonymous advisor points out that investors would borrow shares either to short or to vote. Assuch, the price of a vote should be the same as the price of borrowing a share. In other words, the

The Market Value of Corporate Votes 1237

Using a larger data set pooled from several custodians and brokers, Aggarwal,Saffi, and Sturgess (2012) find that equity lending fees increase on the recorddates, especially when the supply of shares is restricted. Their findings implya significant and positive value of the vote. This method can be applied to alarger cross-section of stocks. However, given that the equity lending marketis negotiated, decentralized, and opaque, one cannot be certain if the reportedlending rate is in fact the clearing rate in the market. More importantly, thevalue of the vote inferred from prices in the equity lending market can be sig-nificantly downward biased.6 Table I provides a brief summary of the literatureon the value of voting rights.

Our method for estimating the value of voting rights uses derivatives on thestock. The derivative market allows for the construction of synthetic stocks.An investor that buys a European call option, sells a European put option withthe same strike price and time to expiration, and invests in a risk-free assetan amount equal to the present value of the strike price creates a syntheticstock. This synthetic stock replicates the cash flows that the stockholder isentitled to (other than cash dividends), but does not give the holder the rightto vote prior to option expiration. Thus, we quantify the value of voting rightsas the price difference between the stock and the synthetic stock (adjusted fordividends).7

The advantages of our method are threefold. First, it allows for the estimationof the value of voting rights for all stocks that have call and put option pairswith the same maturity and strike price traded. Thus, the voting premium canbe measured for a large number of stocks. Second, the trading of options on thestock of a firm is primarily an exogenous event. Hence, the sample does notsuffer as much from selection bias issues. Third, we can estimate the value ofthe voting rights attached to a stock at any point in time.

value of the vote inferred from the equity lending market should be equal to the entire lending fee(as opposed to the incremental fee). Additionally, if the vote is valued throughout the days aroundthe record date, this method will incorrectly measure a zero (or trivial) value of the vote. Duringthe period before the record date, especially when voting is important, lending fees could rise withlimited supply of shares and competition for votes. During the period after the record date, lendingfees could stay high if there is uncertainty surrounding the record date, such as the appearance ofanother bidder.

6 For instance, the reported lending rates are often wholesale rates charged to brokers, asopposed to the retail rates that brokers charge their customers. The retail lending rates would beexpected to be higher and more diverse than the wholesale rates (see Feldman (2010)). Additionally,long-term relationships between lenders/borrowers and financial intermediaries could also impactthe observed lending rates. Furthermore, it can be the case that the custodian bank that providesthe data does not include small-sized loans when reporting the lending rate (see Christoffersenet al. (2007)). Given the negative relationship between the loan fee and transaction size (see Saffiand Sigurdsson (2011)), the reported lending rate would be further downward biased.

7 Two other works also look at put-call parity to compute the value of voting rights. In anindependent PhD dissertation, Hodges (1993) proposes the construction of synthetic stocks tocompute the value of voting rights. In an independent undergraduate honors thesis, Dixit (2003)uses synthetic stocks to value voting rights for the HP-Compaq merger and finds a voting premiumof 0.4%.


Table IValue of Voting Rights: Summary of the Literature

This table reports a brief summary of the empirical literature that quantifies the value of votingrights. Panel A reports the studies based on dual-class shares. Panel B reports the studies basedon controlling block sales. The value of the vote is expressed as a percentage of the market valueof the firm.

Panel A: Studies Based on Dual-Class Shares

Study Country Period N Value of Vote (%)

Levy (1983) Israel 1974–1980 25 45.5Lease, McConnell, and Mikkelson (1983) United States 1948–1978 30 5.4Horner (1988) Switzerland 1973–1983 45 20.0Megginson (1990) United Kingdom 1955–1982 152 13.3Zingales (1994) Italy 1987–1990 96 81.5Zingales (1995) United States 1984–1990 94 10.5Smith and Amoako-Adu (1995) Canada 1981–1992 96 10.4Rydqvist (1996) Sweden 1983–1990 65 12.0Chung and Kim (1999) South Korea 1992–1993 119 10.0Nenova (2003)a United States 1997 39 2.0Hauser and Lauterbach (2004) Israel 1990–2000 84 10.0

Panel B: Studies Based on Controlling Block Sales

Barclay and Holderness (1989) United States 1978–1982 63 20.0Dyck and Zingales (2004)b United States 1990–2000 46 1.0

aNenova (2003) conducts a cross-country analysis of 661 dual-class firms across 18 countries andfinds average voting premia that vary from −5% in Finland to 36.5% in Mexico.bDyck and Zingales (2004) use a sample of 393 control transactions across 39 countries from 1990to 2000 and find an average control value of 14%, with estimates ranging from −4% in Japan to65% in Brazil.

Our method has two main limitations. First, our estimation uses Ameri-can options (as exchange-traded stock options are of American type) and thepossibility of early exercise in these options introduces a downward bias in ourmeasure. This is because we ignore the early exercise premiums of the calland put options generated by voting rights, the value of which are not knownex-ante. We conduct simulations to quantify this bias and find that the size ofthe error is minimized and quite modest (about 10% of the value of the vote)for close-to-the-money options.

Second, frictions in short-selling unrelated to control issues can asymmetri-cally affect the violation of put-call parity.8 Ignoring this possibility introducesan upward bias in our estimate of the value of voting rights. In our estimations,we choose the most liquid options (i.e., closest-to-the-money, highest volume,and shortest maturity options) to minimize this bias. Consequently, while our

8 See, for example, Duffie, Garleanu, and Pedersen (2002), Geczy, Musto, and Reed (2002), Ofekand Richardson (2003), Ofek, Richardson, and Whitelaw (2004), Cremers and Weinbaum (2010),and Battalio and Schultz (2011). There can be other confounding factors that affect our measure.Hedge fund trading activity in the options market in anticipation of M&A events could add noiseto our measure. Additionally, if the underlying share price includes bubbles, these could result inviolations of put-call parity that are unrelated to the value of voting rights (Heston, Loewenstein,and Willard (2007)).


evidence suggests that our measure correlates with the value of shareholdervoting rights, we stop short of implying that our measure captures the exactvalue of voting rights.9

Using options data on 4,768 U.S. firms for the period 1996 to 2007, we doc-ument that our measure of shareholder voting rights is positive. The value ofvoting rights for the average firm in our sample is 0.16% of the stock price withan average option maturity of 38 days. We also find that the value of votingrights is an increasing function of the time to expiration of the options usedto construct the synthetic stock. This is expected as the method synthesizes ashare that is nonvoting only until the options’ maturity and derives the valueof holding control rights only until this maturity.

The voting premium calculated from dual-class firms is (conceptually) closestto our measure of the value of voting rights. For dual-class firms that haveoptions traded on the superior class of shares, we find the two measures tobe close and highly correlated. Where the options are traded on the inferiorclass of shares, our measure captures the smaller residual voting rights, andas expected is not correlated with the dual-class measure.

Zingales (1995, p. 1047) notes “ . . . the price of a vote is determined by theexpected additional payment vote holders will receive for their votes in caseof a control contest.” [emphases added]. This would imply that the value ofvoting rights depends on both the probability that a voting event occurs andthe economic significance of such a voting event. As such, the value of votingrights is expected to be time-varying. We analyze three instances in whichvoting rights are expected to increase in value: shareholder meetings, episodesof hedge fund activism, and M&As. For ease of comparison over time and acrosscompanies, we measure the value of voting rights on a given day as a percentageof the closing stock price.

First, we examine the value of voting rights around annual and special meet-ings for the period 1998 to 2007. We hypothesize that the more likely the meet-ings are to be contentious, the higher is the value of voting rights. In line withthis hypothesis, we find that the value of voting rights increases substantiallyaround special meetings (from 0.09% to 0.24%) whereas it remains relativelystable for annual meetings (around 0.10%). The value of voting rights starts toincrease several days prior to the record date and drops following the recorddate. In the cross-section, we find that the increase in the value of voting rightsis higher for special meetings, for meetings with a high-ranking agenda (e.g.,meetings with proposals about antitakeover rather than miscellaneous/routineissues), and for meetings with proposals that result in a close vote (as measuredby the wedge between the percentage vote required for the proposal to pass andthat actually cast in its favor).

9 Estimation of the value of voting rights using any of the methods described above (dual-class shares, block sales, equity lending, and derivatives) relies on the assumption that the no-arbitrage condition holds (i.e., votes can be easily traded). Votes can be traded for many stocksusing the derivatives and equity lending markets (see, for example, Hu and Black (2006) andChristoffersen et al. (2007)). As such, this is a reasonable assumption, especially for our method,since by construction we only look at stocks that have derivatives.


Next, we focus on hedge fund activism. Klein and Zur (2009) find that activisthedge funds achieve their goals by posing a credible threat of engaging thetarget in a proxy solicitation contest. For this reason, hedge fund activismprovides an ideal setting to study the value of voting rights. We use Brav et al.’s(2008) sample of firms targeted by activist hedge funds between 1998 and 2008.We find that the value of voting rights increases after the announcement ofhedge fund activism (from 0.11% to 0.18%). The increase in the value of votingrights is higher for hostile engagements (0.09%) compared to nonhostile ones(0.06%). These results are important as they demonstrate that the mere threatof a voting event is sufficient to increase the value of voting rights.

Finally, we study M&A events over the period 1997 to 2005. We find a signif-icant jump in the value of voting rights on the announcement date of an M&Aevent. While the average voting premium just prior to the announcement isslightly negative, it jumps to 0.22% at the announcement.10 We observe a sig-nificant drop in the value of voting rights at the merger completion date. Wedocument a large drop only for deals that were effective (i.e., not withdrawn).

The documented decrease in the value of shareholder voting rights at thecompletion of an M&A deal demonstrates that it can be optimal to exercisedeep-in-the-money call options prior to expiration, even if the underlying stockpays no dividends. This might help explain some of the early exercise puzzles inthe literature (e.g., Poteshman and Serbin (2003)). To the best of our knowledge,this study is the first to point out that early exercise of call options can beoptimal even in the absence of dividends on the underlying. In a similar fashion,some put option holders will find it optimal to delay exercise until after the dropin the value of the vote.

Taken together, the results in this paper suggest that shareholder votingrights have value, and this value increases around events when control isexpected to be contested.

The value of voting rights is not bounded by arbitrage activity—to the con-trary, the value of voting rights is an important ingredient in the cost of put-callarbitrage activity. If the price of the synthetic stock is significantly lower thanthat of the stock, arbitrage activity would require a short position in the stockand a long position in the synthetic stock. But around special voting events,shareholders are expected to require substantial compensation for lending theirstocks. Thus, the importance of the vote will partially determine the effectivetransaction costs of the put-call parity arbitrage. We compare our measure tothe value of the vote inferred from equity lending fees for a subsample of share-holder meetings. We find the two measures to be positively correlated and closeto each other, which is also in line with the proposition.

We present evidence suggesting that transaction and shorting costs unre-lated to the vote do not affect our findings. First, we find no clear relationshipbetween firm size and the voting premium. Smaller firms would be expectedto have higher transaction and shorting costs. Second, we find no relationship

10 Negative values of voting rights imply a higher price for synthetic stocks. This is consistentwith the hypothesis that information about future M&A activity has leaked to the market.


between the increase in the voting premium around meetings and the liquidityof the underlying or the liquidity of the options used to construct the syntheticstock. Finally, we find that our results remain unchanged even after controllingfor relative short interest (RSI), a proxy for short-sale constraints as suggestedby Boehme, Danielsen, and Sorescu (2006).11 All of the evidence suggests thatour measure does indeed reflect the value of voting rights and is not just amanifestation of decreased liquidity or high short-sale constraints.

Our measure of the value of voting rights also seems to be a good estimate ofthe private benefits of control. In a related theoretical paper, Kalay and Pant(2012) show that at the time of a control contest the difference between theprices of the stock and the synthetic stock can quantify the private benefitsof control. This is further illustrated in a recent study by Ehling, Kalay, andPant (2012), who present evidence indicating that firms with a higher valueof voting rights exhibit a higher propensity to buy property insurance. Thisresult is consistent with the agency rationale for corporate purchase of propertyinsurance—managers are buying property insurance to protect their rents.

This paper contributes to the literature on corporate control and governanceby introducing a new method for measuring the value of shareholder votingrights. This study also contributes potentially to the option pricing literatureby highlighting the importance of the value of voting rights in put-call parityviolations. Indeed, this literature does not typically account for the value ofvoting rights.

The rest of the paper is organized as follows: Section I outlines the methodand testable hypotheses. Section II describes the data and documents the valueof voting rights. We present an empirical analysis of the value of voting rightsaround shareholder meetings in Section III, for activist hedge fund targets inSection IV, and around M&As in Section V. Section VI concludes.

I. Market Value of Voting Rights: Put-Call Parity Revisited

The put-call parity relationship for European-style options on nondividend-paying stocks is stated as

S + p = c + PV (X), (1)

where c and p are the prices of the call and put options, X is their commonstrike, T is their time to expiration, PV (X) is the present value of investing ina bond with face value X that matures at time T , and S is the underlying stockprice (Stoll (1969)).

Investors can design a synthetic long position in the stock by buying a calloption and writing a put option with common strike X and common time tomaturity T , and investing in a bond with face value X for time T :

S(T ) = c − p + PV (X), (2)

11 RSI is the percentage of shares that are held short for each firm.


where S(T ) represents a position in the synthetic stock. Similarly, investorscan design a synthetic short position in the underlying stock. These syntheticstocks replicate the cash flows of the underlying stock, but do not give investorsvoting rights, that is, the owner of the synthetic stock is not entitled to vote.Hence, an adjustment to put-call parity must be made that reflects the right tovote that is enjoyed only by the owner of the stock. The modified put-call parityrelationship is now stated as

S + p = c + PV (X) + PV (Vote(T )), (3)

where PV (Vote(T )) reflects the present value of the voting rights prior to op-tions’ expiration.

The synthetic stock is a function of the time to expiration of the options usedto construct it. At option expiration, the prices of the synthetic stock and stockconverge. Hence, the difference between the price of the stock and the syntheticstock gives the present value of the market value of the voting rights in thenext T days:

PV (Vote(T )) = S − S(T ). (4)

This implies that the estimated value of voting rights is a nondecreasingfunction of the time to maturity of the options used to construct the syntheticstock.

A. American-Style Options

Exchange-traded equity options are American style. This implies that theoption holder has the right to exercise the options prior to maturity. Put-callparity adjusted for the early exercise premium and for dividends is stated as

S = C − EEPcall − P + EEPput + PV (X) + PV (Div) + PV (V ote(T )), (5)

where C and P are the prices of American call and put options, and PV (Div)is the present value of dividends paid before the options mature.

The term EEPcall quantifies the value of the right to exercise the call optionanytime prior to option expiration. It is well known that American call optionsmay be exercised early if there is a large enough dividend prior to the expirationof the option. Since historical dividend information is readily available, it iseasy to calculate the part of the EEPcall due to dividends (EEPdiv

call). However,if the vote component of the underlying stock is expected to decrease in valueprior to option expiration (e.g., an expected decline in the vote component of thestock price after an important voting event), then it can be optimal to exercisecall options early even if the underlying stock pays no dividends. Since we donot have the vote component of the stock, we are unable to adjust for the earlyexercise premium of the call option due to the vote. This introduces a bias inthe estimation of the value of the voting right. Similar to call options, the partof the early exercise premium of the put (EEPput) due to dividends, EEPdiv

put ,


can be easily calculated. However, the vote component also introduces biasesin the estimation of the EEPput.

A.1. Biases Due to Early Exercise

For simplicity, let us assume that the underlying stock does not pay divi-dends. If the value of the vote is expected to decrease prior to option expiration,then it could be optimal to exercise a call option. In this case, the only way anoption holder can realize the value of the vote is by exercising the call optionon or before the last cum-date.12 Ignoring the early exercise possibility of thecall option introduces a downward bias in the estimation of the value of votingrights. The option holder will exercise only if the expected drop in the valueof voting rights is large enough relative to the time value of the option on theex-vote day. The time value of the call option, other things equal, is smaller thelower is the exercise price. Hence, owners of deep-in-the-money call options aremore likely to capture the vote if it is valuable. Consequently, the downwardbias in the estimation of the value of voting rights is larger for synthetic stocksconstructed with deep-in-the-money call options.

The drop in the value of voting rights introduces an opposite reaction in putoption holders. Put option holders may find it optimal to delay exercising theiroptions until after the drop in the value of the vote. Delaying exercise of aput option implies capturing the vote and hence the price of such a syntheticstock will incorporate a fraction of the vote value. In this case, our measurewill underestimate the value of voting rights. The downward bias is a directresult of overestimating the early exercise premium (ignoring the possibilityof a delay in exercise due to the vote). The question of delay in exercise onlyarises for those put 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. Theseare the options that have a negative time value (when the economic value ofthe forgone interest is larger than the insurance embedded in the put) beforethe ex-vote day. This probability depends on the strike price of the put option.Unlike the call options, the downward bias introduced due to the overesti-mation of the early exercise premium of the put is not a monotonic functionof the strike price. Even for put options where exercise is not delayed, theearly exercise premium is estimated with a bias. This is because the impliedvolatility used to compute the premium is estimated without accounting for thevote.

As detailed in the Appendix, we conduct simulations to better understandhow these biases vary with different strike prices and expected ex-vote days.The aim of this experiment is to find the level of moneyness that results in theleast biased estimates of the value of voting rights. The results of the simulationare reported in Table II. We find that the bias in the estimation of the value

12 The cum-date is three trading days prior to the record date (to allow for the settlement ofstocks in the exchange). Investors holding voting shares on a meeting’s record date are eligible tovote at the meeting.


Table IISimulated Biases in Estimating the Value of Voting Rights

This table reports the average estimation error in the value of the vote as a function of themoneyness of the synthetic stock and the volatility of the underlying process. The value of the rightto vote is calculated as the price difference between the stock and the synthetic stock constructedusing options and is normalized by the stock price. Moneyness is defined as ln(S/X), where S isthe stock price and X is the strike price of the options used to construct the synthetic stock. Theerror in estimation is calculated using simulations of the true price process and simulations ofthe estimation procedure. The binomial option pricing model with 1,000 steps is used to conductthe simulations with the following parameters: price of the underlying stock S = $100, interestrate r = 5%, time to maturity of the options T = 35 days, and Vote = 0.5%. Simulations are runfor ex-vote days ranging from one through 34. The error in the vote estimation is calculated asV 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. PanelB reports the corresponding signed errors.

Panel A: Average Absolute Error in the Estimation of the Value of Voting Rights

Moneyness

Volatility −0.34 −0.26 −0.18 −0.10 0.00 0.11 0.22 0.36

0.1 49.63% 45.92% 40.05% 34.40% 13.99% 9.22% 61.67% 66.46%0.2 45.61% 40.34% 40.82% 20.90% 10.97% 45.29% 61.63% 66.46%0.3 45.59% 39.79% 28.63% 10.15% 9.58% 30.41% 58.47% 66.44%0.4 44.94% 33.40% 16.43% 7.09% 8.67% 22.44% 47.09% 65.53%0.5 36.64% 21.58% 10.84% 5.99% 8.02% 17.89% 36.60% 60.55%

Panel B: Average Signed Error in the Estimation of the Value of Voting Rights

0.1 12.75% 8.14% 0.56% −8.95% 12.00% 9.22% 61.67% 66.46%0.2 8.74% 2.56% 1.93% −1.59% 10.17% 45.29% 61.63% 66.46%0.3 8.79% 3.32% 1.66% 3.53% 9.10% 30.41% 58.47% 66.44%0.4 10.41% 6.58% 5.04% 4.35% 8.35% 22.44% 47.09% 65.53%0.5 11.09% 7.83% 5.71% 4.51% 7.79% 17.89% 36.60% 60.55%

of the vote is minimized substantially when the options are close to the money(around 10% of the value of the vote). Consequently, we use close-to-the-moneyoptions for our analysis. An additional advantage of using close-to-the-moneyoptions is their increased liquidity. These options have higher volumes andlower spreads, which help minimize issues related to nonsynchronous tradingin the option and equity markets.13

13 Applying the insight that the voting rights are akin to a dividend, one can deduce a lowerbound for the value of the voting right from put-call parity bounds for American options. Eventhough we adopt the direct measure of the value of voting rights as the main framework for ourtests, we compare our results to those obtained using the lower bound approach. In general, weobserve that the main results are qualitatively the same with both methods. This suggests thatthe downward bias from ignoring the component of the early exercise premium due to votingevents does not play a major role. The finding also suggests that the model dependency for thecomputation of the early exercise premium is not critical for our results. Please see the Appendixfor a more detailed discussion and comparison of results.


We construct synthetic stocks using the following equation:

S(T ) = C − EEPdivcall − P + EEPdiv

put + PV (X) + PV (Div). (6)

For ease of comparison over time and across companies, we calculate thenormalized value of the shareholder voting rights in the next T days, Vote, bydividing the value of the vote in the next T days by the stock price:

Vote = (S − S(T ))/S. (7)

B. Testable Hypotheses

As noted earlier, the value of voting rights depends on the probability thata voting event occurs and the economic significance of the voting event. Boththe probability of a voting event and the economic significance of the event aretime varying.

We deduce three main testable hypotheses following the above arguments.First, if the probability of an unexpected voting event is nonzero during thelife of the synthetic stock, the market value of the vote should be nonnegative.Second, the difference between the price of the stock and the price of the syn-thetic stock provides a measure (likely downward biased) of the value of theright to vote in the next T days. This implies a nondecreasing relationshipbetween Vote and T . Third, the economic significance should be a function ofhow contentious the event is and the magnitude of the private benefits thatcan be extracted.

We summarize these testable empirical implications as follows:

(1) Vote is nonnegative.(2) Vote is a nondecreasing function of the time to maturity.(3) Vote increases when the value of voting rights is expected to be important.

We look at three scenarios: shareholder meetings, hedge fund activism,and M&A events.

II. Value of Voting Rights

A. Data

To construct synthetic stocks, we use data on options from the Ivy DB Op-tionMetrics database. This database provides end-of-day bid and ask quotes,trading volume, open interest, and option-specific data (e.g., implied volatil-ity, maturity, strike price, etc.) for all American call and put options on stockstraded on U.S. exchanges. It also provides the stock price and dividends of theunderlying stocks and zero-coupon interest rates.

We use data for options with 90 days or less to expiration on stocks from1996 to 2007. The sample covers 4,768 firms. We form option pairs that areused to construct the synthetic stock. An option pair consists of a call optionon 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 eitherthe call or the put option are locked or crossed. We keep only those option pairsfor which the volume for both the call and put is greater than zero and theimplied volatility (calculated using the binomial option pricing model) for thecall and put is defined. The option prices are taken as the midpoints of thebid and ask quotes, which are the best closing prices across all exchanges onwhich the option trades. Since the options are all American style, we computethe early exercise premium for the put and the call using the binomial optionpricing model.14

B. Value of Voting Rights across Time to Maturity

As derived in Section I, we expect to see a nondecreasing relation betweenVote and T . A natural experiment then is to construct synthetic stocks withvarying T and characterize the value of the vote as a function of T .

To test this hypothesis, we first sort the synthetic stocks into three bins ofzero to 30 days to maturity, 31 to 60 days to maturity, and 61 to 90 days tomaturity. We find support for our hypothesis. The average value of the vote is0.09% for the zero 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 of Table III shows the relationship betweenthe value of voting rights and T for 30-day bins. Panel B repeats the exercisefor 10-day bins.

We also look at how the value of voting rights varies with T at daily intervals.The results are depicted in Figure 1. The figure plots the average normalizedvalue of the vote using synthetic stocks with 2 to 89 days to maturity. It alsoplots the standard errors around the average. We find that the general trend inthe data supports our hypothesis that the normalized difference between thestock and the synthetic stock measures the value of the right to vote in the nextT days. The average value of voting rights for options with 2 days to maturityis 0.04% and for options with 89 days to maturity is 0.28%.

The evidence indicates that the value of voting rights increases as the timeto expiration of the options increases. This is consistent with the theory as anunexpected voting event is more likely to occur for synthetic stocks that havea longer life.

C. Value of Voting Rights across Firms

In this section, we calculate the value of voting rights for the firms in oursample. As explained in Section I, the biases in the estimation of the valueof voting rights are minimized when the options used are close to the money.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 valueof the vote for each firm. We keep only those firms that have at least 10 ob-servations in a given year. The average value for each firm in each year is

14 See the Appendix for details.


Table IIIValue of Voting Rights across Time to Maturity

This table reports the normalized value of the vote (in percentages) for different time to maturitybins. The figures are calculated for stocks that have exchange-traded options during the period1996 to 2007. The value of the right to vote is calculated as the price difference between the stockand the synthetic stock constructed using options and is normalized by the stock price. Panel Areports the results for 30-day T bins and panel B reports the results for 10-day T bins. T is thetime to maturity of the options used to construct the synthetic stock. The confidence intervals (CI)reported are based on errors clustered at the firm level.

Panel A: Groups of 30 Days

Vote in %

T (Days) Lower CI (5%) Mean Upper CI (95%)

0 to 30 0.093 0.094 0.09431 to 60 0.140 0.141 0.14161 to 90 0.222 0.223 0.224

Panel B: Groups of 10 Days

0 to 10 0.060 0.061 0.06211 to 20 0.089 0.090 0.09121 to 30 0.109 0.110 0.11131 to 40 0.115 0.115 0.11641 to 50 0.143 0.144 0.14651 to 60 0.169 0.170 0.17161 to 70 0.183 0.185 0.18771 to 80 0.218 0.220 0.22281 to 90 0.260 0.262 0.264

first computed. We then use these firm-year averages to estimate the meanvalue of the vote for each firm. Next, these values are averaged across firmsto get the average value of voting rights in our sample. The results are re-ported in panel A of Table IV. The time to maturity of the options used rangesfrom around 17 days to 58 days. On average, the time to maturity of the op-tions is 38 days. We estimate the average value of the vote to be 0.16% of firmvalue.

Next, we look at the voting premium of the average firm over time. Wecalculate the average voting premium for each firm-year. The average votingpremium for a year is then computed by averaging across the firms in eachyear. We find variation in the voting premium from 1996 to 2007. As shownin panel B of Table IV, the voting premium increases from 0.13% in 1997to 0.21% in 2001, after which it drops to 0.11% in 2004, and then increasesagain to 0.16% in 2005. Interestingly, the variation in the voting premium overtime has a resemblance to the intensity of merger activity during this period.Merger intensity increased steadily from 1996 through 2000, peaking in 2000.This merger wave ended with the market crash in 2001. The next merger wavestarted in 2004.


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Figure 1. Value of voting rights as a function of T . The figure characterizes the normalizedvalue of the vote (in percentages) as a function of time T . The value of the right to vote is calculatedas the price difference between the stock and the synthetic stock constructed using options andis normalized by the stock price. T is the time to maturity of the options used to construct thesynthetic stock.

To check whether transaction costs are driving our results, we divide firmsin our sample into 10 groups based on the market capitalization of the firm.The average value of the vote is computed for each of these 10 groups. Iftransaction costs placed an upper bound on the value of voting rights, wewould expect to see the highest premium for the smallest firms and the low-est premium for the largest firms. As is evident in panel C of Table IV, wefind no relationship between the size of the firm and our estimate of thevalue of voting rights. The estimate of the value of the vote for the small-est firms in our sample is 0.12%, and that for the largest firms is 0.15%.Recall that the voting premium for the average firm in the entire sampleis 0.16%.

It is not surprising that our measure is not affected by transaction costs.Please note that, since our measure looks at the difference in the prices of thestock and the synthetic stock, it is only affected by asymmetric transactioncosts. Firms that have high transaction costs would experience increased vio-lations of put-call parity in both directions. We analyze and discuss this issuemore in Section III.A.1.


Table IVValue of Voting Rights across Firms

This table reports the normalized value of the vote (in percentages) across firms. The figures arecalculated for stocks that have exchange-traded options during the period 1996 to 2007. The valueof the right to vote is calculated as the price difference between the stock and the synthetic stockconstructed using options and is normalized by the stock price. Only options with moneynessbetween −0.1 and 0.1 are used. Moneyness is defined as ln(S/X), where S is the stock price and Xis the strike price of the options used to construct the synthetic stock. The average value for eachfirm in each year is first computed. The firm-year averages are then averaged across years to getan average vote for each firm. Panel A reports results for the average firm. Panel B documents thevalue of the vote for the average firm across 1996 to 2007. Panel C reports the normalized value ofthe vote for different firm size sorts. CI denotes the confidence interval of the mean.

Panel A: The Average Firm, 1996 to 2007

N Mean Lower CI (5%) Upper CI (95%) Min Max

4,768 0.16 0.15 0.18 −3.2 11.6

Panel B: Voting Rights across Years

Year N Mean Lower CI (5%) Upper CI (95%)

1996 1,179 0.14 0.12 0.161997 1,524 0.13 0.12 0.151998 1,645 0.17 0.15 0.191999 1,738 0.15 0.13 0.182000 1,869 0.17 0.14 0.192001 1,705 0.21 0.19 0.232002 1,627 0.16 0.14 0.172003 1,680 0.11 0.10 0.122004 1,945 0.11 0.10 0.122005 2,057 0.16 0.14 0.172006 2,767 0.11 0.09 0.122007 3,082 0.14 0.12 0.16

Panel C: Voting Rights across Size Sorts

Size in $Million Mean Std. Error Min Max

177.76 0.12 0.02 −1.13 3.36317.68 0.18 0.02 −0.74 5.70464.28 0.18 0.02 −1.21 3.65636.00 0.16 0.02 −0.82 4.65849.68 0.15 0.02 −0.55 5.971,186.51 0.14 0.01 −0.27 2.331,727.72 0.18 0.02 −0.82 4.932,705.64 0.16 0.01 −0.83 4.845,152.95 0.16 0.01 −0.14 1.0426,945.81 0.15 0.00 −0.01 0.63

D. Dual-Class Firms

The voting premium calculated from dual-class firms is conceptually closestto our measure of the value of voting rights. Indeed, our method can be in-terpreted as synthesizing an inferior voting share. Technically, there are two


important differences between the two measures. First, the time to maturityis finite in our method, whereas it is infinite in dual-class firms. Therefore,the value of voting rights is expected to be higher in the latter method. Sec-ond, our method generates a synthetic nonvoting share as an inferior vot-ing share whereas in dual-class firms the inferior voting shares usually havesome voting rights. We address this issue by adjusting the voting premiumusing the relative voting rights of different classes of shares following Zingales(1995).

To compare the two measures, we intersect the dual-class firms compiledby Gompers, Ishii, and Metrick (2010) with our sample. A total of 39 firmsare in both samples over the period 1996 to 2006; 27 match through theirinferior voting shares and 12 match through their superior voting shares. Foreach of these companies we calculate the voting premium as follows (Zingales(1995)):

VPZ ≡ PS − PI

PI − rPS, (8)

where PS and PI are the prices of superior and inferior voting shares, and ris the relative number of votes of an inferior voting share versus a superiorvoting one.

To compare our measure in a meaningful way with the dual-class firms,we first annualize our measure.15 Our annualized normalized value of votingrights (AVote) can be thought of as in line with the voting premium calculationwhere PS is the underlying stock, PI is the synthetically generated nonvotingshare, and r is zero. However, as we normalize the value of voting rights bydividing it by the price of the underlying stock, the denominator in our measureis the superior voting share rather than the inferior one as in Zingales (1995).Therefore, to make our measure comparable to the voting premium calculatedabove, we apply the following transformation:

VPO ≡ 11 − AVote

− 1. (9)

Here,VPO stands for the annualized voting premium inferred using options.For the set of 12 dual-class firms that have options traded on the superior classof shares, we find the average VPZ to be 7.0%, whereas the average VPO is6.7%. The simple coefficient of correlation between these two measures of thevalue of voting rights is significantly positive (0.22 at p < 0.0001). RegressingVPO on VPZ with firm clustered errors, we find that VPO is positively correlatedwith VPZ. The coefficient for VPZ is 0.39 (p = 0.029).

For the set of 27 dual-class firms that have options traded on the inferior classof shares, we find the average VPZ to be 3.8%, whereas the average VPO is 1.2%.The simple coefficient of correlation between these two measures of the value ofvoting rights is small and not significant (0.005 at p = 0.727). Regressing VPO

15 See Section I of the Internet Appendix for details on the annualization of the value of votingrights.


on VPZ with firm clustered errors, we find that VPO is positively correlatedwith VPZ. The coefficient on VPZ is again small and insignificant at 0.01 (p =0.775).

These results are interesting and in agreement with economic theory. Fordual-class firms where the options are traded on the inferior class of shares,our measure is only able to capture residual voting rights that the shareholdersof the inferior class are entitled to. As such, we do not expect any correlationbetween our measure and that of the traditional dual-class measures in thesefirms. At the same time, dual-class firms where options are traded on the supe-rior class of shares should exhibit a positive correlation between our measureof the value of voting rights and the voting premium inferred using traditionaldual-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 eventis expected to significantly affect future cash flows, the value of the voting rightcomponent embedded in the stock should be more pronounced. We test thishypothesis by looking at the time-series and cross-sectional variation in theaverage value of voting rights around shareholder meetings.

A. Annual and Special Meetings

Data on shareholder meetings are obtained from Institutional ShareholderServices (ISS) and cover meetings from 1998 to 2007. In addition to the meetingdate and the record date for the meeting, we also know whether the meetingtype is “annual” or “special.” We have a total of 14,501 meetings, of which13,521 are annual and 980 are special. The average number of days betweenthe record date and the meeting date is 53 and 43 days for annual and specialmeetings, respectively.

Our main hypothesis is that the value of voting rights should increase (asinformation about an upcoming voting event becomes available) prior to therecord date. The increase in the value of voting rights should be higher formeetings that are more likely to be contentious (e.g., special as opposed toannual meetings).

We test this hypothesis by looking at the time-series variation in the averagevalue of voting rights around annual and special meetings. For each of the daysin 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 variationin the value of voting rights. The option pair that is closest to the money withthe highest volume and with the least time to maturity is selected. Selectionof close-to-the-money options minimizes biases in our estimation due to earlyexercise premia (see Section I). Selecting options close to the money with highvolume and small time to maturity ensures that our results do not suffer


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Figure 2. Value of voting rights around voting events: cum-date centered. The figurecharacterizes the time-series variation of the normalized value of the vote (in percentages) aroundannual and special shareholder meetings during the period 1998 to 2007. The value of the rightto vote is calculated as the price difference between the stock and the synthetic stock constructedusing options and is normalized by the stock price. Week 0 corresponds to the cum-date. The cum-date is three trading days before the record date. Investors holding voting shares on a meeting’srecord date are eligible to vote at the meeting.

from stale prices and minimizes biases from noncontrol-related short-sellingfrictions.

Figure 2 tracks the weekly time-series variation of the value of voting rightsaround the cum-date of special and annual meetings. We find that for annualmeetings there is very little variation in the value of voting rights (around0.11%). However, special meetings exhibit an increase in the value of votingrights prior to the voting event (from 0.11% to 0.24%). The value of voting rightsincreases several weeks prior to the cum-date. This is expected since the valueof voting rights should be reflected in the price of the underlying as soon asthe possibility of a voting event is known. We also find that the value of votingrights drops after the cum-date.

While we document a drop in the value of voting rights after the cum-date,it takes a few weeks for the voting premium to settle back to its original level.This could be due to uncertainty remaining about the voting event until themeeting occurs. The record and meeting dates are not binding and the boards


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Figure 3. Value of voting rights around voting events: meeting date centered. This figurecharacterizes the time-series variation of the normalized value of the vote (in percentages) aroundannual and special shareholder meetings during the period 1998 to 2007. The value of the rightto vote is calculated as the price difference between the stock and the synthetic stock constructedusing options and is normalized by the stock price. Week 0 corresponds to the meeting date.

of directors have significant discretion in setting and changing these dates.16

Uncertainty about the voting event is likely to be greater when control iscontested and the vote is more valuable.

Figure 3 tracks the weekly time-series variation in the value of voting rightsaround the meeting date of special and annual meetings. The peak in the valueof voting rights (about 0.24%) occurs around eight weeks prior to the meetingdate. The value of voting rights then starts to drop and settles to its originallevel prior to the meeting date (around 0.11%).

We also test our hypothesis by regressing our measure of the value of votingrights on a dummy variable that takes the value one for the event window andzero for the control window. We construct a 20-trading-day window (four weeks)prior to the cum-date, which is labeled the event window. Our control window

16 This is an interesting point since record and meeting dates have generally been (implicitly)assumed to be binding and certain in the literature. A nonexhaustive sample list of instances ofrecord and meeting date changes for U.S. public firms is available from the authors upon request.


Table VValue of Voting Rights around Shareholder Meetings

This table reports regressions of the normalized value of the vote (in percentages) around share-holder meetings during the event window and the control window. The value of the right to voteis calculated as the price difference between the stock and the synthetic stock constructed usingoptions and is normalized by the stock price. The event window is a 20-trading-day window (fourweeks) prior to the cum-date. The control window is a 20-trading-day window two quarters priorto the cum-date. The cum-date is three trading days before the record date. Investors holdingvoting shares on a meeting’s record date are eligible to vote at the meeting. The dummy variableRecord Date takes the value one for the event window and zero for the control window. Regression1 uses all the meetings in the sample, whereas Regressions 2 to 9 only use the special meetings.Regressions 3 and 4 control for the option volume and stock volume. Regression 5 controls for theAmihud (2002) illiquidity measure for the stock. Regressions 6 and 7 control for option illiquiditymeasures defined in Cao and Wei (2010). t-statistics are reported in parentheses. Regression 9controls for relative short interest (RSI), which is a proxy for short-sale constraints as suggestedby Boehme, Danielsen, and Sorescu (2006). Regression 8 repeats Regression 1 but with the samplefor which RSI data exist. Errors are clustered at the firm level.

Dependent Variable: Vote

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Record date 0.007 0.145 0.146 0.145 0.148 0.145 0.143 0.096 0.098[Event:1, Control: 0] (1.11) (4.36) (4.38) (4.52) (4.27) (4.32) (4.07) (2.26) (2.34)

Option volume rank −0.002[High volume: 9, Low: 0] (−0.31)

Stock volume rank −0.001[High volume: 9, Low: 0] (−0.09)

Amihud rank 0.004[More illiq: 9, Less: 0] (0.56)

Option spread rank .001[High spread: 9, Low: 0] (0.17)

Option illiq rank −0.009[More illiq: 9, Less: 0] (−1.21)

RSI rank −0.005[High RSI: 9, Low: 0] (−0.50)

Constant 0.115 0.093 0.099 0.095 0.071 0.087 0.137 0.061 0.093(24.12) (5.27) (3.34) (2.60) (1.98) (2.61) (3.59) (3.07) (5.27)

Meetings 14,501 980 980 980 976 980 931 231 231Special meetings 980 980 980 980 976 980 931 231 231

is a 20-trading-day window two quarters prior to the cum-date.17 Results arereported in Regression 1 of Table V. We find no increase in the value of votingrights during the event window. The value of voting rights remains flat onaverage, around 0.12%. This is expected since most of the meetings in oursample are annual meetings. Next, we run the regression only on the subsetof special meetings. Results are reported in Regression 2 of Table V. We finda significant and positive increase in our measure (about 0.15%) for special

17 We choose a control window that is far away from the event being considered. At the sametime, we do not want to go back too much in time so as to avoid overlap with any past events.Results are not sensitive to the particular event and control window chosen.


meetings. The value of voting rights more than doubles when compared to thecontrol window (from 0.09% to 0.24%). This is consistent with theory since weexpect the value of voting rights to be higher for special meetings.

A.1. Exogenous Transaction Costs

Arbitrage activity cannot put an upper bound on the value of voting rights.If the synthetic stock is significantly lower than the stock, arbitrage activity toprofit from the gap requires a short position in the stock and a long position inthe synthetic stock. But around special voting events, shareholders will requiresubstantial compensation for lending their stocks. Thus, the importance of thevote will partially determine the effective transaction costs of the put-call parityarbitrage.

Put-call parity might be violated due to reasons other than voting issues.18

Ofek, Richardson, and Whitelaw (2004) show that short-sale constraints arelinked to these violations. As we argue above, short-sale constraints wouldautomatically be affected if the value of voting rights increases. However, theremight still be nonvoting-related issues affecting short-sale constraints.

Additionally, market frictions could also violate put-call parity. Please notethat since our measure looks at the difference in the prices of the stock andthe synthetic stock, it is only affected by asymmetric transaction costs. Firmsthat have high transaction costs would experience increased violations of put-call parity in both directions. Our measure, however, would only be affected bythese transaction costs if they are asymmetric in nature.

In the presence of transaction costs and shorting costs unrelated to the vote,the put-call parity relationship is stated as

S = S(T ) + PV (V ote(T )) + TCSCUV, (10)

where TCSCUV are the transaction costs and shorting costs unrelated to thevote.

We investigate the effect of TCSCUV on our measure in several ways. First,we divide the special meetings into 10 groups based on the volume of the op-tions used to construct the synthetic stock. Results are in Regression 3 of TableV. Option Volume Rank takes the value zero through nine, with zero corre-sponding to the group with the lowest volume and nine corresponding to thegroup with the highest volume. We find no relationship between option volumeand the increase in our measure during the event window. The coefficient onthe event window remains unchanged both in magnitude (about 0.15%) as wellas in significance.

We repeat this methodology and divide the special meetings into 10 groupsbased on the volume of the underlying. The increase in the value of voting rightsduring the event window remains unchanged after controlling for the volume

18 See, for example, Duffie, Garleanu, and Pedersen (2002), Geczy, Musto, and Reed (2002), Ofekand Richardson (2003), Ofek, Richardson, and Whitelaw (2004), Cremers and Weinbaum (2010),and Battalio and Schultz (2011).


of the underlying stock (Regression 4, Table V). Next, we divide the specialmeetings into 10 groups based on the Amihud measure (Amihud (2002)) ofthe underlying stocks. As seen in Regression 5 of Table V, our results are notsensitive to the Amihud measure either.

We repeat this exercise using the option spread of the options used to con-struct the synthetic stock and find robust results (Regression 6, Table V). Wealso construct an option illiquidity measure as suggested by Cao and Wei (2010)(similar to the Amihud measure for stocks) and find that our results remainunchanged (Regression 7, Table V).

It might seem puzzling at first that our measure is not affected by measuresof transaction costs. Please note that our measure would only be affected if thetransaction costs are asymmetric in nature, as discussed before. Additionally,since most stocks with options are reasonably liquid and among these we pickthe most liquid stocks and options, liquidity concerns are minimized in oursample.

Shorting costs unrelated to the vote can lead to asymmetric put-call parityviolations. To control for these, we use RSI as a proxy for short-sale constraintsas suggested by Boehme, Danielsen, and Sorescu (2006). RSI is the percentageof shares held short for each firm. Boehme, Danielsen, and Sorescu (2006) showthat RSI is highly correlated with equity lending fees.

We obtain RSI data from COMPUSTAT by dividing the short interest bythe number of common shares outstanding. Note that short interest data aremonthly and the figures reflect the positions held on the 15th business day ofeach month. Following Boehme, Danielsen, and Sorescu (2006), we drop casesin which short interest data are missing. After matching with the RSI data, weare left with only 231 special meetings. Regressions 8 and 9 in Table V presentresults with and without RSI, respectively. We find that RSI does not changeour results. The increase in the value of voting rights with and without RSIis about 0.10%. This coefficient is smaller than that in Regression 2 (0.15%).However, this is due to the (smaller) sample with the RSI data, as is evident inRegression 8.

A.2. Further Analysis

Our estimation procedure uses the ex-post distribution of dividends. Thisassumes away uncertainty regarding future distributions of dividends. Yetdividend payments do change, and they can be initiated and terminated. Moreimportantly, these changes might be nonnegligible due to contesting eventssuch as hedge fund activism or proxy contests.19 Under- (over-) estimationof PV (Div) would lead to over- (under-) estimation of PV (Vote). We test therobustness of our results in Table V by eliminating all synthetic stocks thathave a dividend payment prior to option expiration. We find that our results donot change (see the Internet Appendix20).

19 See, for example, Brav et al. (2008) and Fos (2011).20 The Internet Appendix may be found in the online version of this article.


We use stock prices from OptionMetrics for our analysis. Battalio and Schultz(2006) point out that several microstructure issues, including nonsynchronousstock and option prices at the end of day, might plague the OptionMetricsdatabase. To address this concern, we obtain TAQ quotes and TAQ prices ofthe stock closest to 4:02 pm, the closing time for the options market. We repeatour analysis first with TAQ quotes and then with TAQ prices, and find that ourresults are qualitatively the same as in Table V (see the Internet Appendix).The value of voting rights remains flat around 0.09% to 0.11% for all meetings(Regressions 3 and 5), whereas it more than doubles once we focus on specialmeetings (Regressions 4 and 6). This is not surprising as we pick liquid stockand option pairs for our analysis. Furthermore, the steps in preparing the data(e.g., dropping observations with crossed or locked quotes) are in line with sug-gestions in Battalio and Schultz (2006) to minimize potential nonsynchronousprice problems.

B. Meeting Characteristics

For a subset of the meetings (7,919 out of 14,501) over the period 2000 to2007, we also have data on the description of the proposals, the proponent of theproposals (e.g., shareholders, management), the voting requirement (e.g., ma-jority, supramajority), the vote’s outcome (e.g., percentage of votes for, against,abstained, withheld), the ISS recommendation, and the management recom-mendation.21

We classify each proposal according to its content (e.g., antitakeover related,directors related). We also rank its agenda according to the possibility of acontrol event (the higher the possibility, the higher the ranking). For instance,antitakeover-related proposals have the highest ranking (rank = 1) whereasproposals about environmental and social issues have the lowest ranking(rank = 5). The Internet Appendix reports the classification categories andtheir rankings.

We hypothesize that, in addition to special meetings, meetings that havehigh-ranking proposals (e.g., antitakeover related), meetings with proposalsthat result in a close vote, meetings with conflicts among different parties (e.g.,ISS and management recommendations conflict), and meetings with share-holder proposals should exhibit higher increases in the value of voting rights.22

To test our hypotheses, we regress the difference in the value of the votingrights between the event window and the control window for each meeting ondifferent characteristics of the meeting. More precisely, the dependent variableis the value of the vote for a firm averaged for each shareholder meeting duringthe event window (20 trading days prior to the cum-date) minus the value of

21 See Maug and Rydqvist (2009) for a detailed description of the database.22 Shareholder proposals are important mechanisms for shareholder activism (see, for example,

Gillan and Starks (2007)). However, the literature finds small effects of shareholder activism (see,for example, Karpoff (2001) and Bebchuk (2007)) as opposed to the recent hedge fund activism,which we examine in Section IV.


Table VICharacteristics of Shareholder Meetings

This table reports cross-sectional regressions of the change in the normalized value of the vote (inpercentages) between the event window and the control window across shareholder meetings. Thevalue of the right to vote is calculated as the price difference between the stock and the syntheticstock constructed using options and is normalized by the stock price. The event window is a 20-trading-day window (four weeks) prior to the cum-date. The control window is a 20-trading-daywindow two quarters prior to the cum-date. The cum-date is three trading days before the recorddate. Investors holding voting shares on a meeting’s record date are eligible to vote at the meeting.All of the regressions use all the meetings in the sample. Special meetings among all meetings arereported at the bottom of the table. t-statistics are reported in parentheses. Errors are clusteredat the firm level.

Dependent Variable: Change in Vote

(1) (2) (3) (4) (5) (6) (7) (8)

Meeting dummy 0.074 0.054 0.059 0.054[Special: 1, Annual: 0] (3.38) (2.20) (2.58) (2.21)

Agenda dummy 0.039 0.027 0.009[High ranking: 1, Low: 0] (3.02) (1.95) (0.56)

Closeness −0.054 −0.047 −0.042[|Vote required-vote cast for|] (−4.29) (−3.57) (−2.9)

ISS-Management conflict 0.018[Conflict: 1, Agree: 0] (1.19)

Shareholder proposal 0.023[Shareholder: 1, Management: 0] (1.29)

Meetings 7,919 7,919 7,919 7,919 7,919 7,919 7,919 7,919Special meetings 336 336 336 336 336 336 336 336Firm dummy Yes Yes Yes Yes Yes Yes Yes Yes

the vote averaged over the control window (20 trading days two quarters priorto the cum-date).

Table VI reports the results. The variables are as follows: Meeting Dummytakes the value one if the meeting is a special meeting and zero if it is anannual meeting, Agenda Dummy takes the value one if the meeting has anagenda with rank 1 (e.g., antitakeover related) and zero otherwise,23 Closenessis the absolute difference between the percentage vote required to accept theproposal and that actually cast in its favor, and is a forward-looking measure,ISS-Management Conflict takes the value one if the ISS recommendation forthe proposal conflicts with management’s, and Shareholder Proposal takes thevalue one if the proponent of the proposal is a shareholder. In our tests, we alsoinclude firm fixed effects. The results suggest that the value of voting rightsincreases during the event window for special meetings (0.07%), for meet-ings with a high-ranking agenda (0.04%), and if the proposal has close votes

23 The majority of the cases are clustered at proposals with rank one or two. Therefore, we createthe agenda dummy and pool the proposals with ranking less than or equal to two.


(0.027% for a 50 percentage point deviation in Closeness).24 The coefficientson the other variables also have the expected signs, but are not statisticallysignificant. Overall, these results are consistent with the hypothesis that themore contentious the meetings, the higher the value of voting rights.

One issue with the independent variables is that they are correlated. Forinstance, the meeting’s agenda likely affects the closeness of the vote. There-fore, when included together in the regression, some of these variables losesignificance. In this framework, meeting type and closeness of the votes seemto be the most important explanatory variables.

We repeat our analysis controlling for RSI. After matching with the RSI datawe are left with 5,012 meetings. As is evident in results reported in the InternetAppendix, we find that, even after controlling for RSI, both the magnitude andthe significance of the meeting dummy, agenda dummy, and closeness variablesremain unchanged. Please note that the agenda dummy loses significance inthis sample. However, this is not due to the introduction of RSI, but perhapsto the reduced sample size. These results suggest that our measure is notinfluenced by noncontrol-related shorting difficulties.

C. Equity Lending

Equity lending has been used for vote trading as illustrated by Christoffersenet al. (2007). Therefore, one can infer the value of voting rights from equitylending fees and compare it to our measure of the value of voting rights. Forthis comparison, we obtain equity lending fee data (value-weighted and equal-weighted) for a subsample of firms from Data Explorers, which is a globalinformation company tracking all securities financing–related information.25

The data cover a year around the record dates (about three-quarters before andone-quarter after the record dates).

We construct the subsample by first selecting the 100 stocks with the highestvalues of voting rights and the 100 stocks with the lowest values inferredfrom option prices around the record dates. Since the equity lending data areavailable from 2005 onwards, we choose among the stocks with record datesafter mid-2005. Of these 200 stocks, 175 have the needed equity lending dataand of these, 87 are among the 100 with the highest values of voting rights(“high value sample”) and 88 are among the 100 with the lowest values ofvoting 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.26

The corresponding annualized value of voting rights measured with the option

24 For the majority voting rule, going from 50% to 100% in votes cast for would result in a50 percentage point deviation. This would increase the value of the vote by −0.054% × −0.50 =0.027%.

25 We would like to thank Pedro Saffi for helping us with the equity lending data. See Saffi andSigurdsson (2011) for a detailed description of cross-country equity lending data.

26 All equity lending fees reported are value-weighted figures. Results are similar for equal-weighted fees.


prices is 0.13% (5.40%) for the low (high) value sample. We calculate the changein the equity lending fees and the change in the value of voting rights around therecord date ([−3,3] trading weeks) compared to a quarter before the record date([−18,−13] trading weeks). The simple correlation between these two changemeasures is significantly positive (0.44 at p< 0.001), and is mostly driven bythe high value sample.27

Christoffersen et al. (2007) find that loan volumes spike around record datesfor the period 1998 to 1999. In a recent article, Aggarwal, Saffi, and Sturgess(2012) analyze the equity lending market in the United States around the timeof proxy voting for the period 2005 to 2009. They find that, toward the recorddate, on average, there is a significant reduction in the supply of shares lent andan increase in the demand for shares to borrow. They find that this behavior,in contrast to Christoffersen et al. (2007), leads to an increase in lending fees,especially in cases in which the supply restrictions are higher.28 These resultsare consistent with the view that the increase in the value of voting rightswould also be reflected in the equity lending markets.

IV. Activist Hedge Fund Targeting

In this section, we study the value of voting rights in firms targeted byactivist hedge funds.29 Compared to traditional investors, hedge funds usemore sophisticated financial products (e.g., options, equity swaps, etc.) andmore aggressive tactics (see surveys by Agarwal and Naik (2005) and Brav,Jiang, and Kim (2009)). Klein and Zur (2009) find that activist hedge fundsachieve their goals by posing a credible threat of engaging the target in a proxysolicitation contest. For this reason, hedge fund activism provides an idealsetting to study the value of voting rights.

We use Brav et al.’s (2008) sample of U.S. firms targeted by activist hedgefunds between 1998 and 2008.30 For each target, the data set includes the dateof engagement and detailed information about the engagement such as type orhostility of the engagement (see Brav et al. (2008) for more details).

Of the 1,066 sample firms, 424 have the required options and financial datain the intersection of the OptionMetrics and CRSP databases. Therefore, thefinal treatment sample (“target sample”) consists of 424 firms. Of these, 118are classified as hostile. For each of the targets, we compute our measure

27 Nonsynchronicity due to different frequency of data likely biases the correlation downwards.The equity lending data are reported on a weekly basis before 2007, and daily from 2007 onwards.However, our measure is computed on a daily basis for the whole period.

28 One possible reason that these two papers reach opposite conclusions might be due to differentdata sets. The Aggarwal, Saffi, and Sturgess (2012) paper uses a data set over the period 2005 to2009, and the data are provided by 125 large custodians and 32 prime brokers in the securitieslending industry. The data set used by Christoffersen et al. (2007) spans only one year (1998 to1999) and is provided by only one large lending agent.

29 See, for example, Brav et al. (2008) and Klein and Zur (2009) for hedge fund activism in theUnited States, and Becht, Franks, and Grant (2010) for hedge fund activism in Europe.

30 We are grateful to Brav et al. (2008) for sharing their data with us.


Table VIIHedge Fund Activism

This table reports regressions of the normalized value of the vote (in percentages) during theevent window and the control window around hedge fund activism. The value of the right to voteis calculated as the price difference between the stock and the synthetic stock constructed usingoptions and is normalized by the stock price. The event window is a 16-week window starting atthe announcement of the activism. The control window is a 16-week window two quarters priorto the announcement date. Regression 1 presents the results for the entire sample. Regressions 2and 3 use the entire sample but control for the option and stock volume, respectively. Regressions4 and 5 present results for nonhostile and hostile events, respectively. t-statistics are reported inparentheses. Errors are clustered at the firm level.


(1) (2) (3) (4) (5)

Hedge fund activism 0.071 0.065 0.071 0.060 0.094[After: 1, Before: 0] (2.26) (2.23) (2.35) (1.61) (1.97)

Option volume rank 0.013[High volume: 9, Low: 0] (1.69)

Stock volume rank 0.000[High volume: 9, Low: 0] (0.04)

Constant 0.113 0.056 0.112 0.116 0.105(6.78) (1.71) (3.84) (6.20) (5.13)

Targets 424 424 424 306 118Hostile targets 118 118 118 0 118

of the value of voting rights during the event window and a control window.The event window is a 16-week window following the announcement of thehedge fund activism. The control window is a 16-week window, two quartersprior to the announcement of the activism.31 Table VII presents results of theregression of the value of the voting rights on the hedge fund activism dummy.The hedge fund activism dummy takes the value one during the event windowand zero during the control window. We find a significant and positive increasein our measure of the value of voting rights (0.07%) during the event window(Regression 1).

We also investigate the effect of liquidity on our measure in two differentways. First, we divide the targets into 10 groups based on the volume of theoptions used to construct the synthetic stock. Results are in Regression 2 ofTable VII. Option Volume Rank takes the value zero through nine, with zerocorresponding to the group with the lowest volume and nine corresponding tothe group with the highest volume. We find no relationship between option vol-ume and the increase in our measure during the event window. The coefficienton the activism dummy (about 0.07%) remains very similar and significant.We repeat this method and divide the targets into 10 groups based on the vol-ume of the underlying. The increase in the value of voting rights during the

31 Results are not sensitive to the selection of the particular event windows.


event window remains unchanged (0.07%) after controlling for the volume ofthe underlying stock (Regression 3, Table VII).

Activism that is hostile in nature can be expected to have a higher increasein the value of voting rights. We test this hypothesis by dividing our sampleinto hostile and nonhostile targets. We find that the increase in the value ofvoting rights is higher for hostile targets (about 0.09%). While the increase inthe value of voting rights is still positive for nonhostile targets, the magnitudeis considerably smaller (0.06%) and the significance is reduced when comparedto hostile targets (Regressions 4 and 5, Table VII). The results on hedge fundactivism are interesting since they demonstrate that the value of voting rightscan increase even if the voting event is not realized.

We also repeat our tests with a set of industry (three-digit SIC) and size(market capitalization) matched control firms. The Internet Appendix showsthe results of regressing the difference in the value of the voting rights betweenthe target firm and the control firm on the activism dummy. We find a significantand positive increase in the difference (about 0.05%) during the event window.The constant is not significantly different from zero, suggesting that thereis no difference in the value of the voting rights between target and controlfirms before targeting. The coefficient on the activism dummy is positive andhighly significant (about 0.08%) for hostile targets. For nonhostile targets thecoefficient is small (about 0.01%) and not significant. This again confirms ourresults that the value of voting rights increases substantially for hostile targets.

Regressions 4 and 5 look at the difference in the value of the voting rightsbetween the target and control firms before and after activism for hostile andnonhostile targets. The hostile targeting dummy takes the value one for hostiletargets. We find that before activism there is no difference between the hostileand the nonhostile targets. However, after activism there is a significant dif-ference between the hostile and the nonhostile targets. The constant is positiveand significant (about 0.04%), suggesting that value of voting rights increasesfor target firms after activism compared to control firms. The hostile targetingdummy is positive and significant (about 0.07%) after activism. This suggeststhere is an additional increase in the value of the voting rights for target firmsif the activism is hostile.

V. Mergers and Acquisitions

Control contests are arguably one of the most important events in the life cy-cle of a firm. The value of the voting right component embedded in the commonstock should exhibit large increases during M&A events. To test this hypoth-esis, we observe the time series of the voting premium for targets around theannouncement and completion dates of M&A events.

We obtain M&A data from the Securities Data Corporation (SDC) database.Our sample consists of 1,291 M&A deals in the United States between 1997and 2005 in which a successful acquirer owns at least a 50% stake in thetarget firm. We plot the value of the voting rights during the 200 trading daysbefore the announcement date and up to 200 trading days after the completion


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Figure 4. Value of voting rights around M&A announcement dates. The figure character-izes the time-series variation of the normalized value of the vote (in percentages) around M&Aannouncements. The value of the right to vote is calculated as the price difference between thestock and the synthetic stock constructed using options and is normalized by the stock price. Thevalue of the vote is averaged over groups of 10 trading days.

date. The value of voting rights exhibits a significant and large jump on theannouncement date (Figure 4). The value continues to remain high after theannouncement date.

We note that, as we move further away from the announcement date, thevalue of voting rights continues to increase. The sample consists of deals thathave still not been completed on a particular day, that is, as we move furtheraway from the announcement date, the sample consists of deals that took longerto complete. This apparent time-series drift in the value of voting rights couldbe driven by a different cross-section of firms at each point in time.

The value of voting rights remains high prior to the completion date anddrops around the completion date (Figure 5). The drop, however, is not as largeas the increase around the announcement date. The completion date consistsof both the deal effective date and the deal withdrawn date. For deals involvinga merger that was effective, the firm would cease to exist after the effectivedate. Hence, the sample of synthetic stocks after the completion date consistsof deals that either were withdrawn or were effective but did not consist of a100% acquisition (we include all deals where at least 50% of the target firm issought) of the target firm.


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Figure 5. Value of voting rights around M&A completion dates. The figure characterizesthe time-series variation of the normalized value of the vote (in percentages) around M&A com-pletion dates. The value of the right to vote is calculated as the price difference between the stockand the synthetic stock constructed using options and is normalized by the stock price. The valueof the vote is averaged over groups of 10 trading days.

Panel A of Table VIII presents the regression analysis around the deals’announcement dates. The announcement dummy takes the value one after theannouncement of the acquisition. We find a significant and large increase inthe value of voting rights (about 0.25%) after the announcement of the deal.Regression 2 focuses on the 1,027 deals that were effective and Regression3 on the 264 deals that were withdrawn. We find that the increase in thevalue of voting rights is almost double for the effective deals compared to thewithdrawn deals (0.27% versus 0.14%). Panel B of Table VIII presents theregression analysis around the deals’ completion dates. We find a substantialdecrease in the value of voting rights (around 0.18%) at the completion of thedeal. Regression 2 focuses on the deals that were effective and Regression 3 onthe deals that were withdrawn. We find that, while there is a large drop in thevalue of voting rights for the effective deals (around 0.24%), the deals that arewithdrawn do not see any change in the value of voting rights.

We also divide the deals based on deal characteristics. Deals for which theattitude of the deal is not friendly (as characterized by SDC) or for which thereis more than one bidder are classified as contentious deals (319 deals out of1,291). We find a significant increase in the value of voting rights for both types


Table VIIIM&A Deals

Panel A of the table reports regressions of the normalized value of the vote (in percentages) beforeand after the announcement of the M&A event. The value of the right to vote is calculated asthe price difference between the stock and the synthetic stock constructed using options and isnormalized by the stock price. The after window is a 16-week window starting at the announcementof the deal. The before window is a 16-week window prior to the announcement date. Panel B ofthe table reports regressions of the value of the vote before and after the completion of the M&Aevent. The after window is a 16-week window starting at the completion of the deal. The beforewindow is a 16-week window prior to the completion date. Regression 1 presents the results for theentire sample. Regressions 2 and 3 present results for effective and withdrawn deals, respectively.Regressions 4 and 5 present results for contentious and friendly deals, respectively. t-statistics arereported in parentheses. Errors are clustered at the firm level.


Panel A: Around M&A Announcement

(1) (2) (3) (4) (5)

Announcement 0.246 0.273 0.141 0.347 0.220[After: 1, Before: 0] (6.55) (6.15) (2.35) (3.35) (5.62)

Constant 0.032 0.044 −0.017 0.066 0.023(1.54) (2.02) (-0.34) (1.98) (0.96)

Panel B: Around M&A Completion

Completion −0.176 −0.242 0.028 −0.310 −0.090[After: 1, Before: 0] (−3.47) (−3.12) (0.53) (−3.10) (−1.17)

Constant 0.334 0.384 0.138 0.434 0.305(8.65) (8.14) (3.51) (4.65) (7.29)

Deals 1,291 1,027 264 319 972Deal type All Effective Withdrawn Contentious Friendly

of deals on the announcement date, with a larger increase for contentious deals(about 0.35%) compared to friendly deals (0.22%) (Regressions 4 and 5, panel Aof Table VIII). At the completion date, the contentious deals have a significantdrop in the value of voting rights (0.31%), whereas the friendly deals do notexperience a drop in the value of voting rights (Regressions 4 and 5, panel B ofTable VIII).

In the Internet Appendix, we plot the call and put option open interest andvolume around the deal announcement date. All four measures exhibit anincrease in value around the announcement date. This further assures us thatthe difference between the stock and the synthetic stock is not a manifestationof reduced liquidity.

The magnitude of the increase in the value of voting rights is much higherin contentious M&A deals (about 0.35%) in comparison to special shareholdermeetings (about 0.15%) or hostile hedge fund activism (about 0.09%). This isnot surprising since M&As are, on average, more important and bigger controlcontests compared to shareholder meetings or hedge fund activism.


VI. Conclusions

This paper employs a new approach using option prices to estimate the valueof the shareholder voting rights embedded in the stock price. The method doesso by synthesizing a nonvoting share using put-call parity, and by comparingits price to that of the underlying stock. The method allows for the estimationof the value of voting rights for a large number of stocks at any point in time.

Empirically, we find our measure to be positive and increasing with theexpected life of the synthetic stocks. We also document that the measure in-creases around events in which control may be more valuable. First, the valueof shareholder voting rights increases around special meetings, around meet-ings with a high-ranking agenda, and around meetings where the proposalhas close votes. Second, we find that the value of voting rights increases afterthe announcement of hedge fund activism, especially for hostile engagements.Finally, we find a significant increase (decrease) in the value of voting rightson the announcement (completion) date of the M&A activity.

Our method should be used with the understanding that the measure doesnot capture the exact value of voting rights. The measure may be underesti-mated due to the possibility of early exercise of the options used, or overesti-mated due to short-selling constraints unrelated to control issues. Our simula-tions and choice of liquid and close-to-the-money options, however, ensure thatthese biases are minimized and quite modest. More importantly, our robustnesschecks confirm that our results are not driven by these biases.

The method can be used to study the determinants of the voting premium.Indeed, it can be applied to any study in the corporate finance/governance liter-ature focusing on control. The method also has asset pricing implications. Forinstance, it provides a potential explanation for some put-call parity violationsand seemingly irrational early exercise of call options. Whether such an expla-nation is empirically important remains to be tested and is beyond the scope ofthis paper.

Initial submission: January 24, 2011; Final version received: September 26, 2013Editor: Campbell Harvey

Appendix

A. Bias in the Estimation of the Value of Voting Rights

As explained in Section I, the inability to account for the vote while computingthe early exercise premiums of call and put options biases our estimate of thevalue of voting rights. First, not accounting for the early exercise premium ofthe call due to the vote introduces a downward bias in the estimation of votingrights. Additionally, the downward bias is a decreasing function of the strikeprice. Second, not accounting for the delay in the exercise of put options due tothe vote introduces a downward bias for synthetic stocks where the put optionsare in the money. Lastly, even for put options where exercise is not delayed due


to the vote, the implied volatility used to compute the early exercise premiumis biased. This is because the implied volatility computation does not accountfor the vote. This bias can go in either direction.

We conduct simulations to better understand how the biases vary with thestrike price of the synthetic stock. The aim of our experiments is to identifythe strike price that minimizes these biases. The binomial option pricing modelwith 1,000 steps is used to conduct the simulations. The true price process andthe true call and put option prices are first simulated using a tree, and thefollowing parameters: price of the underlying stock S = $100, interest rate r =5%, time to maturity of the options T = 35 days, and Vote = 0.5%. Simulationsare run for all possible ex-vote days. The ex-vote days range from one through34. Using simulations, we obtain the true American prices for the call and putoptions, and the true early exercise premiums for the options.

Once we have the true price process, we then estimate the early exercisepremium for the put. The estimation procedure ignores the value of the vote.Once we have the estimated early exercise premium of the put, we constructthe synthetic stock. Note that the synthetic stock does not account for theearly exercise premium of the call due to the vote. Next, we calculate ourestimate of the voting rights, Voteest. The error in the estimation is quantifiedas Voteerror = (Voteactual − Voteest)/Voteactual. The absolute Voteerror is computedas the absolute error in the estimation of the voting rights. For each strikeprice we run simulations for all possible ex-vote days. We compute the meanof the absolute errors across different ex-vote days for a given strike price.These simulations are conducted for different strike prices. The strike pricevaries from $70 through $140, which corresponds to moneyness levels rangingfrom 0.36 through −0.34, where moneyness is defined as ln(S/X). We repeatsimulations for different volatilities of the underlying ranging from 0.1 through0.5. Results are reported in Table II.

B. Lower Bound Approach

Applying the insight that voting rights are akin to a dividend, the followinglower bound for the value of voting rights can be deduced from put-call paritybounds for American options (see Hull (2002)):

PV (Vote(T )) ≥ S − X − C + P − PV (Div). (B1)

As mentioned in Section I, the lower bound approach for the value of votingrights is a complementary approach to the direct approach. While the lowerbound approach is more difficult to interpret since it is mostly negative, it hasthe advantage of not being model dependent and being less difficult to compute.The approach implicitly assumes that the lower bound of the value of votingrights has similar properties to the value of voting rights itself.

The measure is normalized by the closing stock price of the underlying stock.The empirical evidence indicates that the lower bound is negative for 88% of


the option pairs.32 For these cases, the lower bound of the voting rights isinferred to be zero as it cannot be negative theoretically. Although this biasesthe measure of voting rights upwards, it is useful for interpretation and thebias does not seem to be critical in results.

Focusing only on cases with nonnegative lower bounds (12% of the optionpairs), the empirical evidence indicates that the value of the vote increases asthe time to maturity of the option pairs used increases. This result is consistentwith the finding that the value of voting rights increases with the time tomaturity of the options previously documented using the direct approach.

When the analysis is focused around the record date, the evidence showsthat the lower bound for the value of voting rights spikes at the record datefor special meetings and stays flat for annual meetings. In the cross-sectionalanalysis, the lower bound measure is higher around the record date if theproposal discussed in the meeting is about antitakeover, merger and reorgani-zation, capitalization, or maximizing-value issues rather than about compensa-tion, director-related, miscellaneous/routine, environmental/social, and otherissues. The lower bound for the value of voting rights is also significantly higherfor proposals that result in a close vote, as measured by the wedge betweenthe percentage vote required for the proposal to pass and that actually cast inits favor, as well as for proposals where the ISS recommendation conflicts withthat of management. These results are in line with the hypothesis that thefiercer the control contest, the higher the value of voting rights. These resultsare consistent with the findings using the direct approach.

Overall, these findings suggest that the main results of the paper are robustto different approaches for estimating the value of voting rights. The findingsalso suggest that the model dependency of the main framework for the calcu-lation of the early exercise premium is not critical for our results.

C. Early Exercise Premium

The early exercise premium for put and call options with dividends is cal-culated using the binomial option pricing model. We use the Cox, Ross, andRubinstein (1979) method to generate the lattice. This implies that the up anddown factors for the lattice are generated using the equations u = eσ

√�t and

d = e−σ√

�t.For the inputs to the algorithm, we get the implied volatility, time to expi-

ration, strike price, price of the underlying, dividends, and ex-dates from theOptionMetrics database. OptionMetrics also provides risk-free rate data forcertain maturities. We interpolate the risk-free rate data to get the risk-freerate for the exact maturity of the option being considered.

We calculate the early exercise premium for the put and call options using1,000 steps. Over the course of each step, the security price is assumed to move

32 Note that, in the absence of the value of voting rights, the bound should always be less thanor equal to zero due to no arbitrage. Since the observed value of voting rights is on average small,it is not surprising that the lower bound is positive only 12% of the time.


either up or down. The size of this move is a function of the up and downfactors that are in turn determined by the implied volatility and the size of thestep. To determine the early exercise premium, we start at the current securityprice S0 and build a “tree” of all the possible security prices at the end of eachsubperiod. Next, we price the option at each node at expiration by setting theoption expiration value equal to the exercise value, C = max(Si − X, 0) andP = max(X − Si, 0), where X is the strike price and Si is the projected priceat expiration at node i. The option price at the beginning of each subperiod isdetermined by the option prices at the end of the subperiod. At each node, wedetermine whether early exercise is optimal. Working backwards, we estimatethe price of the American option. In a similar fashion we determine the price ofthe equivalent European option (the only difference being that early exercise isnot an option until the very end of the tree). The difference between the priceof the American option and the European option gives us the early exercisepremium.

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Supporting Information

Additional Supporting Information may be found in the online version of thisarticle at the publisher’s web site:

Appendix S1: Internet Appendix.



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the market value of corporate votes: theory and evidence from option prices

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