Do Stock Prices Incorporate the Potential Dilution of

Employee Stock Options?∗

Gerald T. Garvey† Todd T. Milbourn‡

February 3, 2003

∗We wish to thank Gene Fama for the Fama-French factors and Stuart Gillan for the data on option exercises.Thanks also to Kerry Back, Murray Carlson, Jennifer Carpenter, Heber Farnsworth, Ron Giammarino, David Hirsh-leifer, Steve Huddart, Kathy Kahle, Ali Lazrak, Mike McCorry, Harold Mulherin, Greg Roth, Richard Smith, SiewHong Teoh, Sheridan Titman, JeffWurgler, and seminar participants at Washington University in St. Louis, Univer-sity of British Columbia, and Barclays Global Investors for useful suggestions. We are grateful to Xifeng Diao whoprovided expert research assistance and computational support.

†Peter F. Drucker School of Management, Claremont Graduate University, Claremont CA 91711 Tel: 909-607-9501e-mail: gerald.garvey@cgu.edu

‡Washington University in St. Louis, John M. Olin School of Business, Campus Box 1133, 1 BrookingDrive, St. Louis, MO 63130-4899 Tel: 314-935-6392 Fax 314-935-6359 e-mail: milbourn@olin.wustl.edu website:http://www.olin.wustl.edu/faculty/milbourn/

1

Do Stock Prices Incorporate the Potential Dilution of

Employee Stock Options?

Abstract

Employee stock options represent a significant potential source of dilution for shareholders

in many firms. It is well known that reported earnings systematically understate the associated

costs, but an efficient stock market will show no such bias. If by contrast stock prices fail to fully

incorporate the future costs implied by stock option grants, option exercises will produce negative

abnormal returns. We design and implement a stock-picking strategy based on predictions of

stock-option exercise using publicly-available information. We are able to identify stocks that

subsequently exhibit significant negative abnormal returns using either a CAPM or three-factor

Fama-French benchmark. We also find weak evidence that the returns are more negative for firms

whose earnings shocks are more persistent, as predicted in a recent theoretical model in which

limited investor attention is the source of mispricing. More consistent with the notion of limited

investor attention, we find our results to be stronger in months where firms issue quarterly reports

which alert investors to any dilution stemming from the exercise of employee stock options.

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1 Introduction

In the growing controversy over off-balance sheet liabilities and potentially inflated earnings re-

ports, employee stock options take pride of place (see The Economist (2000), Byrnes (2002), and

Morgensen (2002)). For example, the Investor Responsibility Research Center (2001) reports that

just over 14% of the equity of the average S&P 500 firm has been promised to employees through

stock option plans.1 Under current US accounting rules, stock option grants are not expensed,

are not recorded on balance sheets, and are only partially reflected in diluted Earnings Per Share.

In 2003, Standard & Poor’s will introduce a new data item that it terms “Core Earnings” which

will expense employee stock option grants using Black-Scholes values, and major firms such as

Coca-Cola and General Electric have promised to do the same to their future earnings reports.2

The controversy over how employee stock options should be treated in accounting reports has

largely neglected the question of whether market prices already account for the associated costs.3

If prices do not reflect these costs, it should then be possible to devise a profitable stock selection

strategy based on public information. Jenkins (2002) states the case with much stronger language:

Myth: Failing to deduct an expense for management stock options inflated earningsand therefore stock prices. Good grief. We’ve been discussing this rule change for adecade now. It would be the overripe short-selling opportunity of the century if themarket were somehow fooled into mispricing stocks simply because we failed to adopta particular accounting treatment for the non-cash value of options.

To formulate a test of this hypothesis, we begin with the assumption that investors effectively

disregard at least a portion of the costs of stock option grants.4 An obvious implied trading

strategy is to short or downweight firms with large amounts of employee options outstanding, but

this is an incomplete strategy. The unaddressed question is exactly when do investors realize the

costs of options and drive prices back to fundamentals?5 We assume that prices do not reflect

1The Economist (2000) reports that the Black-Scholes value of employee stock option grants in 1999 was just over6% of the earnings of an average S&P 500 firm. Core and Guay (2000) document that the Black-Scholes value ofemployee stock options average almost 4% of the market capitalization of the average large corporation, with valuesat the upper end of the spectrum approaching 24%. Sanford F. Bernstein & Co estimates that if option grants hadbeen expensed, profit growth for the S&P 500 over 1997 through 2001 would drop from 9% to 6% (see Morgensen(2002)).

2See Standard and Poor’s (2002).3One can also interpret these costs as dilution, as the distinction between the two is semantic. Interpreting stock

options as a cost to shareholders affects the expected cash flows to a firm, whereas treating them in terms of theirdilution affects the number of outstanding shares. Both interpretations result in the same price per share. Thesubstantive problem we analyze is that current accounting standards do not report either dilution or cost at the grantdate.

4While our work simply posits such behavior as our starting point, Hirshleifer and Teoh (2002) show explicitlyhow such mispricing can stem from limited attention and processing power on the part of investors.

5See DeLong, et al (1990) for an example of a research design that seeks to identify how quickly market mispricingis corrected.

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option costs until they materialize upon exercise by employees. Observe that we cannot rule out

“temporary” mispricing in which the market adjusts to reflect the costs of option grants with some

unspecified lag. Searching for such an effect would inevitably result in data-snooping, because in

hindsight there is sure to be at least one period in which option-granting firms have lower than

expected returns. Indeed, Yermack (1997) and Ittner, et al (2002) find that firms tend to perform

somewhat better than expected in the year following large option grants. Our contention is that if

investors neglect option costs, there is no reason to expect any correction in the subsequent year

since no additional information about the option grant will emerge.

A benefit of formulating the test as a trading rule is that it forces the researcher to recognize

many of the constraints that an active investor would face.6 Most importantly, we must use

forecasted option exercises, rather than realized option exercises used by Carpenter and Remmers

(2001) and Huddart and Lang (2002). Their research can ascertain whether executives made well-

timed trades based on their own information, but it is mute on the question of market efficiency

unless the market is sluggish in its reaction to the revelation of an insider sale.7 By contrast, we

use public information to forecast future exercises and form our portfolios in anticipation of such

exercises. This empirical strategy is most sensible for two reasons. First, the relevant data for the

exact date at which employees exercise is unavailable save for the top executives in the firm. This

data constraint precludes the use of an event-study methodology. Second, even if we were to use

a longer estimation window, the results would be biased because employees will only exercise their

options if the stock has performed well enough to make the options sufficiently valuable to exercise.

To predict the year in which employee exercise will take place, we rely on a typical, three-

year vesting schedule of employee stock options, in conjunction with results documented in existing

research on the decision to exercise such options (see Huddart and Lang (1996) and Heath, Huddart

and Lang (1999)).8 We then test the more refined proposition that prices will reflect exercises

primarily in months where the firm issues quarterly reports; such reports alert shareholders to the

net effect of stock option exercises on the firm’s balance sheet.

6Core, et al (2000), Huson, et al, (2000) and Aboody, et al (2001) find some evidence that market values of equityare lower when option liabilties are greater. While these studies are consistent with the view that stock prices alreadyincorporate option costs, they have limited power to reject the hypothesis of market efficiency. First, the regressionsrequire that book value, earnings, and earnings forecasts provide an adaquate control for other determinants of value.Perhaps as a result of potential misspecification problems, the result that option costs are reflected in lower marketvalue does not hold in all specifications. Second, the estimated effect of option costs on value is generaly less thanone-for-one. We cannot tell if this is due to error in measuring option costs or to the market only taking partialaccount of stock option costs.

7See Seyhun (1998) for an exhaustive treatment of the investment value of insider trading disclosures.8That is, we assume that options granted during the year 1992 will have vested by the beginning of 1996 since at

least three full years will have passed. In our empirical analysis of how well our predicted exercises explain realizedexercises in a small sample (Table 4 ), we document successes for both this “three-year cliff-vesting” schedule and the“25%-per-year vesting” schedule.

4

To estimate the costs of expected option exercises, we use Standard and Poor’s ExecuComp

data for each of the years 1992 to 1996, thereby forming our trading strategy over the years 1996

to 2000. This restricted time-series is driven by our assumption that stock options don’t vest

until the beginning of the fourth year after which they were granted, coupled with the fact that

the ExecuComp data does not begin until 1992. Despite this limitation, we estimate a reliable

and negative relationship between abnormal returns and our measure of the unrecognized cost of

employee stock options. Specifically, using either a portfolio “alpha” approach or the Fama and

MacBeth (1973) method, we find that the results are significant at the 5% level or better for both

CAPM and Fama-French abnormal returns. Moreover, we find that the effects tend to be stronger

in months when quarterly reports are issued. Obviously, our time-period is unrepresentative in that

the market performed better than its historical average. However, we continue to find evidence that

the market underestimates the costs of stock options even after controlling for firm fixed effects,

that is, after setting each firm’s expected returns equal to its average realized return over our time

period 1996 to 2000.

The paper is organized as follows. Section 2 presents a simple model that highlights the key

measurement and accounting issues, as well as the assumptions required for our trading rule to

work. Section 3 summarizes our data and how we put together our stock selection rule. Section 4

analyzes the performance of our trading rule. In Section 5 we provide further evidence on Hirshleifer

and Teoh’s (2002) model of limited investor attention. Section 6 presents our sensitivity analyses

and Section 7 concludes. The Appendix contains the proof of our main proposition.

2 A Simple Model

Consider an all-equity firm with n shares outstanding plusm identical employee stock options, each

with an exercise price X. The present value of the firm’s future cash-flows is denoted by V . We

consider two periods. The first period corresponds to the time that we make our stock selections,

at which point all parties agree that V = V0 and that firm value in the second and final period

is distributed according to the distribution F (V ). In this terminal period, employees can exercise

their options and will choose to do so if their options are in the money. While the results in this

section hold for any distribution of terminal values, in our empirical work we will effectively assume

that it is log-normal because we use the Black-Scholes-Merton formula to approximate the value of

options.

Denote by P0 the stock price at the initial period and denote the stock price in the terminal

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period by P1. If options expire out of the money, there will be only n shares outstanding so

P1(out) ≡ Vn . If by contrast options expire in the money, the shareholders receive a cash infusion

of mX, but must also issue m additional shares, thus P1(in) ≡ V+mXn+m . Denote by V ∗ ≡ nX the

critical terminal value of V at which the options are just at the money. This value is unique since

P1(in) = P1(out) only at V = V∗ = nX.

Our interest in this paper is whether the market properly anticipates the costs of stock options,

so our attention is focused on the initial price P0. Since the expected market rate of return is

assumed zero, a price that appropriately anticipates stock option costs along with the distribution

of returns simply equals the expected value of the terminal price. Since the terminal price is Vn if

V ≤ V ∗ and V+mXn+m otherwise, we can write the price that correctly anticipates option dilution as

P ∗0 =V ∗Z0

V

ndF (V ) +

∞ZV ∗

V +mX

n+mdF (V ). (1)

Observe that an estimate of P ∗0 in our model requires knowledge of the number of options

granted m and the exercise price X. In practice, these values have in fact been reported at the

option grant date in footnotes of annual reports since 1992. The costs are not, however, integrated

into firm earnings at the grant date, nor is the evolving liability recorded on the balance sheet. An

extreme view would be that the market completely ignores stock option costs, in which case the

initial price would simply be given by E(V )n . While we present evidence consistent with this view in

the empirical section, we focus on the somewhat less extreme hypothesis that investors make use of

the information summarized in diluted earnings per share according to SFAS 128, but do not take

account of the full costs of options. SFAS 128 requires firms to recognize an additional number

of shares equal to max[0, m(P0−X)P0]; see, for instance, Core, et al (2000). Put into valuation terms,

SFAS 128 assumes that if options are currently not in the money, then there is no option dilution,

while if they are currently in the money, the options will be immediately exercised.9 Following this

logic we define:

PAcc0 =

∞R0

Vn dF (V ) if

∞R0V dF (V ) ≤ V ∗

∞R0

V+mXn+m dF (V ) otherwise.

(2)

Clearly, the above price does not correctly incorporate the expected cost of option exercises as

is done in equation (1). It either assumes that the options will never be exercised, or that they

will always be exercised. Our purpose in this section is to derive the empirical implications of a

9“Currently” here means “at the fiscal year-end”. For convenience, we henceforth assume that time 0 is the endof the fiscal year. We incorporate differences between price at portfolio formation time and at the end of the fiscalyear in our empirical work.

6

world where investors are misled by the accounting treatment of stock options to systematically

underestimate their cost. Formally, the model yields the following result.

Proposition 1

If the initial stock price is P ∗0 , then the expected abnormal return on the stock is zero. However,

if the initial price is PAcc0 , the expected abnormal return is equal to −mUnP0

, where nP0 is the firm’s

initial market capitalization and U =∞RV ∗

V−nXn+m dF (V )−max[0, P0 −X] is the unrecognized cost of

a single employee stock option.

The intuition behind this result is straightforward. If investors underestimate the expected

costs of employee stock options, the expected abnormal return is clearly negative. This implica-

tion is a direct consequence of our assumption that PAcc0 effectively ignores the time value of the

options. Hirshleifer and Teoh (2002) provide a model that endogenizes such a specification, and

their Proposition 5 contains the analogous prediction that if some investors have limited attention

and stock options are not expensed at the time they are granted, the market will overvalue firms

relative to fundamental value, with greater overvaluation being associated with larger employee

stock option grants.10 An additional implication of their model that is beyond the scope of our

reduced-form approach is that as the persistence of earnings increases, the greater will be the over-

valuation due to employee stock options and the more negative the abnormal return will be upon

exercise. We test the proposition empirically in Section 5.

Proposition 1 effectively characterizes expected returns, conditioning only on the characteristics

of the stock option grant (m and X). While we report results with raw returns in our empirical

section, we focus on market-adjusted returns to each stock to isolate underperformance from any

correlation between stock option costs and systematic risk factors. In addition to the relationship

between raw and risk-adjusted returns and option values, it is also possible to estimate expected

returns conditional on observing option exercise. Such a test would not address the question of

whether or not the market appropriately prices the costs of employee stock options, because em-

ployees will exercise only if V > V ∗. That is, we expect to see a positive relationship between

employee stock option exercises and prior stock market performance, even if investors had overval-

ued the firm by neglecting the fact that employees will share in good stock price performance.11

10Hirshleifer and Teoh (2002) provide an opposite prediction for the situation in which the expected option costs arefully expensed at the time of granting, resulting in firms being undervalued. However, since current U.S. accountingstandards do not require such full expensing, this prediction remains untested.11As emphasized earlier, prior research has documented a negative relationship between option exercises and

7

We confirm this relationship empirically in our Table 3, but it is of secondary interest. The more

important implication of Proposition 1 is that the stocks of firms with large amounts of expected

option exercise will perform worse than they otherwise would have, and operationally this means

that they will underperform their market-based benchmarks.

There are two key issues that our simple two-period model does not address. The first is the

choice of the initial period. This is arbitrary in the theory. To reflect accounting reality, however,

we have to recognize that PAcc refers to the price at the end of the last fiscal year since this is the

price that is used in computing the most recent version of diluted EPS. The second timing issue

is the terminal point. In the model, the ending point is the date that the employees exercise their

options. The contractual maturity of most employee stock options is 10 years. Thus, if employees

behave according to risk-neutral option pricing, we would observe exercises before 2002 only for

those firms that grant options with maturities less than 10 years and for those with extremely high

dividend payouts. It is, however, well known that employees exercise grants soon after vesting if

the option is in the money (see Huddart and Lang (1996) and Heath, Huddart and Lang (1999)).

Indeed, SFAS 123 requires firms to disclose in footnotes (not earnings) the Black-Scholes value of

option grants but leaves them free to assume maturity dates far less than the contractual maturity

in so doing.

Our model does not endogenize early exercise (see, e.g. Meulbroek (2001) and Hall and Murphy

(2000) for models that do so based on employees’ lack of diversification), but the model is consistent

with this practice. We interpret V ∗ as the level of firm value at which the employee chooses to

exercise. In the real-world with early exercise, if the actual value at the end of a period before

maturity falls below V ∗, it does not mean that the option actually expires out of the money. Rather,

it means that the option remains alive, to be potentially exercised in subsequent periods. We now

turn to the construction of our stock selection rule to delineate exactly how we deal with these

issues.

3 Data and the Stock-Selection Procedure

3.1 Estimating the Costs of Option Exercises

Our stock selections are based on employee option information from Standard and Poor’s Execu-

Comp, combined with market data from CRSP. ExecuComp reports key information about option

subsequent stock returns, but this is most plausibly explained as reflecting employees’ informational advantages anddoes not address the question of semi-strong-form market efficiency.

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grants to executives for the S&P 1500 firms (including the S&P 500, the S&P Midcap, and the

S&P Smallcap) starting in 1992. The database covers at most five executives, but also reports the

percentage of total option grants in a given year represented by a given executive option grant.12

ExecuComp also provides summary information on options granted before 1992, but only for the

top five executives. We have no data on the scale of grants to all employees before that date.

For the grant data starting in 1992, we assume that other employees have options with the same

exercise price as the executives, which amounts to assuming that they receive their grants at the

same time. For most firms in our sample, this is sufficient. However, nearly 35% of the firms in our

sample made multiple grants to the CEO and/or to other executives. We assume that employees

receive grants in the same proportion as the CEO. That is, the CEO’s grant is assumed to be a

scale replica of the total option grant at his/her firm.

Our trading rule also requires an estimate of when employees exercise their options, and the

associated costs to shareholders. Huddart and Lang (1996) and Heath, Huddart, and Lang (1999)

both document spikes in employee exercises at options vesting dates if they are in the money. We

make our stock selections at the beginning of each year and can only use information at that time.

Proposition 1 tells us that the expected negative abnormal return is just equal to the unrecognized

cost of the options, scaled by the current market capitalization of the firm’s equity. To estimate

the unrecognized cost we use the Black-Scholes-Merton value less the intrinsic value of the options

at the end of the fiscal year. Since our selections are made for a given year, we also assume a

maturity of one year in computing our Black-Scholes values. Obviously, more frequent selections

would increase the power of our tests, but the underlying option data is only annual. Below, we

describe two ways in which we can at least use stock price information to update our option cost

estimates more frequently than once per year.

Our primary rule for computing option costs is computed as follows. In 1992, we take the

number, n1992, and exercise price of options granted, X1992, for each firm, and then look forward

to the end of fiscal-year 1995. At this point we estimate the volatility for each firm’s stock returns

using the previous five years of monthly data. We compute the intrinsic value version of the dollar

option cost as the maximum of zero and the difference between the stock price at the end of the

firm’s fiscal 1995 and the exercise price. This number, scaled by market capitalization, is 1992’s

contribution to diluted earnings per share computed according to SFAS 128 (see Core, Guay, and

Kothari (2000)). Our forecast of the unrecognized dollar cost of options that will be realized in

1996 computes the Black-Scholes value of options granted in 1992, valued at the end of 1995, and

12Thanks to Wayne Guay for alerting us to the presence of this data item.

9

assumes a one-year maturity. More formally, for each firm we compute

U1996 =n1992 (C(P1995, X1992, d,σ, T = 1)− L×max[0, PFiscal1995 −X1992])

MCap1995, (3)

where C() is the Black-Scholes-Merton formula adapted for the payment of continuous dividends,

P1995 is the stock price at the end of fiscal-year 1995, d is the dividend yield averaged over the

previous five years, σ is the estimated volatility, and T = 1 is the assumed time to exercise (one

year). The next term is the intrinsic option cost at the end of 1995 and MCap1995 is the market

capitalization at the end of fiscal 1995. Finally, the indicator variable L takes on the value of one

if the firm had positive earnings for the year and zero otherwise. The reason is that SFAS 128 does

not allow the firm to use option dilution to reduce losses per share. We call our resulting measure

the unrecognized option cost to remind the reader that we are focusing on that part of option cost

that is not already recognized in diluted earnings per share. Our research question is whether they

are also unrecognized in market prices.

Our procedure is similar for subsequent years; we use options granted in 1993 to form our

portfolios for 1997, and so forth. The difference as we move beyond 1992 is that we also track

whether options granted in 1992 did in fact come into the money in 1996. If the maximum stock

price in 1996 did not exceed the exercise price of options granted in 1992, we use these options as

well as those granted in 1993 to compute our option cost at the end of 1996 for our portfolio choices

for the year 1997. Formally, at the end of fiscal 1996 we save the maximum stock price during the

fiscal year, PMax1996 , and the associated indicator variable:

I1992 =

1 if PMax1996 < X1992

0 otherwise.

We then compute the unrecognized 1997 stock option cost as

U1997 =

n1993 (C(P1996,X1993, d,σ, T = 1)− L×max[0, PFiscal1996 −X1993])+I1992n1992 (C(P1996,X1992, d,σ, T = 1)− L×max[0, PFiscal1996 −X1992])

MCap1995

. (4)

If again the 1992 options do not fall in the money, we retain them for the following year. We do

not exogenously drop any options unless their maturity is exceeded, which is a rare event in our

sample given the 9-year window and the fact that most options have a 10-year maturity.

The above procedure embodies an assumption that options vest by the beginning of the fourth

year after they were granted, and that employees exercise such options in the first year they are

vested and in the money. Both assumptions are only a rough approximation of reality. Some options

10

are vested in three years and many vest 25% per year in each of the first four years. Our portfolio

choices are not overly sensitive to the precise assumptions we make about vesting and exercise. In

the next section, we show that our estimates are also strongly related to actual (realized) option

exercises, and that the relationship is somewhat weaker if we instead assume that employees are

able to exercise one fourth of their grants in each of the four years following the grant.

In an ideal world, we would update our option cost measures more frequently than once a year.

While our procedure makes full use of the annual report and proxy statement data summarized

in ExecuComp, it does not fully exploit all available information within a given year. Specifically,

stock price changes are available throughout the year. We construct two supplementary measures

in an attempt to update our option cost figures on a monthly basis. First, for each of the months of

February through December for the years 1996 to 2000, we simply recompute our estimate of the

unrecognized option costs at the beginning of each month, taking account of the change in price

over the previous month and of the fact that the end of the year is one month closer. Thus, for

example, for February 1996 we have

UFeb1996 =n1992

³C(PJan1996,X1992, d,σ, T =

1112

´− L×max[0, PFiscal1995 −X1992])

MCap1996. (5)

This is sensible, but still makes the assumption that options are exercised only at the end of

the year. While we do not have intra-year data on all stock option exercises, we can estimate the

amount of option exercise if we take our model to its logical extreme. Specifically, we can assume

that any negative abnormal stock performance is due to option exercise, and then take out this

fraction of option cost from our forward-looking measure. Thus, if the previous month’s abnormal

return was positive, we use the value in (5). If the previous month’s abnormal return was negative,

we set the next month’s unrecognized option cost equal to (5) plus the abnormal return, or zero

if the abnormal return exceeded the unrecognized option cost in absolute value. We refer to this

last measure of option costs as “updated and trimmed”. As we detail in the main section of the

paper, neither of these two alternative approaches materially affects our results.

3.2 Descriptive statistics and calculation of abnormal returns

Table 1A summarizes the raw data for the years 1996 to 2000. The first thing to note is that

our sample size is smaller than might be expected with five years of returns and the 1,500 firms

covered by ExecuComp. The main reason is that we must match firms’ option grants with their

stock return data four and more years later. To give some idea of the resulting sample selection,

Table 1B summarizes key data for the overall 1992 to 2000 ExecuComp sample. Not surprisingly,

11

we tend to oversample large firms, and to undersample those firms for whom employee options are

large relative to total shareholder wealth.

The option cost values in Table 1A are approximately one-third of those reported in Core and

Guay’s (2001) study of employee stock options for a similar sample. The reason is that Core and

Guay (2001) characterize the entire portfolio of options held by employees, and thus adds non-

vested options. We focus attention on options that are at least four years old, where the options

that are older than four years had not previously come into the money.

Our estimates of volatility, beta, and other factor exposures use monthly returns data for our

sample period, covering the years 1996-2000. Our sample period is constrained by the fact that

option grant data is not electronically available before 1992 and we assume that options don’t

vest until three years later. Observe that it would still be possible to use historical stock return

information to estimate factor sensitivities. For example, we could use data from well before 1996

to estimate exposures in 1996. However, it is well-known (see, for example, Murphy (1999)) that

stock option grants have become increasingly important over time. Employee stock options give

workers a claim on equity value that is more valuable as the value of the underlying equity increases.

Thus, the shareholders’ claim is more sensitive to market-wide factors in “down”-markets (when

employees are unlikely to share in firm value) than in “up”-markets. The consequence is that if

we were for example to use betas estimated over 1991 to 1995 for our returns in 1996, we would

tend to systematically overstate the betas for firms that made heavy use of options because 1996

was an “up” market year. This would in turn lead us to falsely conclude that heavy option users

underperform in “up” markets and outperform in “down” markets.

To counter this problem, we estimate our factor exposures and abnormal returns using con-

temporaneous data to capture the risk-effects of stock options. The beta estimates in Tables 1A

and 1B come from a regression of firm-specific monthly returns minus the T-bill return on the

value-weighted CRSP index returns less the T-bill return from January 1996 through December

2000, allowing the sensitivity to differ for each firm. Thus, we estimate

rjt − rft = k + βj (rmt − rft) + εCAPMjt , (6)

where εCAPMjt is the CAPM abnormal return for firm j in month t.

We estimate exposures to the Fama-French size and market-book factors along with Fama-

French abnormal returns in a similar manner. That is,

rjt − rft = k + βj (rmt − rft) + γjSMBt + δjHMLt + εFFjt , (7)

12

where SMBt is the Fama-French small firm premium and HMLt is the high book-to-market pre-

mium, respectively, for month t. With this approach to estimating factor sensitivities, we find that

there is no longer any relationship between our estimated abnormal performance εjt and the market

premium.

Table 2 presents some of the key correlations in our database using annual data. The first

and most important result is that all measures of stock returns (raw, CAPM adjusted (εCAPM),

and Fama-French adjusted (εFF )) are negatively and significantly correlated with our unrecognized

option cost measure (UnOpCostMCap ). There is no such relationship with the intrinsic value portion of

the option’s cost that is reflected in diluted earnings per share (FASBCostMCap ). There are two potential

reasons why the intrinsic value portion has no relationship to subsequent stock returns. The first is

that investors do correctly account for this portion of option cost, arguably because it is reflected

in diluted earnings per share. The second is that investors do not correctly account for even the

intrinsic value portion, but the negative subsequent returns of such overpricing are obscured by

the fact that intrinsic value of 4-year old stock option grants is strongly positively related to past

stock returns and the resulting momentum effect documented by Jegadeesh and Titman (1993).

Our unrecognized option cost measure has no relationship to momentum and is in fact maximized

(all else equal) when the stock price has been unchanged in the preceding four years.

The other correlations are unsurprising. High option-dilution firms tend to be smaller and

have a positive exposure to the Fama-French small firm premium. They also tend to have higher

betas and higher stock return volatility. The latter effect obtains not only because high-volatility

firms tend to grant more options, but also because high volatility increases the unrecognized cost

component of the stock option’s value. While raw volatility is not a theoretically reasonable risk

factor for widely traded firms, all the results below hold after controlling for its effects in addition

to the more widely accepted Fama-French factors. Similarly, all our results also hold if we use

dummy variables to remove the effects of 2 or 3-digit SIC industry codes.

3.3 Actual versus predicted option exercise

Our stock selection approach has two separate requirements to be successful. The first is that

the market does not in fact recognize what we term “unrecognized” option dilution until it is

realized. The second is that we can adequately predict such dilution using public information and

existing research. Table 3 provides some evidence on the latter requirement using hand-collected

option exercise data on a subset of our firms for the years 1997 to 1999, kindly provided to us by

13

Stuart Gillan. In the first column of results in Panel A, we ask how well our rule predicts the raw

number of options exercised, and in the second column we scale actual and predicted exercises by

shares outstanding at the beginning of the year. We do not have data on the actual price received

by employees when they exercised and so cannot check how well we predicted the total cost of

exercises. Our predicted number of options exercised is equal to the number of options that we

deem exercisable (at least four years past grant date and not previously in the money if more than

four years past grant date), times the hedge ratio from the option pricing formula in equations (3)

or (4). This automatically adjusts for both volatility and the extent to which options begin the

year in the money.

The results are encouraging. Just under 40% of the variability in actual option exercises can

be predicted from our estimates alone. Moreover, we can (i) reject the hypothesis that predicted

option exercise is unrelated to actual exercise at better than the 1% level and (ii) cannot reject

the hypothesis that actual option exercise increases one-for-one with predicted exercise at even the

10% level. We did not have strong theoretical priors for our size variable and regard it primarily

as a control. The final explanatory variable is the realized stock returns over the year. At first

blush it might appear that if our theory of unrecognized option costs is correct, there should be

a negative relationship between actual exercises (and consequent dilution of existing shareholders)

and stock returns. As indicated in the theoretical section, we expected a positive rather than a

negative relationship. Our forecast of option cost is formed at the beginning of the year, while

employees can condition their exercise decisions on the actual path of the stock price during the

year. A run-up in the stock price also makes employee exercise more likely since it reduces the

value of waiting to exercise the option. It also increases the value of exercising and selling in order

to diversify their portfolios (see Meulbroek (2001)).

Panel B of Table 3 repeats the analysis assuming instead that one-fourth of each grant is vested

in each of the four years following the grant. We adopt the same rule of carrying over vested options

into subsequent years if they do not come into the money in the year in question. The results are

similar although the predictive power is somewhat less. The return effect is somewhat weaker,

perhaps because as documented by Ittner et al (2002), there is a positive relationship between

recent option grants and returns.

We now turn to the empirical performance of our trading strategy using a portfolio approach,

as well as a firm-specific analysis.

14

3.4 Zero-Investment Portfolios

The first test of the performance of the stock-selection rule separates firms into deciles based on

our estimate of each firm’s unrecognized option cost. We compute the return from taking a long

position in the decile of highest-dilution firms and an offsetting short position in the decile of firms

with the lowest such costs. The first and third columns of results in Table 4 indicate that if we take

equal-weighted portfolios, this strategy would result in a negative return of just over 1.2 percent

per month after controlling for market, size, and market-to-book factors. Moreover, the second

and fourth columns show that the effects roughly double if we use value-weighted portfolios. Both

results are significant at the 5% level with only 60 observations; we compute robust standard errors

allowing for both heteroskedasticity and correlated errors between years because the option cost

information that we use to form the portfolios is annual. Not surprisingly, the high-option cost

firms have a higher market exposure (owing primarily to their higher raw volatility) and tend to

load positively on the small firm factor and negatively on the high book-to-market factor.

While we use monthly returns for the results presented in Table 4, the portfolio selections use

our basic measure of unrecognized option costs from (3) or (4). We therefore select the same firms

each month within a given year, which has the benefit of avoiding any hidden transaction costs,

but may mask potentially useful information. However, our results are almost identical if we use

either of the monthly-updating methods described in Section 3. The reason is that the intramonth

changes are not generally large enough to generate large swings in the firms’ rankings

The reason for analyzing portfolios rather than individual stocks is to reduce noise in the

estimation of factor exposures and abnormal returns. In the current application, however, there

is also a significant loss of information from grouping stocks according to their unrecognized stock

option costs. Much of the potential information about the effects of unrecognized option costs is

contained within the highest decile where unrecognized costs range from a high of just under 11%

of market capitalization to just over 1%. Put another way, our measure of unrecognized option

costs is less than 1% once we enter the second decile. One way to respond is to replace the lowest

decile returns in the preceding section with returns to a portfolio consisting of all stocks not in the

highest decile. While the results are qualitatively similar to those reported in Table 4, we still lose

the information contained within the highest option decile. To exploit the full range of our option

cost measure, we now analyze firm-level data using the method of Fama and MacBeth (1973).

15

3.5 Stock-Specific Results

We begin with firm—specific abnormal returns, estimated according to equations (6) or (7) depending

on whether we use CAPM or Fama-French abnormal returns, respectively. For the case of the

Fama-French abnormal returns, we estimate 60 cross-sectional regressions, one for each month, as

εFFjt = kt + ωtUnrecOpCostjt + φjt, (8)

where t ∈ [1, 60] represents a given month from January 1996 through December 2000. The first

row of results in Table 5 reports the mean and standard error for the coefficient estimates ωt. The

mean is negative and statistically different from zero at the 1% level using Fama-French abnormal

returns, at 5% using CAPM abnormal returns, and continues to be significantly different from zero

at the 10% level even if we use raw returns.

The last two columns of the first row use the two alternative monthly-updated measures of

unrecognized option cost with Fama-French abnormal returns. The first updates the Black-Scholes-

Merton option values to reflect changes in the stock price and time to exercise (“updated”), and

the second also assumes that the prior month’s abnormal returns were all due to option exercise

(“updated and trimmed”). The results are virtually identical to those with the simple estimate

of option cost that is the same for all months in a given year. One reason the results do not

improve despite using more information is that we are now effectively betting against the short-run

momentum documented by Jegadeesh and Titman (1993). If returns early in the year are negative,

both our updating rules imply a reduction in unrecognized option cost and thus a reduction in future

underperformance. If early returns are positive, the increased option cost will further increase and

we will therefore predict greater underperformance.

The results thus far consistently support the hypothesis that the unrecognized option cost

is associated with subsequent underperformance. The second row of results in Table 5 tests a

stronger-form hypothesis. Since our unrecognized option costs are computed as a fraction of total

firm value, abnormal stock returns should be reduced one-for-one with higher option cost. While

this may appear to be a precise and powerful prediction, our ability to test it is hampered by the

fact that our option data are available on an annual basis only and we are only able to predict that

one-for-one underperformance will take place over the course of a given year. The second row of

results reported in Table 5 cumulates abnormal returns for each year and then re-estimates equation

(8) on an annual basis. The average of the resulting annual coefficients is strongly negative, but

the associated t-tests have only four degrees of freedom. We are unable to reject the hypothesis

that the average coefficient is equal to negative one in any specification, but we are also unable to

16

reject the hypothesis that it is zero in all but one specification.

4 Tests of Limited Investor Attention

4.1 Effects of Earnings Persistence

As indicated earlier, Hirshleifer and Teoh (2002) explicitly model the source of the mispricing

that is the basis of our tests. Their Proposition 5 outlines two distinct predictions of how limited

investor attention should affect stock returns when employee stock option costs are not expensed.

The first prediction is essentially the same as our Proposition 1 and receives empirical support

from the results in the previous section. Their second prediction is that the mispricing due to

employee stock options should be greater for firms in which earnings shocks are more persistent.

The intuition is that investors with limited attention extrapolate future performance from recent

earnings reports, neglecting any potential dilution owing to options. Since the employees as holders

of the stock options share in future value increases, the effect on misvaluation from (unrecognized)

stock options is greater in firms where current earnings shocks have a larger effect on future cash-

flows (i.e., where earnings persistence is higher).

Hirshleifer and Teoh’s (2002) persistence hypothesis implies that the estimated effects in the

previous section should be amplified for firms where earnings shocks have more persistent effects.

The large accounting literature on the subject of earnings persistence guides our empirical approach

in two major ways (see, for example, Freeman, et al (1982)). First, it is important to recognize

that earnings tend to grow over time so that earnings levels are not stationary. We therefore

focus on departures from average earnings growth for each of our sample firms, and also follow

the literature by scaling earnings by lagged assets. Second, there is a tendency for earnings to

mean-revert so the average firm should have negative persistence. This is not a problem for the

Hirshleifer and Teoh (2002) prediction which focuses our attention on cross-sectional variation in

the degree of earnings persistence. Formally, for each firm j, we estimate earnings persistence (bpj)for our firm-year starting in 1996 as:

Earnjt −Earnjt−1Assetjt−1

= baj1996 + bpj1996Earnjt−1 −Earnjt−2Assetjt−2

, t ∈ [1986, 1996].

Thus, we use a rolling 10-year window of earnings changes for each firm-year. Consequently, we

exclude all firms that do not have an earnings history back to at least 1986, but the results reported

below are qualitatively unchanged if we instead estimate earnings persistence by industry at the

two-digit SIC code level, or if we use operating cash-flow in place of earnings.

17

The last row of Table 1A reports summary statistics for our estimates of earnings persistence.

Consistent with the existing literature, the means and medians are negative, but more importantly

for our tests, there is significant dispersion. The last row of Table 2 shows that earnings persistence

has little correlation with any of our other control variables, except for some tendency for larger

firms to have greater persistence.

To test the prediction that option dilution will have a greater effect on returns for firms with

more persistent earnings, we repeat our tests from the previous section, distinguishing between

firms according to their level of earnings persistence. The first columns of Tables 6A and 6B begin

by estimating the underperformance of firms (relative to a CAPM and Fama-French benchmark,

respectively) in the top decile of option costs, and confirms that it is statistically significant in

all specifications. The second and fourth columns of Tables 6A and 6B analyze the difference

between returns on a portfolio of high-option cost firms with above-median earnings persistence

and a portfolio of high-option cost firms with below-median earnings persistence. The intercepts of

these regressions represent the expected additional underperformance due to earnings persistence,

after controlling for market and Fama-French factors. In all cases, the point estimates are negative

as predicted by Hirshleifer and Teoh (2002). But in no case are the estimates statistically different

from zero. The results are qualitatively similar if we use more extreme quantiles of persistence.

However, it is important to recognize that while the results are statistically insignificant, the

point estimates are economically nontrivial. An annualized monthly negative return of -0.017

(the average underperformance of the high-dilution subsample using value-weighted returns and

controlling for Fama-French factors) translates into about -18.7% annually. Our point estimate of

the difference between the high and the low persistence subsamples implies that the returns fall to

-24.5% for the high-persistence subsample.

Table 7 summarizes the results from estimating monthly cross-sectional regressions of returns

on option costs for firms with differing degrees of earnings persistence. Hirshleifer and Teoh’s (2002)

model predicts that option costs should have stronger negative effects for firms with high levels of

earnings persistence. Table 7 documents that the effect is indeed largest for firms in the top decile

of earnings persistence, but consistent with the portfolio results in Tables 6A and 6B, the effects

are not statistically significant. Specifically, the average coefficient on option cost for firms in the

highest decile of earnings persistence is not statistically distinguishable from that for firms in lower

deciles of persistence.

One explanation for our results is that earnings persistence does not in fact have any systematic

effect on mispricing. An alternative is simply that our tests do not have sufficient power to reject

18

the null hypothesis of no effect. First, in the Fama-Macbeth regressions in Table 7, the coefficient

estimates for the top and bottom decile of earnings persistence are highly variable in part because

of the relatively small number of observations (just over 50 in an average month). Second, and more

importantly, the key earnings persistence variable is surely measured with significant error. Our

results continue to hold if we remove outliers in earnings growth or if we group data by industry

code, but it remains an open question to what extent our weak results reflect errors in estimating

the key earnings persistence variable.

4.2 When does the market learn about option exercises?

Hirshleifer and Teoh’s (2002) model focuses on limited investor attention as the source of misval-

uation. Our trading rule effectively assumes that investors eventually pay attention to employee

stock options when they are exercised and the firm must issue the shares. Table 3 indicates that

our approach is successful in predicting the year in which options are exercised. In this section,

we pursue further the question of when investors learn about such exercises. Observe that the

estimates in Table 3 use information about option exercises which are available only from proxy

statements issued at the end of the firm’s fiscal year. But while quarterly income statements and

balance sheets do not separately detail option exercises, they do in fact adequately summarize their

value effects. They report the current number of shares outstanding and associated EPS values,

and the updated book equity values summarize the net effect of any cash paid into the company

from option exercises less cash paid out to repurchase shares. Thus, if Hirshleifer and Teoh (2002)

are correct that investors tend to focus on earnings and related numbers, and tend to neglect stock

option information from footnotes and related sources, we should expect to find stronger results in

months where quarterly reports are released.

Unlike earnings persistence, there is no error in identifying quarterly earnings months. However,

the data are still less than ideal because just over 70% of our sample firms have a December fiscal

year. While we have quarterly reporting in every month of the year for some firms in our sample,

there is a strong clustering of reports in March, June, September, and December. However, our

market and Fama-French factors should control for any market-wide monthly return regularities.

Table 8A estimates the effect of reporting months in the highest decile of expected option cost.

The dependent variable in each of the regressions is the difference in returns for a portfolio of firms

that have a quarterly earnings report and a portfolio of those firms that do not. The negative and

generally significant intercepts indicate that our annual option cost measures have their strongest

19

effects in months where investors receive quarterly reports. This finding lends support to our idea

that investors move prices once they recognize the effect of the options.

Recall that the average monthly underperformance of the high-option cost firms is given by the

intercept terms in the odd-numbered regressions in Tables 6A and 6B, and ranges from approxi-

mately -1.3% to -2.4%. Our point estimates in Table 8A of approximately -0.7% for the difference

in returns between a portfolio of firms with and without quarterly reports indicate that the such

reports approximately double the negative effect of option costs. This is consistent with some

investors gleaning information about option exercises from sources other than quarterly reports,

but a large fraction of investors reacting only when the information is summarized in earnings per

share.

As noted above, firms’ quarterly reports tend to cluster in the months of March, June, Septem-

ber, and December, and there is some tendency for such firms to be larger and to have smaller

option cost levels. To exploit the full range of option cost data, Table 8B summarizes cross-sectional

monthly regressions of abnormal returns on option cost, distinguishing between firms that issue and

those that do not issue quarterly reports in the given month. The results are consistent with the

portfolio results in Table 8B. The negative effect of option costs is substantially larger in months

where there are quarterly earnings reports. In the case of Fama-French abnormal returns, the

difference is statistically significant at the 10% level.

5 Additional Evidence

5.1 The Effect of Changes in Accounting Standards

Most of the current debate about accounting for stock options centers on the question of whether

and how they should be expensed (see Aboody, et al (2001), Morgensen (2002), and Byrnes (2002)).

We cannot test for the effects of accounting regulations regarding the expensing of stock options for

the simple reason that there were no major changes in regulation during our sample period. The

most recent such change was in SFAS 123 which required the disclosure of the exact items that we

use to construct our option cost measures. Before 1992, the necessary information was not public

nor was it covered electronically in the ExecuComp database.

Our model and our empirical tests do, however, take account of SFAS 128 and its effect on

diluted earnings per share. We can test for this decision’s effect on the pricing of stock option

liabilities because it applied only to companies whose fiscal year ended after December 1997. We

begin by reintroducing our variable of intrinsic option cost from equations (3) and (4) as a separate

20

regressor to test whether the market accurately takes account of this more tangible portion of

option cost. We then create a dummy variable, denoted the FASB Dummy, indicating that SFAS

128 was in effect, setting it equal to one for all fiscal years beginning in January 1998 and zero

otherwise.

The regressions in Table 9 pool all the observations together and include controls for the Fama-

French factors allowing for firm-specific coefficients as in equation (7). To more fully ensure that

features such as firm size do not drive the results, we also include direct measures of size and

book-to-market values. The first column of results in Table 9 estimates the specification:

rjt − rft = k + ω × UnrecOpCostjt + θ × FASBOptionCostjt + η1Mcapjt

+η2BookMcap jt

+ βj (rmt − rft) + γjSMBt + δjHMLt + ϕjt

, (9)

where the subscript t now refers to the years 1996 to 2000. Since the data is a pooled, cross-sectional

time series, we estimate standard errors allowing for both heteroskedasticity and the possibility that

errors are correlated within any given year. Consistent with the results presented in the previous

section, the unrecognized option cost has a negative effect on abnormal returns that is different

from zero at the 1% level. While the point estimate is less than negative one, it is not statistically

different from negative one at the 10% level. There is no evidence that the market underestimates

the intrinsic value portion of option cost; indeed, our estimate of the coefficient θ is greater than

zero at the 5% confidence level although it is less than one-third of the effect of the unrecognized

option cost in absolute value.

The next two columns of Table 9 test whether SFAS 128 had any effect on either of the above

results. The second column shows that while there is some evidence that the market took greater

account of the intrinsic value portion of option cost after SFAS 128 became effective, it seemed also

to do so before the statement became effective. The third column allows for the possibility that

the attention drawn to stock options by SFAS 128 also caused the market to take account of the

unrecognized part of option costs. We find no statistical evidence that this is the case.

Our inability to identify any systematic effect of the application of SFAS 128 does not show

that the accounting treatment of options is irrelevant. First, and most obviously, we could not

have conducted this study without the disclosure requirements contained in the earlier decision on

the expensing of earnings, SFAS 123. Second, the tests in Table 9 are essentially an event-study

focusing on the date where SFAS 128 was actually in effect. As with most significant accounting

decisions, the issues had been exposed and debated for some time before the issuance of the final

statement. Thus, the statement was by no means a surprise and the relevant issues had already

21

been publicly disclosed and heavily debated. A related process may be in effect with the current

debate about expensing employee stock options, which has been ongoing since the issuance of SFAS

123. If this publicity and debate had led to a greater awareness of the true costs of employee stock

options, we might expect our method for selecting overvalued stocks to become less powerful over

time. We cannot locate any systematic evidence of this in our data, however. For example, while

it is true that the monthly coefficients used for the Fama-Macbeth analysis of Table 5 are smaller

in absolute value in 2000 than they are in 1996, there is no statistically significant time-trend and

in fact the smallest absolute effects are found in 1999, and not in 2000.

5.2 Robustness Checks

In this final subsection, we assess the robustness of our results to omitted variables and to the

presence of outliers. While our tests control for market, size, and book-to-market factors, it is

still possible that we are picking up some version of some other factor. Despite appearances, it

is not possible for either short-term momentum (Jegadeesh and Titman (1993)) or longer-term

reversals (DeBondt and Thaler (1987)) to drive our results. The reason is that all else equal, our

unrecognized option cost is greatest for firms that have had essentially flat stock prices over the

prior 4 years, because the time component of the option’s value is maximized when the option is

just at the money. Empirically, there is no statistically significant relationship between our dilution

numbers and historical six-month, twelve-month, or five-year stock performance. Nonetheless, there

remains a long list of potential alternative explanations, especially given the fact that our option

costs are higher for small growth firms and our tests only use the last years of the 20th century.

Moreover, our estimates of the option cost are directly related to estimates of dividend yield and

volatility.

To control for the widest possible set of alternative reasons for our results, the first column of

results in Table 10 control for firm fixed effects as well as our other controls. In effect, we allow

each firm to have its own alpha (kj) and restrict option costs to explaining intertemporal variations

in abnormal returns by estimating:

rjt − rft = kj + ω × UnrecOpCostjt + θ × FASBOpCostjt + η1Mcapjt

+η2BookMcap jt

+ βj (rmt − rft) + γjSMBt + δjHMLt + ϕjt

.The conclusion that unrecognized option costs are in fact unrecognized by the market until they

materialize is actually strengthened by controlling for firm fixed effects, and as the third column

shows, the conclusion continues to hold if we omit the Fama-French controls.

22

The remaining results in Table 10 address the concern that outliers in either stock returns or

option costs could be driving our results by estimating median regressions, which minimize the sum

of absolute errors rather than squared errors. Again, our key results are unaffected.

6 Concluding Remarks

One common explanation for the popularity of employee stock options as a compensation tool

is their “favorable” accounting treatment, in that the accounting costs tend to understate the

true economic costs. Such considerations should of course be irrelevant to a manager interested

in maximizing firm value in a setting where market participants can see through the accounting

treatment. Our results suggest that the stock market tends to undervalue the costs of employee

stock options until such costs are realized. The aggressive use of employee stock options may

thus represent a transfer of wealth from long-term to short-term shareholders. They also suggest

that firms that have recently granted a large amount of employee stock options will tend to be

overvalued.

23

7 Appendix

7.1 Proof of Proposition 1

Observe that realized returns are given by P1−P0P0

, and expected returns are given by

E(r) =

V ∗R0

Vn dF (V ) +

∞RV ∗

V+mXn+m dF (V )− P0P0

, (10)

which is identically zero if P0 = P∗0 . Since the required return in the modelled economy is zero,

expected returns equal abnormal returns. If P0 = PAcc0 , there are two cases to consider. Consider

first the case where the options begin out of the money, so that PAcc0 =∞R0

Vn dF (V ). In this case,

expected returns can be written as

E(r) =

V ∗R0

Vn dF (V ) +

∞RV ∗

V+mXn+m dF (V )−

∞R0

Vn dF (V )

∞R0

Vn dF (V )

=

∞RV ∗

m(nX−V )n(n+m) dF (V )

∞R0

Vn dF (V )

=−mUV ∗−∞R0V dF (V )

=−mUV ∗−nPAcc0

. (11)

Here, U denotes the unrecognized cost of a single stock option as the difference between the value of

the option if it were optimally exercised and its current intrinsic value. Since PAcc0 =∞R0

Vn dF (V ) <

X, this can be expressed as

UV ∗− =

∞ZV ∗

V − nXn+m

dF (V )−max[0, P0 −X]

UV ∗− =

∞ZV ∗

V − nXn+m

dF (V )− 0 (12)

UV ∗− =

∞ZV ∗

V − nXn+m

dF (V )

In the second case where the options are currently in the money, PAcc0 =∞R0

V+mXn+m dF (V ) and

expected returns can be written as

E(r) =

V ∗R0

Vn dF (V ) +

∞RV ∗

V+mXn+m dF (V )−

∞R0

V+mXn+m dF (V )

∞R0

V+mXn+m dF (V )

=

V ∗R0

m(V−nX)n(n+m) dF (V )

∞R0

V+mXn+m dF (V )

. (13)

24

When the option begins in the money, and thus PAcc0 =∞R0

V+mXn+m dF (V ) > X, we can write the

unrecognized cost of a single stock option as the difference between the value of the option if it

were optimally exercised and its current intrinsic value. We denote this value as U as estimate it

as

UV ∗+ =

∞ZV ∗

V − nXn+m

dF (V )−max [0, P0 −X]

UV ∗+ =

∞ZV ∗

V − nXn+m

dF (V )− ∞Z0

V +mX

n+mdF (V )−X

UV ∗+ =

∞ZV ∗

V − nXn+m

dF (V )−∞Z0

V − nXn+m

dF (V )

UV ∗+ = −V ∗Z0

V − nXn+m

dF (V ). (14)

We can therefore express the expected return as

V ∗R0

m(V−nX)n(n+m) dF (V )

∞R0

V+mXn+m dF (V )

=−mn UV ∗+

∞R0

V+mXn+m dF (V )

=−mUV ∗+

∞R0nV+mXn+m dF (V )

=−mUV ∗+nPAcc0

, (15)

where PAcc0 =∞R0

V+mXn+m dF (V ). QED

25

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28. Murphy, K. J., 1999, “Executive Compensation”, in Handbook of Labor Economics, OrleyAshenfelter and David Card, eds, North-Holland, v. III.

29. Rappaport, A., 1999, “New thinking on how to link executive pay with performance”, HarvardBusiness Review, March-April, 91-101.

30. Seyhun, H. N., 1998, Investment Intelligence from Insider Trading, MIT Press.

31. Standard and Poor’s, 2002, “Fact Sheet-Measures of Corporate Earnings for Equity Analysts”,May.

32. Yermack, D., 1997, “Good timing: CEO stock option awards and company news announce-ments”, Journal of Finance 52, 449-76.

33. Zellner, A., 1962, “An efficient method of estimating seemingly unrelated regressions andtests of aggregation bias”, Journal of the American Statistical Society, 57, 348-68.

27

Table 1A: Summary Statistics for Full Sample 1996-2000

The following table contains summary statistics for our key variables across the years 1996-2000 for ourestimation sample. Shares outstanding and the market capitalization of each firm’s equity are calculated atthe beginning of each firm’s fiscal year. The Number of 4-year old Options as a % of Shares Outstandingis simply the ratio of the total number of options granted in year t− 4 to the number of shares outstandingat the beginning of year t ∈ {1996, ..., 2000}. The intrinsic value of 4-year old options is calculated at thebeginning of each firm’s fiscal year and given by the maximum of zero and the difference between the stockprice at the beginning of the firm’s fiscal t and the exercise price. This value, scaled by market capitalization,is 1992’s contribution to diluted earnings per share computed according to SFAS 128, and denoted below asIntrinsic Value of 4-year old Options as a % of Market Capitalization. Unrecognized Options Cost as a %of Market Capitalization is the difference between the Black-Scholes value of options granted in year t− 4(valued at the beginning of year t, assuming a one year maturity) and the intrinsic value of the options at thebeginning of year t, scaled by the firm’s market capitalization. Raw Annual Return is the firm’s percentagereturn over the year t. The volatility for each firm’s stock returns is estimated using the previous five yearsof monthly data. The betas are estimated from an OLS regression of raw returns on the raw returns of theCRSP value-weighted index return over 1996 to 2000. Earnings Persistence is estimated by regressing thechange in earnings over year t scaled by firm assets on the change in earnings over year t−1 scaled by laggedassets. There are 4,462 observations in this sample.

Variable Mean Median SD Min Max

Shares Outstanding (million) 149 53.7 317 2.98 5,160

Number of 4-year old Options

as a % of Shares Outstanding1.50 0.921 1.69 0 14.6

Market Capitalization ($ billion) 7.16 1.51 25.6 0.0365 651

Intrinsic Value of 4-year old Options

as a % of Market Capitalization0.847 0.068 1.34 0 11.8

Unrecognized Options Cost

as a % of Market Capitalization0.285 0.041 0.981 0 10.8

Raw Annual Return (%) 17.8 9.53 72.6 -97.7 2,619

Volatility

(annualized % standard deviation of returns)32.9 29.3 14.5 8.33 243

Beta 1.06 0.987 0.533 -1.32 4.05

Earnings Persistence -0.191 -0.135 0.298 -1.29 0.757

28

Table 1B: Summary Statistics for ExecuComp Firms WithAt Least Two Years of Coverage 1992-2000

The following table contains summary statistics for our key variables across the years 1992-2000 for thefull sample. The Number of 4-year old Options as a % of Shares Outstanding is simply the ratio of thetotal number of options granted in year t− 4 to the number of shares outstanding at the beginning of yeart ∈ {1996, ..., 2000}. The market capitalization of each firm’s equity are calculated at the beginning ofeach firm’s fiscal year. The Raw Annual Return is the firm’s percentage return over the year t. The betasare estimated from an OLS regression of raw returns on the raw returns of the CRSP value-weighted indexreturn over 1992 to 2000. There are 10,532 observations in this sample.

Variable Mean Median SD Min Max

Number of 4-year old Options

as a % of Shares Outstanding1.972 1.476 2.76 0 23.3

Market Capitalization ($ billion) 4.51 1.19 14.2 0.020 343

Raw Annual Return (%) 19.7 13.2 100.4 -97.2 715

Beta 1.10 1.057 0.577 -1.96 5.50

29

Table 2: Simple Correlations 1996-2000(3,580 Annual Observations)

Unrecognized Options Cost as a % of Market Capitalization (UnOpCostMCap ) is the difference between the

Black-Scholes value of options granted in year t − 4 (valued at the beginning of year t, assuming a oneyear maturity) and the intrinsic value of the options at the beginning of year t, scaled by the firm’s marketcapitalization. The intrinsic value of 4-year old options is calculated at the beginning of each firm’s fiscalyear and given by the maximum of zero and the difference between the stock price at the beginning of thefirm’s fiscal t and the exercise price. This value, scaled by market capitalization, is 1992’s contribution todiluted earnings per share computed according to SFAS 128, and denoted below as FASBCostMCap . Raw r is

the firm’s percentage return over the year t. εCAPM and εFF are the firm-specific abnormal returns usingCAPM and the three-factor Fama-French model, respectively. Mkt Prem is the market risk premium, Small

Firm is the Fama-French small firm factor, and MktBook is the market value of equity plus book values of debt

and preferred stock divided by book assets. Market capitalization of each firm’s equity are calculated atthe beginning of each firm’s fiscal year. The volatility for each firm’s stock returns is estimated using theprevious five years of monthly data. Earnings Persistence is estimated by regressing the change in earningsover year t scaled by firm assets on the change in earnings over year t− 1 scaled by lagged assets. Observethat * denotes that the correlation coefficient is significantly different from zero at the 1% level, and **denotes significance at the 5% level.

UnOpCostMCap

FASBCostMCap Raw r εCAPM εFF

Mkt

Prem

Small

Firm

MktBook MCap Volat

UnOpCostMCap 1

FASBCostMCap 0.318∗ 1

Raw r -0.062∗ 0.074∗ 1

εCAPM -0.073∗ -0.003 0.841∗ 1

εFF -0.110∗ 0.005 0.773∗ 0.933∗ 1

Mkt

Prem0.061∗ 0.051∗ 0.118∗ -1.191∗ -0.164∗ 1

Small

Firm0.075∗ 0.082∗ 0.023 0.050∗∗ 0.065∗ -0.065∗ 1

MktBook 0.007 0.006 0.029 0.193∗ 0.123∗ -0.517∗ -0.27∗ 1

MCap -0.025∗∗ -0.025∗∗ -0.045∗ -0.08∗ -0.085∗ -0.123∗ 0.038 0.024 1

Volat 0.332∗ 0.107∗ -0.11∗ 0.015 0.015 -0.036 0.005 -0.021 -0.083∗ 1

Earns

Pers.0.072 0.010 0.001 0.000 -0.001 0.001 0.002 -0.003 0.027∗∗ 0.038∗∗

30

Table 3: Actual Versus Predicted Option Exercises

The dependent variables (either raw number of options exercised or options exercised as a percentageof total shares outstanding) in each of these two panels are based on 927 firm-years with data on actualoptions exercised in years 1997 to 1999. The first panel assumes that all options vest by the beginning oftheir fourth year, while the second panel assumes that 25% of a total option grant vests each year. Predictedoption exercise equals our estimate of the number of exercisable options times the hedge ratio of the optionsassuming one year to maturity. Standard errors in parentheses are Huber-White sandwich errors, allowingfor correlated errors within years. * indicates different from zero at the 1% level and ** at the 5% level.

Panel A

VariableNumber of Options

Exercised (millions)

Options Exercised as a %

of Total Shares Outstanding

Intercept −3.500∗∗(0.293)

0.00218∗(0.000594)

Predicted Option Exercise 2.276∗(0.904)

0.797∗(0.239)

Market Capitalization 0.0792∗∗(0.0386)

0.000443∗∗(0.0000873)

Raw Returns 0.707∗(0.253)

0.00698∗(0.000364)

adj. R2 0.412 0.568

Panel B

Variable

Number of Options

Exercised (millions)

(1/4 each year vesting)

Options Exercised as a % of Total

Shares Outstanding

(1/4 each year vesting)

Intercept −0.0521(0.555)

0.000893∗(0.000290)

Predicted Option Exercise 3.642∗∗(1.58)

1.033∗(0.0351)

Market Capitalization 0.0836∗(0.0359)

0.000567∗(0.000148)

Raw Returns 0.273∗∗(0.137)

0.00496∗∗(0.00224)

adj. R2 0.364 0.513

31

Table 4: Monthly Returns for a Portfolio of Firms in the Highest Decile ofUnrecognized Option Cost Minus Returns for Firms in the Lowest Decile

The first (third) and second (fourth) columns have as dependent variables the monthly returns of aportfolio of firms in the highest decile of unrecognized option costs minus the monthly returns of a portfolioof firms in the lowest decile of unrecognized option costs, using equal-weighted and value-weighted returns,respectively. In the first two columns, the dependent variables are regressed on the market factor, whereasin the last two columns, the dependent variables are regressed on market, small firm, and market-to-bookfactors. Standard errors in parentheses are Huber-White sandwich errors, allowing for heteroskedasticityand for correlated errors within years. * indicates different from zero at the 1% level, ** at the 5% leveland *** at the 10% level.

VariableEqual-weighted

returns

Value-weighted

returns

Equal-weighted

returns

Value-weighted

returns

Intercept −0.0107∗∗(0.0054)

−0.0262∗∗(0.0114)

−0.0123∗∗(0.0049)

−0.0245∗∗(0.0105)

Market Factor 0.428∗(0.110)

0.533∗(0.236)

0.279∗∗(0.123)

0.281(0.221)

Small Firm Factor 0.511∗(0.160)

0.704∗(0.199)

Market-to-Book Factor −0.357∗∗(0.152)

−0.584∗∗(0.271)

Adjusted R2 0.0987 0.0845 0.165 0.147

Observations 60 60 60 60

32

Table 5: Fama-MacBeth Results

This table contains the time-series average of coefficients from regressing returns on unrecognized optioncost, over the months January 1996 to December 2000, after controlling for the Fama-French (FF) factors(columns I, IV, and V), the market (CAPM) factor (column II), and based on raw returns only (column III),respectively. Standard errors in parentheses. * indicates different from zero at the 1% level, ** at the 5%level and *** at the 10% level. We cannot reject the hypothesis that the estimated annual coefficients areequal to -1 at the 1%, 5% or 10% levels for any of the specifications.

Variable

Annual

dilution

(FF abnormal

returns)

Annual

dilution

(CAPM abnormal

returns)

Annual

dilution

(raw

returns)

Monthly

updated

dilution

(FF abnormal

returns)

Monthly

updated &

trimmed

dilution

(FF abnormal

returns)

Monthly

Coefficients

(n = 60)

−0.564∗(0.176)

−0.535∗∗(0.258)

−0.401∗∗∗(0.201)

−0.562∗(0.1.71)

−0.557∗(0.191)

Annual

Coefficients

(n = 5)

−4.587∗∗∗(2.149)

−3.526(2.558)

−1.113(5.890)

−3.911(2.194)

−1.768(1.331)

33

Table 6A: Monthly Returns for a Portfolio of Firms in the Highest Decile ofUnrecognized OptionCost: The Effect of Earnings Persistence (CAPM)

The first and third columns have as dependent variables the monthly returns of a portfolio of firms in thehighest decile of unrecognized option costs, using equal-weighted and value-weighted returns, respectively.The second and fourth columns use the difference between the monthly returns on a portfolio of firms in thehighest decile of unrecognized cost and above median earnings persistence, versus firms in the highest decileof unrecognized option cost and below the median in earnings persistence. Standard errors in parenthesesare Huber-White sandwich errors, allowing for heteroskedasticity and for correlated errors within years. *indicates different from zero at the 1% level, ** at the 5% level and *** at the 10% level.

VariableEqual-weighted

returns

Equal-weighted

returns,

High-low persistence

Value-weighted

returns

Value-weighted

returns,

High-low persistence

Intercept −0.0159∗(0.0058)

−0.00285(0.00533)

−0.0236∗(0.0080)

−0.00674(0.00423)

Market Factor 1.216∗(0.119)

−0.0959(0.135)

1.40∗(0.164)

−0.0305(0.223

Adjusted R2 0.624 0.001 0.421 0.006

Observations 60 60 60 60

Table 6B: Monthly Returns for a Portfolio of Firms in the Highest Decile ofUnrecognized OptionCost: The Effect of Earnings Persistence

(Fama-French)

The first and third columns have as dependent variables the monthly returns of a portfolio of firms in thehighest decile of unrecognized option costs, using equal-weighted and value-weighted returns, respectively.The second and fourth columns use the difference between the monthly returns on a portfolio of firms inthe highest decile of unrecognized cost and above median earnings persistence, versus firms in the highestdecile of unrecognized option cost and the below median earnings persistence. Standard errors in parenthesesare Huber-White sandwich errors, allowing for heteroskedasticity and for correlated errors within years. *indicates different from zero at the 1% level, ** at the 5% level and *** at the 10% level.

Variable

Equal-

weighted

returns

Equal-weighted

returns,

High-Low persistence

Value-

weighted

returns

Value-weighted

returns,

High-low persistence

Intercept −0.0127∗(0.0042)

−0.00278(0.00514)

−0.0170∗(0.006)

−0.00604(0.00418)

Market Factor 1.232∗(0.103)

0.0139(0.109)

1.168∗(0.156)

0.0687(0.173)

Small Firm Factor 0.866∗(0.130)

0.0613(0.133)

0.690∗(0.197)

0.365(0.289)

Market-to-Book Factor 0.262∗∗(0.120)

0.0575(0.199)

−0.206(0.182)

0.269(0.262)

Adjusted R2 0.8118 0.0031 0.526 0.0038

Observations 60 60 60 60

34

Table 7: Fama-MacBeth Monthly Coefficients Under Varying Levels ofEarnings Persistence

This table contains the time-series average of coefficients from regressing returns on unrecognized optioncost, over the months January 1996 to December 2000, after controlling for the Fama-French (FF) factors(column I), the market (CAPM) factor (column II), and based on raw returns only (column III), respectively.Standard errors in parentheses. * indicates different from zero at the 1% level, ** at the 5% level and *** atthe 10% level. We cannot reject the hypothesis that the estimated annual coefficients are equal to -1 at the1%, 5% or 10% levels for any of the specifications.

Variable

Annual

dilution

(FF abnormal

returns)

Annual

dilution

(CAPM abnormal

returns)

Annual

dilution

(raw

returns)

Highest Decile

of Earnings

Persistence

−1.02(0.505)

−0.707(0.586)

−0.390(0.593)

Deciles 2 - 9

of Earnings

Persistence

−0.545∗(0.187)

−0.460∗∗(0.245)

−0.361(0.284)

Lowest Decile

of Earnings

Persistence

−0.657(0.467)

−0.689(0.556)

−0.262(0.566)

35

Table 8A: Monthly Returns for a Portfolio of Firms in the Highest Decileof Unrecognized OptionCost: The Effect of Quarterly Reports

The dependent variable in each column is the difference between the monthly returns of a portfolio offirms in the highest decile of unrecognized option costs and also in a quarterly reporting month, minus thereturns of firms in the highest decile of unrecognized option costs and not in a quarterly reporting month.The first and third columns control for the market return (CAPM), whereas the second and fourth columncontrol for all three Fama-French factors. Standard errors in parentheses are Huber-White sandwich errors,allowing for heteroskedasticity and for correlated errors within years. * indicates different from zero at the1% level, ** at the 5% level and *** at the 10% level.

VariableEqual-weighted

returns

Equal-weighted

returns,

Fama-French

Value-weighted

returns

Value-weighted

returns,

Fama-French

Intercept −0.00775∗(0.00207)

−0.00758∗(0.00514)

−0.00719∗∗∗(0.00330)

−0.00495(0.00550)

Market Factor 0.0836∗(0.0298)

0.0717(0.0526)

0.214(0.205)

0.0676(0.193)

Small Firm Factor 0.0274(0.109)

0.366(0.156)

∗∗∗

Market-to-Book Factor −0.0131(0.0621)

−0.154(0.110)

Adjusted R2 0.0254 0.0215 0.0203 0.0277

Observations 60 60 60 60

Table 8B: Fama-MacBeth Monthly Coefficients in MonthsWith and Without Quarterly Earnings Reports

This table contains the time-series average of coefficients from regressing returns on unrecognized optioncost, over the months January 1996 to December 2000, after controlling for the Fama-French (FF) factors(column I), the market (CAPM) factor (column II), and based on raw returns only (column III), respectively.In the first row, only monthly firm returns are included if there is no quarterly report released in that month.The second row contains only the monthly firms returns for months in which the quarterly report is released.Standard errors in parentheses. * indicates different from zero at the 1% level, ** at the 5% level and *** atthe 10% level. + indicates that averages are different at 10%.

Variable

Annual

dilution

(FF abnormal

returns)

Annual

dilution

(CAPM abnormal

returns)

Annual

dilution

(raw

returns)

Months with quarterly report −1.34∗,+(0.512)

−1.05∗(0.573)

−0.991(0.603)

Months without quarterly report −0.327∗∗∗(0.193)

−0.358(0.267)

−0.241(0.296)

36

Table 9: The Effect of SFAS 128 Diluted Earnings Per Share

FASB is a dummy variable taking on the value one if the firm’s fiscal year fell after December 15, 1997and zero otherwise. FASB Option Cost is dilution according to SFAS 128, equal to the sum of Max[0,Fiscalyear end price-exercise price] for each option divided by market capitalization. The dependent variable in allthree specifications is each firm’s annual return. Standard errors in parentheses are Huber-White sandwicherrors, allowing for correlated errors within years. 3,580 annual observations, spanning 1996 to 2000. *indicates different from zero at the 1% level, ** at the 5% level and *** at the 10% level.

VariableDilution

measures only

SFAS 128 effects

on accounting dilution

SFAS 128 effects

on all forms of dilution

Intercept 0.0291∗(0.00707)

−0.00749(0.315)

−0.00408(0.334)

Unrecognized Option CostMCap −3.036∗

(1.290)−2.996∗(1.063)

−3.146∗(1.227)

FASB CostMCap 0.858∗∗

(0.411)0.138(0.453)

0.219(0.374)

Market Cap (MCap) −0.0016∗(0.000212)

−0.00126∗(0.000199)

−0.00111∗(0.00023)

BookMCap 0.599

(0.315)0.459(0.362)

0.523(0.297)

FASB Dummy ×Unrecognized Option CostMCap 1.087

(1.893)

FASB Dummy ×FASB CostMCap 4.588

(2.96)4.784(6.10)

FASB Dummy 0.059(0.0683)

0.0522(0.654)

Fama-French Controls yes yes yes

Adjusted R2 0.215 0.203 0.197

37

Table 10: Robustness Checks

The dependent variable in each regression is the firm’s annual return. Standard errors in parentheses areHuber-White sandwich errors, allowing for correlated errors within years. For median regression, standarderror is bootstrapped with 20 replications. 3,580 annual observations, spanning 1996 to 2000. * indicatesdifferent from zero at the 1% level, ** at the 5% level and *** at the 10% level.

VariableFirm

Fixed Effects

Median

Regression

Firm

Fixed Effects

Median

Regression

Intercept 0.0478∗(0.00904)

0.0359∗(0.00471)

0.125∗(0.0226)

0.0821∗(0.00939)

Unrecognized Option CostMCap −5.036∗

(1.986)−4.036∗(1.257)

−4.013∗(1.737)

−3.971∗(1.083)

FASB CostMCap 1.203∗∗

(0.587)0.430(0.990)

2.104∗(0.873)

1.694(1.524)

Market Cap (MCap) −0.00173∗(0.000354)

−0.000955∗(0.0026)

−0.0033∗(0.000877)

−0.000294(0.00842)

CRSP Value-Weighted Index Return 0.414(0.449)

0.0513(0.290)

0.963∗(0.319)

0.735∗(0.0842)

BookMCap 0.609

(0.464)0.523∗∗∗(0.296)

0.305∗(0.0985)

0.694∗(0.0799)

Fama-French Controls yes yes no no

Adjusted R2 (pseudo-R2 for median) 0.015 0.127 0.024 0.035

38