Stocks or Options? Moral Hazard, Firm Viability, and
the Design of Compensation Contracts
∗
Ohad Kadan
†Jeroen M. Swinkels
‡This version: March 2006
Abstract
We consider the choice between stocks and options as a means of providing effort incentives to a risk averse manager. We show that stocks dominate options as a means of motivation only if non-viability risk is substantial, as infinancially distressed firms or start-ups. Options dominate stocks for other firms. These results hold regardless of the existing portfolio of the manager. The results hold both in a static and in a dynamic setting in which the manager can partially undo incentives by savings decisions or by trading thefirm’s shares. We provide empirical evidence that higher bankruptcy risk is indeed correlated with more use of stock.
1
Introduction
Stock based compensation has steadily increased over the last decade. Typically, stock based compensation is implemented by one of two methods: granting the man-ager restricted stock, or granting her stock options. Recently, several events have spurred the debate on the optimal compensation method. In February 2004, IBM announced that it will no longer grant “at the money” stock options to its executives. Instead, the exercise price will exceed the current market price by 10%. In contrast, Microsoft announced in July 2003 that it will no longer use stock options to com-pensate its executives and will favor restricted stock instead. Thus while IBM chose ∗We are grateful to Sreedhar Bharath and Tyler Shumway for sharing with us their code for calculating the KMV-Merton expected default frequencies, and to John Graham for sharing with us his simulated marginal tax rates. We thank an anonymous referee, Kerry Back, Martin Cripps, Peter DeMarzo, Bart Hamilton, Mike Faulkender, Yaniv Grinstein, Armando Gomes, Wayne Guay, Glenn MacDonald, Todd Milbourn, Maureen O’Hara, Neal Stoughton, JeffZwiebel, seminar partic-ipants at Colorado Boulder, Michigan, Northwestern, UCSD, and Washington University, as well as participants at the FRA 2004 conference and the EFA 2005 conferences for helpful comments and suggestion.
†John M. Olin School of Business, Washington University in St. Louis, [email protected] ‡Corresponding author. John M. Olin School of Business, Washington University in St. Louis, [email protected]
to increase the strike price on its executive stock options, Microsoft decided to lower it to zero. A third relevant example is Conseco. The one time insurance giant has recently emerged from the third largest bankruptcyfiling in US history. Interestingly, in March 2004 it announced that its top executives made nearly $34 million in awards primarily from restricted stock granted while the company was under Chapter 11.
The goal of this paper is to shed light on the choice between stocks and options in compensation design. To do this, we study a principal-agent relation between risk neutral investors and a risk averse and effort averse manager.
We depart from the standard Holmstrom (1979) model in three ways. First, for much of the paper we restrict the set of contracts to include only a base salary plus a stock or a stock option. Restricting attention to this set seems realistic to us, given the contracts one actually observes. Ross (2004) takes a similar approach, and with a similar motivation, in studying the risk attitude of managers compensated by options.1
Second, we assume that there is some lower bound on how much the manager can be paid. This minimum payment constraint could arise because the manager is wealth constrained, so that payments cannot be arbitrarily negative, or for legal reasons. It seems very rare in practice for a contract to specify that the manager gives the firm money. A firm that begins from a salary package and adds incentive pay may feel constrained from lowering base salary.
Of course, incumbent managers will typically already own stock or previously granted options. So, the manger’s wealth can certainly decline when the stock price decreases. This however, in no way impacts our central point. The key to our results is thatnew compensation seems, as a matter of practice, to be bounded from below. So, a firm can typically choose how many stocks or options to grant as part of the current compensation package, but cannot revoke stocks or options granted in previous years. It is this bound that will matter for our results, not bounds on the changes in the manager’s total wealth.
Introducing the minimum payment constraint has the important implication that at the optimal contract, the manager may be strictly better off than at her outside option. So, the participation constraint may or may not bind. It does seem that in many real-life cases, CEOs’ compensation inside the firm exceeds outside opportu-nities.2 For the purposes of our theoretical results, we will focus on the case where
1
Kadan and Swinkels (2004) examine the issues involved with characterizing a solution when contracts can be arbitrary. See Section 4 for a discussion.
2
only the minimum payment constraint, and not the participation constraint, binds. Broadly similar results obtain when both the minimum payment constraint and the participation constraint bind; we discuss this below.
Third, we allow the stock price to be zero with a non-negligible probability. We refer to this as “non-viability risk.” One example of non-viability risk is, of course, bankruptcy. But, it can also describe, for instance, the demise of firms that are unable to market their products, or raise additional capital tofinance their operations or further product development. This case is common for start-up companies. Our main results about the choice between stocks and options follow from an interesting interaction between the minimum payment constraint of the manager and the non-viability risk faced by the company.
The first key step in our analysis is to understand the effect of the minimum payment constraint. The contribution to the manager’s incentives of a small change in stock price at any given level depends both on how quickly her compensation changes and on her marginal utility of income given that stock price level. When there is no minimum payment constraint, the main thing connecting compensation at one stock price to compensation at another is the participation constraint. With a minimum payment constraint, another issue arises: The more that compensation is responsive to stock price changes at one stock price level, the higher is the manager’s wealth at all higher stock price levels. But, since higher wealth translates into a lower marginal utility of income, the manager is less motivated by compensation changes at those higher levels. So, there is a real trade-off between providing more motivation at one stock price, and the ease of providing motivation at higher stock prices. Without the minimum payment constraint, this is less of an issue, since one could simultaneously increase the slope of compensation but decrease the lowest payment given. So, without the minimum payment constraint, the typical way to increase motivation is by a combination of carrots at good outcomes and sticks at bad outcomes, while with a minimum payment constraint, only the carrots may be feasible.
With this in hand, we turn to the effect of a change in the exercise price of stock options on the incentives of risk averse managers. We find that a significant determinant of the effect of such a change is the role of additional effort by managers in maintaining the viability of thefirm. If non-viability is not a major issue then stock options always dominate stocks. In contrast, if a major effect of increased managerial effort is to lower the probability offirm demise (as will typically be true infinancially distressed firms and in start-up companies), then stocks can dominate options.
Two forces drive this result. Thefirst is as described above: increasing the exercise price makes risk averse managers less wealthy at any given stock price and hence more responsive to stock price changes above the exercise price. On the other hand, the utility of managers is unaffected by stock prices below the exercise price: the manager is numb over this range. Increasing the exercise price also reduces incentives by increasing the numb region. The key is that if non-viability is not a major issue, then changes in effort by the manager will have little effect on the probability of low stock prices anyway, and hence increasing the numb region will have little negative effect on the manager’s incentives. For this reason, if non-viability is not an issue, investors will prefer a higher exercise price, which improves the manager’s incentives in more relevant parts of the price distribution. If non-viability is important, then an exercise price of 0, namely a stock, may be optimal, because it is near zero that the price distribution is most affected by managerial effort.
We develop this result first in simple static setting. We then extend the result to a dynamic setting that allows for optimal consumption and savings decisions by the manager. In the dynamic setting, the manager tries to hedge risks using her savings decisions, and so undoes some of the incentives induced by the compensation contract. Similarly, the manager can undo some of the incentives by buying or selling the firm’s stock in the open market (see Ofek and Yermack 2000). We show that neither of these affects our main result - options still dominate stock unless there is significant non-viability risk. The difficulty in analyzing the dynamic case lies in the fact that in response to a change in the strike price in a specific period, the manager will optimally alter her savings/consumption in other periods. To pin down the manager’s response we develop a variational argument with the flavor of an envelope theorem. This argument allows us to study the effects of a change in compensation on the manager’s incentives by considering a relatively simple change in the manager’s consumption plan.
Our results suggest that start-ups should use stock (grant partial ownership) to executives in early stages, while they should migrate to option based compensation after undergoing and IPO, since the non-viability risk is then much smaller. Similarly, our results suggest that foundering firms (such as firms in Chapter 11) should use restricted stock, and then move toward options as they emerge from bankruptcy.
Exploiting the trade-offbetween increasing incentives at one stock price level and making incentives less effective at higher stock price levels, we demonstrate how an ill-designed options contract can make a risk averse manager of a healthy company “too rich too soon,” and hence less responsive to incentives. In particular, granting
managers more stocks or options with a low exercise price can make them exertless effort.
Our model provides guidelines for exercise price design. We show that compen-sation should consist of base salary only (plus any prior stock or options holding) for all price realizations at or below a threshold level at which effort is most influential to the stock price (in a sense that we will make precise). This threshold is signifi -cantly distant from zero for healthy firms, and can be zero only if non-viability risk is substantial.
A prediction of our model is that higher bankruptcy risk should be associated with a higher tendency by firms to compensate their executives by stock instead of stock options. We test this prediction empirically. Using data from 1992 to 2004, we show a significant statistical relation between several proxies for bankruptcy risk and both the likelihood that thefirm uses restricted stock and the fraction of total stock based compensation made up of restricted stock. In particular,firms with lower Altman’s Z-Score, higher KMV-Merton expected default probabilities, and lower debt ratings are more likely to compensate their CEOs by restricted stock. Our empirical formulation controls forfirm characteristics, prior stock ownership by the manager, and differences in both the taxation and the expensing rules of restricted stock compared to stock options.
Theoretical research on option based compensation has traditionally focused on the effect of option compensation on the risk taking attitude of managers. The tradi-tional view is that compensation by options induces more risk taking (as was originally suggested by Jensen and Meckling (1976)). More recently, Carpenter (2000) and Ross (2004) have challenged this view. They show that the effect of option compensation on risk taking by the manager is ambiguous and depends on the manager’s utility function. The focus of our paper is on motivation for effort — an issue that was not studied by Carpenter or Ross. However, our results are complementary to theirs both in the sense that the effects of changes in compensation on effort need not always be in the obvious direction in the presence of a risk averse manager and in the sense that higher effort (induced by options) can lead to higher or lower volatility of the stock price.
The inability of risk averse managers to diversify affects their valuation of stock options relative to risk neutral shareholders. Lambert, Larcker and Verrecchia (1991) study this divergence. Using a certainty equivalence framework they demonstrate that if a risk-averse manager has a significant portion of her wealth tied to herfirm’s stock price, then her value for a compensation contract can be substantially lower
than its cost to the shareholders. Hall and Murphy (2000) use this framework to derive optimal exercise prices for stock options. Hall and Murphy (2002) use a similar technique to analyze the cost, value and pay-performance sensitivity of non-tradable options held by undiversified, risk averse executives. Unlike our model, these papers do not take into account effort choice, and do not consider non-viability risk.
Hemmer, Kim and Verrecchia (2000) study the restrictions on the price distrib-ution and utility functions that induce a convex optimal contract in a moral hazard problem without a minimum payment restriction and bankruptcy risk. Our results show that even when the optimal contract without a minimum payment constraint is concave, introducing this constraint may result in a convexity of the contract as long as non-viability risk is not a main issue.
We are unaware of previous theoretical work linking non-viability risk to optimal compensation. But, aspects of capital structure (which is related to bankruptcy risk) on managerial compensation have been studied. John and John (1993) show that the agency relationship between shareholders and managers can mitigate the risk-shifting effect between shareholders and debt holders. They show that the optimal sensitivity of the manager’s pay to the stock price is decreasing in the debt level. Intuitively, when the level of debt increases, shareholders have increased risk shifting incentives. A less sensitive compensation contract allows shareholders to commit to less risk shifting, thus lowering their cost of debt. Cadenillas, Cvitanic and Zapatero (2004) study the incentive effects of debt on a risk averse manager in a dynamic continuous time framework. Their numerical results suggest that levered stock (an option) is optimal for managers that are more effective in affectingfirm value through effort, and infirms with high momentum, largefirms, andfirms for which additional volatility implies a small decrease in returns.
Innes (1990) studies debt contracts in a moral hazard setting with a wealth con-strained agent. Innes does not allow for non-viability risk, and only considers a risk neutral agent. Managerial risk aversion and non-viability risk are at the heart of our results. Finally, Lambert and Larcker (2004) discuss a principal-agent problem with limited liability but without non-viability risk. In their framework, the optimal contract is always option-like, and the trade-offthat is central to our results does not occur. In particular, we show that stock options may or may not dominate stocks depending on non-viability risk.3
3
Stoughton and Wong (2003) consider a different aspect of the choice between stocks and stock options. In their model, industry competition, accounting choice, and the possibility to reprice options play a role in optimal compensation. Kadan and Yang (2005) study the earnings management
Section 2 presents the static model. Section 3 studies the choice between stocks and options. Section 4 discusses general optimal contracts and introduces the notion of the critical price. Section 5 presents a dynamic generalization of the model. Section 6 presents our empirical evidence. Section 7 concludes. Proofs not central to the development are in Appendix A. Appendix B presents some worked examples.
2
Model
We study a principal-agent model between investors (the principal) and a manager (the agent). Our focus is on incentives for effort rather than, say, incentives to choose among projects.
Investors and Managers: A set of risk neutral investors own afirm. The firm, in turn, employs a manager. The manager is risk averse over her final wealth w, with utility over wealth u(w). We assume u(w) is twice continuously differentiable, with u0>0, u00<0.
Effort and Utility: The manager chooses an effort level e ∈ [0,¯e]. Effort is un-observable to the firm. Effort e costs the manager ψ(e). We assume ψ(·) is twice continuously differentiable, withψ0 >0, ψ00>0.Effort and wealth enter utility in an additively separable fashion, so that the net utility of a manager who chooses effort level eand has terminal wealthw isu(w)−ψ(e).
Effort and Firm Value: For simplicity, we introduce our results in a single period model (see Section 5 for a dynamic extension). Onceeis chosen, there is a realization of the terminal value of thefirmx∈[0,x¯]that is stochastically related toe. This value is then divided by the investors and the manager.4 For simplicity, we will typically refer toxsimply as the “stock price.” The distribution ofxgiven effort leveleby the manager is F(x|e). We assume that F(·|·) is twice continuously differentiable and has full support for eache. This rules out atoms in values except at zero, and implies that F has a density f on (0,x¯].Higher effort moves the distribution of stock prices to the right in the sense of strict first order stochastic dominance (FOSD). That is, Fe(x|e)<0except whenx= ¯x and possibly when x= 0.
implications of executive stock options. Cadenillas, Cvitanic and Zapatero (2005) show that options can serve as a screening mechanism for executives.
4Thinking ofxas a value to be divided between the investors and managers avoids the technical
complications of a setting where compensation is a function of stock price, but (even holding effort fixed), the distribution over stock price is a function of compensation. For practical purposes, the difference is typically minor.
Non-Viability Risk: A key feature of our model is that we allow non-viability risk (as for example bankruptcy risk or the failure of a start-up). We capture this by allowing a positive probability of a zero stock price, so that a firm with a risk of non-viability has F(0|e) > 0. Note that Fe(0|e) is the marginal effect of effort on the probability that the firm becomes non-viable and that for x > 0, F(x|e) = F(0|e) +R0xf(y|e)dy.
Compensation: The manager is compensated as a function π(x)of the stock price x. We assumeπ(·) to be continuous and piecewise differentiable. For given eand π, the manager’s utility is thus
UM(π, e)≡F(0|e)u(π(0)) +
Z x¯ 0
u(π(x))f(x|e)dx−ψ(e). (1) The first term reflects compensation to the manager if the firm becomes non-viable, while the second term reflects compensation when the firm is solvent. One might think, for example, of π(0) being the salary paid to the manager before the stock price is realized.
Incentive Compatibility Constraint: The incentive compatibility constraint is
e∈arg max
e0∈[0,e¯]U
M(π, e0). (IC) For the compensation contractsπ we will consider, there will be a unique effort level satisfying IC. We denote this effort level by e∗(π), writing simply e∗ when the π
under consideration is clear.
Minimum Payment Constraint: We take seriously the idea that payments to the manager cannot fall below certain levels. This minimum payment constraint can be motivated by thinking about a credit constrained manager who needs to maintain a certain standard of living before her stock options vest, or by thinking about a setting where a firm which already has an existing manager working on salary considers adding an incentive component, but feels constrained from simultaneously lowering the base salary. Additionally, the wealth of the manager can already be tied to the stock price due to past compensation that consisted of stocks or options. As a matter of practice the firm can grant stock or options as part of a new contract but cannot revoke previously awarded securities. Thus, the prior stock and options holding of the manager serves as a lower bound on the payments to the manager under the new contract.
This is modelled by assuming that there is a non-decreasing, continuous and piece-wise differentiable functionm(x) such that
π(x)≥m(x) ∀x. (M)
A base salary or limited liability would result in m(x) being constant. If there are non-revokable prior stock or options holdings, then m(x) increases over the relevant range of stock prices.
Participation Constraint: The participation (individual rationality) constraint for the manager is of the form
UM(π, e∗)≥u0. (IR)
In the standard principal agent framework (such as Holmstrom 1979), the IR constraint is always binding. Intuitively, if the IR constraint is not binding one can decrease the utility of the manager by a small constant for any realization without changing her incentives. When payments to the manager are bounded from below this is no longer true. If M is sufficiently tight, the IR constraint may cease to be relevant.
We think thatIR does not bind in many cases of practical interest. An example is the setting where a firm which already has an existing manager working on salary adds an incentive component. Another example is the case of an entrenched manager, or a manager with special skills appropriate for a specific firm. In this case, the compensation to the manager exceeds the outside option, hence the IR constraint will be slack. We also find it hard to imagine that the IR constraint explains the magnitude of expected compensation for most CEOs.5 For these reasons, and for
simplicity, we consider mostly the case of a non-binding IR constraint. Section 4 shows that our main results are robust to this assumption.
The Investors’ Maximization Problem: The total utility of the investors given contractπ(·) and effort leveleis
UI(π, e) =−F(0|e)π(0) +
Z x¯ 0
(x−π(x))f(x|e)dx (2)
Investors choose π(·) and e to maximize UI(π, e) subject to IC, M and IR (which we typically assume is not binding).
5
Grinstein and Hribar (2004) use mergers and acquisitions to provide evidence that managers can actually influence their compensation. This supports the claim that participation constraints may not bind.
Marginal Incentives: Recall that UM(π, e)≡u(π(0))F(0|e) + Z x¯ 0 u(π(x))f(x|e)dx−ψ(e). So, ∂UM(π, e) ∂e =I(π, e)−ψ 0(e), (3) where I(π, e) =u(π(0))Fe(0|e) + Z x¯ 0 u(π(x))fe(x|e)dx. (4) Thus,I(π, e)measures the marginal incentive to the manager (before effort costs) to expend extra effort.
Integrating by parts,
I(π, e) =− Z x¯
0
u0(π(x))π0(x)Fe(x|e)dx. (5) So, incentive intensity depends on how much utility is affected by changes inx (this is given by u0(π(x))π0(x)) and by how much effort affects the probability of a stock price below x(this is given by Fe(x|e)).
The First Order Approach. It will be convenient for us to work this problem via first order conditions. A sufficient but not necessary condition for the validity of this approach is to assume that there are decreasing marginal returns to effort as measured by the stock price distribution. Formally,Convexity of the Distribution Function (CDFC) is satisfied if Fee(x) ≥ 0. Recalling that the effect of effort is to lower F(x),this indeed implies that successive increases in effort lowerF(x) less.6
Using thefirst order approach, we would like to replace IC by
I(π, e)−ψ0(e) = 0. (IC0)
For this to be valid, we need to know that first order conditions are in fact sufficient (and not just necessary) conditions for optima. To see this, note that, using (5),
∂ ∂e ¡ I(π, e)−ψ0(e)¢=− Z x¯ 0 u0(π(x))π0(x)Fee(x|e)dx−ψ00(e).
By CDFC, Fee is positive , while ψ00 and u0 are positive by assumption. A sufficient condition for ∂e∂ ¡I(π, e)−ψ0(e)¢≤0 is thus thatπ0(x) is everywhere non-negative. We thus obtain:
6
Rogerson (1985b) studies CDFC and its relation to the first order approach. Jewitt (1988) provides different sufficient conditions for thefirst order approach to be valid. All our results are not changed if we use the Jewitt conditions instead of CDFC.
Lemma 1 Suppose thatCDF C is satisfied. For any given non-decreasing, piecewise differentiable contract π, there exists a unique solution e∗ to IC0. Hence, IC can be replaced with IC0 and so the first order approach is valid.
In the rest of the paper we focus our attention on stock options and stock con-tracts. These result in non-decreasing and piecewise differentiable contracts. Thus Lemma 1 allows us to use thefirst order approach.
3
Stocks and Stock Options
In this section we consider the case where compensation contracts can take either the form of options or stock (an option with exercise price of 0). Thus π(x) takes the form
π(x) =m(x) +αmax(0, x−k), (6)
where m(x) represents the previous stock or options holdings of the manager and any base salary payment, αis the proportion of thefirm granted in new options, and k∈[0,x¯]is the exercise price on these options. Thus, a contract can be represented by a pair(α, k). The casek= 0corresponds to a stock.
Since prior compensationm(x)is composed of stocks and options only, it is con-tinuous, piecewise linear and (weakly) convex, and hence steepest at x¯. We assume that α∈[0,1−m0(¯x)],so that the manager never owns more than the wholefirm.
The payoff to the investors givenα, k andeis (in a mild abuse of notation) UI(α, k, e) =
Z x¯ 0
(x−π(x))f(x|e)dx−m(0)F(0|e). (7)
The payoffof the manager is
UM(α, k, e) = u(m(0))F(0|e) + Z k 0 u(m(x))f(x|e)dx (8) + Z x¯ k u(m(x) +α(x−k))f(x|e)dx−ψ(e). Note that (4) becomes
I(α, k, e) = u(m(0))Fe(0|e) + Z k 0 u(m(x))fe(x|e)dx (9) + Z x¯ k u(m(x) +α(x−k))fe(x|e)dx.
Since α≥0,and m0(x)≥0, π is non-decreasing and so by Lemma 1, we can replace IC by its first order conditionI(α, k, e)−ψ0(e) = 0.
Integration by parts yields I(α, k, e) = − Z k 0 u0(m(x))m0(x)Fe(x|e)dx (10) − Z x¯ k u0(m(x) +α(x−k))(m0(x) +α)Fe(x|e)dx.
Thus, to make the manager exert high effort, the contract should induce a high marginal utility in those regions of the distribution in which effort is most influential (where |Fe|is large).
Higher effort induces a better distribution of stock prices, but since the contract is non-decreasing it also induces a higher costs to investors. Thus, a priori it is not clear that the investors want the manager to exert higher effort. For a manager for whom both previously granted and current compensation is paid using stocks and options,x−π(x) is non-decreasing. This guarantees that the investors would always like the manager to work harder. In general:
Lemma 2 Assume thatx−π(x) is non-decreasing. Then for anye∈[0,e¯], ∂U∂eI ≥0.
To see this differentiate (7) to obtain ∂UI ∂e = Z x¯ 0 (x−π(x))fe(x|e)dx−m(0)Fe(0|e) = − Z x¯ 0 (1−π0(x))Fe(x|e)dx≥0.
The last equality follows from integration by parts and the fact that π(0) = m(0). The inequality follows since x−π(x) is non-decreasing and byF OSD. It is strict if x−π(x) is not a constant.
3.1
Exercise Price and Incentives
Figure 1 illustrates the effect of an increase in exercise price on the utility of the manager. The horizontal axis is the stock price, while the vertical axis is the utility of the manager. For simplicity, the figure considers the case of a constant minimum payment m(x)≡m.For stock prices less thank the manager always getsu(m),and thus does not care about changes in the stock price over this range. We term [0, k)
the numb region. For values in [k,x¯] the utility of the manager is increasing and concave, reflecting the linearity of the contract over that region and the risk aversion of the manager.
x Ut il it y k1 k2 u(m) u(m+α(x-k1)) u(m+α(x-k2))
Figure 1: The Effect of a Change in the Exercise Price on the Manager’s Utility
When the exercise price increases fromk1tok2 there are two effects on the utility of the manager. First, the numb region is enlarged and hence the manager does not care about changes in stock price over a larger region. But, for stock prices abovek2, the marginal utility of the manager is higher, and hence her incentives are increased: for all x∈[k2,x¯),u0(m+α(x−k1))< u0(m+α(x−k2)).
To see this formally, note that the optimal effort level e∗ is given implicitly by IC0. The implicit function theorem then gives us
Remark 1 The sign of ∂e∂k∗ is equal to the sign of ∂k∂ I(α, k, e∗).7
7
By the implicit function theorem
∂e∗ ∂k =− ∂ ∂k(I−ψ 0(e∗))/∂ ∂e(I−ψ 0(e∗)).
By the agent’s second order condition the denominator is negative at e∗.Hence the sign of ∂e∂k∗ is
equal to the sign of
∂ ∂k(I−c
0(e)) = ∂I
Differentiation of (10) yields ∂I ∂k = αu 0(m(k))F e(k|e) (11) +α Z x¯ k u00(m(x) +α(x−k))(m0(x) +α)Fe(x|e)dx.
Thefirst term is negative and represents the increase in the numb region. The second term is positive and reflects that the manager is “hungrier” over the interval [k,x¯]. The effect of a change in the strike price on effort is the net effect of these two conflicting forces.
3.2
Stocks vs. Options: The Role of Non-Viability Risk
Equation (11) allows us to think systematically about when investors might prefer options and when they might prefer stock as a motivational tool. Ourfirst observation is that if non-viability is not an issue (i.e., F(0|·) ≡ 0), then pure stock is never optimal. In particular, increasing the exercise price a little above zero induces a higher effort level by the manager at a lower cost. So,only if non-viability is important could compensation purely by stock be optimal. Healthy and stable firms should prefer options.
Figure 2 clarifies the intuition behind this result. It depicts cumulative distribu-tion funcdistribu-tions for two levels of effort,eH> eL.The left graph illustrates a case with no non-viability risk. Since F(0|·) ≡0, Fe(0|·) = 0 as well, and so, near zero, |Fe| is small. But then by (11), neark= 0, the effect of a small increase in the numb region on incentives is second order. There is a first order improvement in incentives over the rest of the support. Hence, incentives are increased on net. The contract is of course cheaper for any given stock price. We obtain
Proposition 1 Suppose that F(0|e) = 0 for all e ∈ [0,e¯], so that there is no non-viability risk. Then, for any contract that involves granting pure stock, there is an option based contract that pays the manager less at each stock price realization, but induces a strictly higher effort level.8
Proof: See Appendix A.
The key observation here is that regardless of the existing compensation or stock holdings of the manager, lowering compensation to the minimum near zero has a
8
Logically (but less realistically), bankruptcy risk could be significant (F(0|e)>0), but the efforts of the manager on bankruptcy risk irrelevant (Fe(0|e) = 0). The proposition would also hold in this
x F(x|eH) F(x|eH) F(x|eL) F(x|eL) 0 0 x 1 1
No Non-Viability Risk With Non-Viability Risk
Figure 2: The Effect of Effort on the Price Distribution
second order effect on incentives if Fe(0|e) ≡0 (the no non-viability risk case), but improves incentives everywhere else. A corollary is:
Corollary 1 Suppose that F(0|e) = 0 for all e ∈ [0,e¯], so that there is no non-viability risk. Then, granting stock to the manager is never optimal.
Proof: See Appendix A.
The point here is that under stock and option based compensation, compensation never rises faster than the total value of the firm.9 But then, the net payoff to the investors x−π(x) is non-decreasing, and so Lemma 2 applies. Since the contract pays less at each stock price realization, the investors are thus strictly better off.
When managerial effortdoes affect the probability of non-viability, as in the right graph of Figure 2, this conclusion need not follow. In particular,
∂I(α, k, e) ∂k ¯ ¯ ¯ ¯k=0 = αu0(m(0))Fe(0|e) +α Z x¯ 0 u00(m(x) +αx)(m0(x) +α)Fe(x|e)dx. 9In contrast, for example, to a situation with bonuses.
While the second term is positive, the first term, which reflects non-viability avoid-ance, is negative. Appendix B provides two worked examples. ExampleB1is critical: it shows that with sufficient non-viability risk, pure stock can indeed be optimal. Ex-ampleB2illustrates a case where options are optimal.
3.3
Too Rich Too Soon - Number of Options and Incentives
The previous section showed that with a risk averse manager, increasing the strike price on options granted may increase effort. This risk aversion has other effects as well. For example, one would expect an increase in the number of options (or stocks) granted to increase effort. Interestingly, this need not be true: granting a risk averse manager too many options might make her quite rich at moderate stock prices. This lowers her responsiveness to stock price changes at higher levels, potentially by enough to actually decrease her optimal choice of effort.
To see this, assume for simplicity thatm(x)≡m(a constant) and recall from (5) that incentives are determined by
I(π, e) =− Z ¯x
0 ∂
∂xu(π(x))Fe(x|e)dx.
The derivative of the manager’s utility with respect to the stock price for a given contract(α, k)and price x≥k is
∂
∂xu(m+α(x−k)) =αu
0(m+α(x−k)).
If the manager is risk neutral, this clearly increases in α.But, if the manager is risk averse, the decrease inu0 may swamp the increase inα. Example B3 in Appendix B shows that this can lead to a net reduction in incentives. We obtain
Proposition 2 An increase in the number of granted options (or stocks) may damage incentives.
Thus, scaling up an ill-designed compensation contract can push a risk averse manager to lower effort levels. Note again the critical role of the minimum payment constraintM. In this setting, increasingαhas the unavoidable effect of making the manager rich, perhaps damaging her incentives at higher stock prices. AbsentM,an increase inαcan be accompanied by a decrease in base salary (perhaps to a negative value), and this effect is mitigated.
Figure 3 illustrates the effect of a change in the number of options granted to a mildly risk averse manager. Figure 4 illustrates a more highly risk averse manager.
To the right of y, the increase in α is dominated by the (richer) manager’s lower marginal utility and incentives are weakened.
As suggested by Figure 3, the “too rich too soon” phenomenon cannot occur if the manager is only mildly risk averse. Let the coefficient of relative risk aversion at w beρ(w)≡ −wuu000((ww)) >0.Then
Proposition 3 Assume m(x)≡m≥0. If ρ(w)≤1 for all w (with strict inequality somewhere), then ∂e∗∂α(α,k) >0 for allα and k.10
3.4
Do Options Imply Higher Risk?
Beginning with Jensen and Meckling (1976), it has been argued that compensation by options induces managers to take more risk (since option value increases with volatility). Two recent papers suggest a more nuanced conclusion. Carpenter (2000) solves a dynamic investment problem of a risk averse manager compensated with a call option. She shows that option compensation may or may not lead to greater risk seeking. Essentially, the risk averse manager may respond to the increased exposure inherent in owning more options by choosing a safer strategy. Ross (2004) argues that the conventional “folklore” fails to account for the shape of the manager’s utility function. He argues (p. 224) that “It is routine for commentators to argue that call options increase the manager’s willingness to take risk. We now know, though, that this also depends on the wealth effect of the options...”.
Our paper considers a different aspect of managerial choice. Carpenter and Ross consider project choice but not effort. In our model, the focus is on the effort choice. Of course, the choice of effort does indirectly affect the volatility of returns. The effect of options compensation on stock price volatility in our setting is complicated by two effects. First, as we have shown, because of the same sorts of wealth effect that are central to Ross (2004), changes in options contracts can have counter-intuitive effects on the choice of effort (as in Proposition 2). Second, it may well be that increases in managerial effort either increase or decrease the volatility of the stock price. For example, if extra effort primarily reduces bankruptcy risk, but does not affect the stock-price distribution conditional on survival, then extra effort reduces volatility. But, if extra effort means taking on new projects, then variance may well increase. So, as in Ross (2004) and Carpenter (2000), the relationship between incentives and volatility is highly ambiguous. We thus view our results as complementary to theirs.
1 0A common figure used in asset pricing calibration exercises isρ = 3. Hence, this proposition
x Uti lit y k u(m) u(m+α2(x-k)) u(m+α1(x-k))
Figure 3: The Effect of the Number of Options on a Mildly Risk Averse Manager
x U til it y u(m) k y u(m+α2(x-k)) u(m+α1(x-k))
Figure 4: Too Rich Too Soon - The Effect of the Number of Options on a Highly Risk Averse Manager
4
Critical Prices and General Contracts
Our central result (and the one that we empirically test) is that forfirms with no non-viability risk, options dominate pure stock. Given that essentially all real world stock based compensation consists solely of stock and options, this seems a highly relevant comparison. But, one could also ask the distinct question of whether something “option-like” arises in the absence of non-viability risk when the contract space is general.
We begin with a definition.
Definition 1 Returns to effort are single peakedif for each e, there isx∗e such that
Fe(x|e) is decreasing inx for x < x∗e, and increasing in x for x > x∗e.
So, x∗e, the critical price, is the one at which the distribution over price is most responsive to effort. For afirm with no non-viability risk, and single peaked returns to effort, it must be thatx∗e >0(sinceFe(0|e)is then0).For healthyfirms, one would expect x∗
e to be considerable. On the other hand, if the probability of firm failure is both significant and affected by managerial effort, then it may well be that|Fe(x|e)| is largest at 0, so thatx∗(e) = 0.
A primitive condition for returns to effort to be single peaked is the Monotone Likelihood Ratio Property (M LRP), which requires that
Fe(S|e) F(S|e) <
Fe(T|e)
F(T|e) (12)
for any two intervals S, T ⊂[0,x¯]whereS lies strictly to the left of T.11
Lemma 3 If M LRP is satisfied then returns to effort are single peaked. If there is no non-viability risk then x∗e >0.
Proof: In Appendix A.
Assume that M LRP holds, and assume also that fe(x|e)
f(x|e) is bounded.
12 Then,
if the IR constraint is not binding at the optimum, the optimal contract is given implicitly by 1 u0(π(x)) = ( maxnu0(m1(x)), μfe(x|e) f(x|e) o x >0 1 u0(m(0)) x= 0 (13) 1 1
This generalizes the standard definition ofM LRP to allow for distributions which contain an atom. Note thatM LRP impliesF OSD.
1 2
where μ >0 is the Lagrange multiplier on the IC constraint.13
An immediate implication of (13) is that the optimal contract in the absence of non-viability risk is option-like: it specifies paying the minimumm(x)for allx up to a price levelkˆ (a “strike price”) that exceedsx∗
e.Formally,
Proposition 4 Suppose that the IR constraint is not binding at the optimal effort level e. Then, there isk > xˆ ∗e such that the optimal contract paysm(x) for all x <ˆk.
If there is no non-viability risk then ˆk >0.
This follows immediately from (13), sinceμfe(x|e)
f(x|e) > 1
u0(m(x)) can only hold where fe is strictly positive. Forx≤x∗e, Fe(x|e) is decreasing inx by M LRP and Lemma 3, and hence fe(x|e)≤0.
In particular, note that when there is no non-viability risk, then by Lemma 3 x∗e >0, and hence ˆk >0. So, as was the case when considering the choice between stocks and options, afirm with full latitude in choosing compensation will still choose to pay more than the minimum for low stock prices only when there is significant non-viability risk.14
4.1
Start-Ups and Dinosaurs
Our results make a strong case for the use of stock (granting partial ownership) in motivating the managers of start-ups. For most start-ups, there is a significant chance that the firm fails, so that F(0|e) is high. This makes it likely that x∗
e is near 0.At the time a start-up goes public, many of the hazards of having no viable product or securing early financing have already been overcome. So, one could well imagine that F(0|e) is less affected by effort than before. Hence, a transition toward options makes sense.
Start-ups may also be more likely to face a binding IRconstraint. For example, part of what fills out the IR constraint in a typicalfirm is the prospect of generous future compensation. In start-ups, managers may view these long-term benefits skep-tically. But, whenIRis binding, payments below x∗e can be optimal, making stock a more sensible choice.
The same forces hold when attempting to turn around a founderingfirm, as for ex-ample, one in Chapter 11. Here again, managerial effort focuses on whether thefirm
1 3
See Holmstrom (1979) and Kadan and Swinkels (2005) for the details of characterization and existence.
1 4
Kadan and Swinkels (2005) show that under a convexity condition on the principal’s problem, the optimal contract will pay the minimum near zero even if theIRconstraint is binding, as long as theM constraint actually harms the principal.
survives at all, so thatx∗
e may well be close to0.15 And, here theIRconstraint argu-ment (i.e., retaining the employee) for payargu-ments below x∗e is perhaps even stronger, because if the firm fails, the manager may suffer damage to her reputation as well. As the firm emerges from Chapter 11 and the threat of bankruptcy is removed, our results suggest that options should be used.
5
Stocks or Options - A Dynamic Setting
Thus far, we have considered the choice between stocks and options in a static setting. This allowed us to convey the trade-off between these two compensation contracts in a simple and transparent way. Real compensation contracts often extend over long periods of time and hence current period effort affects compensation in multiple periods. In this section, we study such a setting.
Effort incentives in a dynamic setting are complicated by the consumption and savings decisions of the manager. Potentially, the manager can undo some of the contract incentives by saving some of her income. For example, Rogerson (1985a) shows in a dynamic principal-agent model that if thefirm can monitor the savings de-cisions of the manager, then the optimal contract will induce an unmet precautionary demand for savings by the manager. Bizer and DeMarzo (1999) generalize Roger-son’s model by allowing borrowing and saving, and study the effect of bankruptcy protection on contract efficiency.
In this section we provide a dynamic extension to the model studied in Section 3. Our goal here is to show that the dominance of options over stock in the absence of non-viability risk holds in a dynamic setting where the manager makes optimal savings/consumption decisions. For simplicity, we begin in the context of saving using a risk free asset. We discuss generalizations below.
There areT + 1periods indexed by t= 0, . . . , T.At period 0 the investors grant the manager a contract specifying stock based compensation in each period. Com-pensation in periodt∈{1, . . . , T} is given by
πt(xt) =mt+αtmax(xt−kt),
where xt is the stock price realization at time t, mt is the base salary, αt is the 1 5That is,x∗
emay be low even relative to existing stock prices. A typical example would be TWA,
which, shortly before its takeover by AA had a stock price of around 14 cents. Holders of this stock presumably thought of themselves as holding a lottery with a very large atom at 0 and a small chance that the company (and its stock price) would at some point return to health.
proportion of the firm granted, andktis the strike price for timet.16 These can thus be thought of as stocks and options granted in period 0, but with various vesting dates. In this formulation, the compensation schedule in period t does not depend on the stock price in previous periods. Thus, as before, we are restricting attention to a set of contracts corresponding to those we actually see used. We assume that kT <x,¯ so that in the last period the manager is given strict incentives and not just a base salary. As we shall see, this is without loss of generality.
Effort e is exerted once, immediately after the contract is accepted. The stock price is then realized sequentially in periods 1, . . . , T.17 Note that even if returns (differences in prices) are independent across periods (as for example, if stock prices follow a random walk), the stock prices themselves will typically be dependent. The joint distribution of the sequence of stock prices given effort e is F(x1, . . . , xT|e), with support [0,x¯]T. We denote by F(x1, . . . , xt|e) the marginal (joint) distribution of the stock price in the first t periods. Similarly, F(xt|e;x1, . . . , xt−1) denotes the conditional distribution of xt given prior stock price realizations. We assume that higher effort increases the stock price in the sense of F OSD in each period and for each realization of the stock price history to date. We further assume that a higher stock price at any timet, moves the price distribution at any timet0 > tin the sense of F OSD, so that Fxt(xt0|e;x1, . . . , xt0, . . . , xt−1) < 0.
18 As before, an atom at 0 in
F(xt|e;x1, . . . , xt−1) represents a probability that thefirm is non-viable at time t. Let ct =ct(x1, . . . , xt, e) be the consumption of the manager at time t = 1, .., T given the history of price realizations up to time t. Denote by st = st(x1, . . . , xt;e) the total savings of the manager at time t. To save notation we assume that the interest rate is 0. The following must then hold:
ct=πt(xt) +st−1−st=mt+αtmax(xt−kt) +st−1+st fort= 1, . . . , T, (14) where sT = 0and wheres0 represents exogenous initial wealth.
We assume the manager has time additive utility with discount factor0< δ≤1. 1 6For brevity we assume in this section that the minimal payment constraint at periodtism
t(a
constant). As before, one can easily extend the model to more generalmt(·).
1 7Thus, we do not consider multiple period effort choice. An interesting complexity arises here.
Imagine that a change in incentives causes the manager to work harder in some period. Some of the time, this will result in so much success that the manager is already rich, and hence less responsive to incentives, in later periods. If the incentives are sufficiently poorly designed, this may occur often enough that the principal may actually wish the manger would work less hard in the current period. How this interacts with the forces identified here is a topic we leave for future work.
1 8
Thus, given a high stock price today, the manager is more optimistic about the value of her options in upcoming years. This will cause her to adjust her borrowing/savings decisions. The results also hold (with a slightly more complicated proof) with a weaker version ofF OSD.
The manager’s expected utility is UM = T X t=1 δt Z x1...xt u(ct)dF(e;x1, . . . , xt)−ψ(e). (15)
Letc∗t =c∗t(x1,. . . , xt)ands∗t =s∗t(x1, . . . , xt)be the optimal consumption/savings of the manager at time t as a function of price realizations up to time t. These are unique by the concavity of the utility function, and are assumed to be interior, so that the marginal utility of consumption at timetis equal to the expected discounted marginal utility of consumption at time t+ 1:
u0(c∗t) =δ Z x¯
xt+1=0
u0¡c∗t+1¢dF(xt+1|e;x1, . . . , xt) fort= 1, . . . , T −1. (16) We begin with a preliminary result: Managerial consumption in each periodt is increasing in the period tstock price, and strictly so fort < T.
Lemma 4 For all t < T and for all x1, . . . , xt−1 ∂c
∗ t(x1,...,xt) ∂xt > 0. In period T, ∂c∗ t(x1,...,xT) ∂xT >0 for xT > kT. Proof: In Appendix A.
The second part of this is trivial since consumption in periodT is equal to savings plus income. To see the intuition for the first part, consider first a 2 period model. Then, a higherfirst period stock price induces weakly higher income in thefirst period and by F OSD is strictly good news about periodT income, sincekT <x.¯ So, if the manager spends weakly less in the first period in response to an increase in thefirst period stock price, then, since her savings are weakly higher, in period two she spends at least as much for every stock price. Since the distribution over next period stock prices has strictly improved, her expected marginal utility of income thus falls, which contradicts the optimality of spending weakly less in the first period.
In a multiple period setting, it can be that a higher stock price today lowers consumption in some future periods and for some histories: the manager may spend more based on good news today, but sometimes then has to save more than she otherwise would have when future news is less good. So, an argument about the expected marginal utility of consumption becomes more subtle. The key to the proof is to show that if the manager spends weakly less today in response to an increase in the stock price, then no matter what is her continuation plan for consumption, there
must be a later moment that replicates the essence of the two period situation.19 Using Lemma 4, we can establish our main result of this section, a dynamic analog to Proposition 1:
Proposition 5 Suppose for some ˆt that there is no non-viability risk as of time
ˆ
t, so that F(xt|e;x1, . . . , xt−1) = 0 for all e, for all t ∈ ©1, . . . ,ˆtª, and for all (x1, . . . , xt−1). Consider any contract that grants pure stock in periodt.ˆ Then, there
is a contract that differs only in using options in period ˆt, that pays the manager less at each stock price realization at time ˆt (and the same for any given stock price in other periods), and that induces a strictly higher effort level.
Proof: In Appendix A.
Thus, as in the static model, compensation by stock in any periodˆtis suboptimal if there is no non-viability risk as of time ˆt.20
To see the intuition, note that as before, increasing the strike price at time ˆt lowers compensation costs for any given realization of the stock price path. However, changing the strike price in one period affects savings and consumption decisions in all periods. The total effect on incentives of such a change is thus complex.
To address this issue we use an envelope theorem style variational argument. In particular, consider a contract that grants pure stock in some period ˆt, and consider the effect on the incentives of the manager of increasing the strike price a little bit from0,and so lowering her compensation in periodˆtbeyond the strike price by some ε. One way for the manager to restore her consumption/savings plan to feasibility in the face of this is to set ε more aside in period 1 and spend it at time ˆt. We show that since the manager had previously optimized her consumption/savings decision, this is, to the first order, an optimal adjustment to the change in circumstance, and can be used to understand the change in her effort incentives.
But, when there is no non-viability risk and when εis small, this has the effect of undoing essentially any effect on consumption except that consumption is lowered by ε in the first period for every stock price (because only when the time ˆt stock
1 9
Imagine that T is the last period in which the manager receives incentive pay, but that the manager consumes for some time after T. Then, from time T onward, the agent solves a (trivial) intertemporal optimization problem, the solution to which certainly satisfies that the agent consumes more in periodT when her wealth at periodT is greater. So, there is no loss of generality in assuming that incentives are not trivial in periodT (i.e,kT <x¯).
2 0
So, afirm for which the probability of bankruptcy in the near term as small, but the longer term probability is large (as, for example, with a large enough unfunded pension liability) might tend to use options for stock based compensation that vests in the near term, and stock after that.
price is below kˆt is there any change in time ˆt consumption). But, by Lemma 4, consumption in thefirst period is strictly increasing in the stock price. Hence, because the manager has diminishing marginal utility of consumption, this uniform reduction in consumption at each stock price increases the amount by which afirst period stock price increase benefits the manager. Incentives are thus strictly improved, and the sub-optimality of stock holds true also in the dynamic setting.
5.1
General Savings Technologies
The result as proved uses the fact that savings are risk free. Assume first that there are a set of assets in addition to the risk free one, where the returns to these assets are uncorrelated with the price of the shares in the firm. Then, all of the analysis goes through with only notational additions, as long as the risk free asset can be freely bought and sold. In particular, if one augments the savings-consumption decision by a choice of asset allocation at the end of each period, and augments the state space to be the cross product of the original space and the realizations of other asset returns, then all of the relevant integrals become one level deeper, but easy analogs to Lemma 4 and Proposition 5 obtain. The critical variational argument remains unchanged: in the face of a change from pure stock in period ˆt to options with a small strike price kˆt, have the manager increase her savings in the risk free asset in period 1 to cover the reduction in her compensation in period ˆt when the strike price is reduced (so that, as before, she ends up consuming the same amount in periodˆtexcept when the stock price lies belowkˆt) and have the managerin every other way (including in the rest of her asset allocation decisions) remain with her original plan. As before, this variation can be used to assess the relevant derivatives of incentives, and the only significant impact of this variation is to lower consumption by a constant in period 1, which, given that period 1 consumption is a strictly increasing function of the stock price, increases the value to the manager of increments to the stock price.
Of course, one asset that the manager might be very interested in trading is the shares of her own firm. For example, Ofek and Yermack (2000) find that high-ownership managers negate some of the impact of incentive contracts by selling pre-viously owned shares. Let us consider then, a setting in which there are three types of assets: a risk free one, a set of assets uncorrelated with the shares of the firm, and shares of the firm. Reflecting actual law, assume that the manager is forbidden from short selling the shares of her firm. So, as before, the compensation of the manager is weakly increasing in the share price of the firm, and critically, the value
of the manager’s wealth is increasing as well. Then, while the proof is slightly more complicated, Lemma 4 continues to go through, because the new force (changes in wealth from stock owned) also drives the manager in the direction of spending more in period 1 when the stock price goes up.
If the manager could short the stock of herfirm, it is conceivable (without further restrictions) that the manager might view some increases in the stock price as bad news and Lemma 4 could fail. The same point, of course, holds if the manager can take positions in assets which are sufficiently correlated with the stock. It strikes us as unlikely, in a fully worked out setting, that the manager would find it optimal to take positions extreme enough that the implication of Lemma 4 would fail to hold, and especially to the extent that the manager is then on average made worse off in the first period by the effects of extra effort. This is, of course, especially true given that by law, she cannot take such a position directly by shorting her own stock.
6
Empirical Analysis
Our model suggests thatfirms with a higher non-viability risk will tend to grant their managers more restricted stock while firms with a low non-viability risk will tend to grant options. In this section we provide evidence supporting this prediction. In the absence of data on compensation in start-up companies, we restrict attention to bankruptcy risk, which is a specific type of non-viability risk. Thus, we hypothesize (and find) a positive correlation between bankruptcy risk and the use of stock in compensation contracts.
6.1
Related Empirical Literature
The empirical literature on the determinants of executive pay is extensive. Smith and Watts (1992) find that firms with more growth opportunities have higher lev-els of executive compensation and greater use of stock options plans. They also show that large and non-regulated firms have higher levels of executive compen-sation. Gaver and Gaver (1992) find that growth firms pay higher levels of cash compensation to their executives. Controlling for firm size, they show that the in-cidence of bonus plans, performance plans and restricted stock plans does not differ between growth and non-growth firms. Kole (1997) shows that restricted stock is most prevalent among research-intensive firms, and firms in innovative industries. Aggarwal and Samwick (1999) provide empirical evidence supporting the claim that pay-performance sensitivity is decreasing in the variance of the firm’s performance.
Barron and Waddell (2003) suggest a model in which the manager not only makes an effort choice but also affects project selection. Their empirical evidence shows that executive rank is a major determinant of the extent of use of incentive pay.21
Despite these extensive investigations, the relation between bankruptcy risk and compensation mix has been relatively unexplored.22 Gilson and Vetsuypens (1993) provide an empirical examination of compensation in financially distressed firms from 1981 to 1987. They show that after debt renegotiations, CEO compensation is strongly related to the stock price. They do not, however, study the compensation mix between stocks and options. One of their interesting findings is that sometimes senior managers’ compensation is tied directly to the successful resolution of bank-ruptcy. This is consistent with the idea of granting incentives at points where the effort of the manager affects the distribution of prices the most.23
Bryan, Hwang and Lilien (2000) provide an extensive empirical investigation of the mix, incentive intensity and economic determinants of stock based compensation. They focus on a comparison between restricted stock and stock options. Although bankruptcy risk is not explored in their paper, it can be considered a first cut test to our hypothesis, because they do look at capital structure. They show that firms with high leverage ratios tend to grant their managers restricted stock both in terms of amounts, and in terms of incentive intensity (defined as the sensitivity of the grant to changes in stock price). Bryan et al. find this result puzzling (pp. 684) since they do not expect stock-based incentive pay to be used in firms experiencing debt-related agency costs. Our model provides an explanation. Incentive pay in the form of restricted stock is an efficient way to motivate managers, when bankruptcy risk is substantial. The goal of this section is to provide a deeper and more extensive test of this claim.
2 1The literature is split on whether stock based compensation can be attributed to an optimal
compensation scheme. Smith and Watts (1992) and Mehran (1995), for instance, provide evidence supporting advocates of incentive-contract compensation. By contrast, several authors have criticized the contracting approach and assign at least a portion of managerial compensation to windfall, luck or managerial intervention. See for instance Yermack (1995), Bertrand and Mullainathan (2001), Bebchuk and Fried (2003), and Garvey and Milbourn (2004).
2 2Guay (1999) studies the relation of the mix between stock and stock options holdings and the
sensitivity of CEOs’ wealth to equity risk. Hefinds that this sensitivity increases with stock options holding and provides evidence on cross-sectional determinants of convexity in executive incentive schemes. He does not, however, study the effect of bankruptcy on the compensation mix.
2 3
Another interestingfinding of Gilson and Vetsuypens (1993) is that almost one third of thefirms in their sample reset the exercise price of outstanding options which have fallen out of the money. Our model does not consider the costs and benefits of resetting executive stock options. These are captured in an elegant way in Acharya, John, and Sundaram (2000). In their model, there is some information revelation after the contracting stage, resulting in a value enhancing role for exercise price resetting, even from an ex-ante point of view.
6.2
Data and Methodology
Our empirical approach consists of examining a panel offirms and regressing measures of stock based compensation mix on bankruptcy proxies. We use control variables that have been identified in the papers above as determinants of stock based com-pensation. This empirical approach is motivated by papers such as Yermack (1995) and Bryan et al. (2000).24
We draw data from five different sources. Executive compensation data comes from S&P ExecuComp. An observation is a payment by a firm to an executive in a given year. We restrict attention to CEOs only, so eachfirm has just one observation in each year. Since our purpose is to study the determinants of restricted stock vs. stock options grants, we restrict attention to observations in which the firm granted its CEO either stock options or restricted stock. The sample period is 1992-2004. Financial statement data used for calculating different proxies for bankruptcy risk is drawn from the S&P Compustat data base. Return data are taken from the CRSP database. We use this data to calculate firms’ return volatility, an important control variable in our analysis, and to estimate the KMV bankruptcy measure discussed below.
Corporate taxes are another important control variable. For this purpose we use Graham’s Marginal Tax Rates (see Graham 1996). These tax rates account for many important features of the tax code including uncertainty about taxable income, deferred taxes, net operating loss carryforwards and carrybacks, and certain tax credits.
Finally, to account for the expensing decision of stock options we obtained from Bear Stearns Inc. a list of all the firms that announced their intention to voluntary expense options during the years 2002-2004. We provide more details about this dataset in Section 6.5.
Overall, our dataset consists of 14,478 observations coming from 2,418 different firms over 13 years.25 Table 1 provides general descriptive statistics: stock options
2 4Core and Guay (1999) offer an alternative approach. Theyfirst specify and estimate an empirical
model for CEOs’ optimal portfolio holdings of equity incentives in year t−1. The residuals from this model proxy for the deviation from optimal holdings. They then use these residuals as an explanatory variable when studying the determinants of equity grants at time t. Recall that our theoretical model shows that our key prediction holds regardless of the current portfolio of the manager (Proposition ??). In particular, our model suggests that when firms are more affected by bankruptcy considerations, they will tend to use restricted stock regardless of the form of prior compensation. This justifies the cross-sectional approach that we use in our test.
2 5
To avoid outliers we removed 31 observations in which the CEO was granted more than 100 million dollars in stock or options in one year. Our estimates are essentially unaffected by this.
are significantly more popular than restricted stock, with an average stock option grant of $2.6 million compared to $475 thousand of restricted stock. The median restricted stock grant is 0.
We use three proxies for bankruptcy risk:
Altman’s Z-Score. This measure is defined (see Altman, 1968) as
Z = 1.2X1+ 1.4X2+ 3.3X3+ 0.6X4+ 1.0X5,
where X1 is net working capital scaled by assets, X2 is retained earnings scaled by assets, X3 is pre-tax earnings scaled by assets, X4 is market value of equity scaled by book liabilities, and X5 is sales scaled by assets.26 The average Z-Score in our sample is 4.55 (see Table 1).
The KMV-Merton Expected Default Probability. This measure applies the framework of Merton (1974), where the equity of the firm is a call option on the underlying value of the firm with a strike price equal to the face value of debt. The model defines the distance to default as the number of standard deviations by which the market value of the firm exceeds the face value of debt. This number is then plugged into a cumulative distribution function to calculate the probability of default for a specific horizon (see Duffie and Singleton, 2003). The difficulty lies in the fact that both the total value of the firm and its volatility are unobservable. These are inferred from the value of equity, the volatility of the equity, and several other observable variables by numerically solving a set of non-linear simultaneous equations. We estimate the KMV-Merton expected default probabilities for a one year horizon using the detailed algorithm given in Bharath and Shumway (2004), which is also similar to the method used in Vassalou and Xing (2004). The average KMV-Merton, one-year horizon expected default probability in our sample is 2.4% (see Table 1).
Standard and Poor’s Long Term Credit Rating. S&P credit ratings range from AAA (extremely strong capacity to meetfinancial obligations) to D (firm is in default). The values of long-term debt ratings in Compustat (data item 280) range from 2 (for AAA) to 27 (for D). Thus, a higher score corresponds to poorer creditwor-thiness.27 Credit ratings are only available for about 57% of our observations; thus
2 6For this measure, we restrict attention tofirms in which the Z-Score is non-negative. 2 7
Compustat does not assign a credit rating to the scores 3, 22, 25, and 26. The analysis presented below uses the Compustat score as is. We have also tried different ways to transform this coding into a schedule with no gaps. The results are materially the same.
tests using this measure are of significantly lower power. The average debt rating in our sample is 10.4, which corresponds to an S&P long term rating between BBB and BBB+.
6.3
Results
To get a preliminary look into our results we split the sample into two groups. In Group 1, with 4,073 observations, firms used restricted stock to compensate their CEO in a specific year, while in Group 2 (10,405 observations) they exclusively used stock options. Table 2 gives the mean, median and standard deviation of debt and liquidity measures for the two groups. The results show that companies in Group 1 have higher debt ratios and less favorable liquid asset positions. All differences in means are significant at the 1%. For instance, the average debt ratio of companies that compensate using restricted stock is 64%, as compared to 55% for firms that do not. The average current ratio of companies that use restricted stock is 1.76 compared to 2.24 for companies that only use options. These results suggest that companies that are more likely to go bankrupt tend to use more restrict stock.
To conduct a formal multivariate test of our hypothesis we employ two kinds of regression analyses. Thefirst are logistic regression which look at the likelihood that restricted stock is part of the compensation package as a function of the bankruptcy measures. The second set consists of OLS regressions relating the fraction of stock based compensation that consists of restricted stock to bankruptcy risk.
First is a set of three logistic regression models employing the three bankruptcy measures of the form
RSTi,t = α+βBKRPi,t+γ1V OLi,t+γ2SIZEi,t (17) +γ3M Bi,t+γ4DIV Y LDi,t+γ5RDi,t+γ6ROAi,t
+γ7RETi,t+γ8OW N ERSHIPi,t+γ9M T Ri,t+εi,t where:
RSTi,t = a dummy variable equal to 1 if firm i compensated its CEO using restricted stock in yeartand 0 otherwise.
BKRPi,t=the main explanatory variable. In each one of the three regressions we use one of the above three bankruptcy measures (Altman’s Z-Score, KMV-Merton, and S&P debt rating).