Pay More Stocks and Options to Directors? Theory and Evidence of Board Compensation

Abstract

The compensation of board directors has received much attention, along with the growing debates on corporate governance in recent years, partly due to the ongoing financial crisis. While prior studies including Hall and Liebman (1998) have shown evidence of a dramatic increase in the use of equity-based incentives, resulting in an increase in the sensitivity of executive pay to firm performance, we ask whether it benefits shareholders to offer similar incentive contracts to board directors. This paper suggests that equity-based compensation for board directors is necessary and the level of incentives depends on directors’ effectiveness in monitoring and friendliness in advising CEOs. Using the market competition and pay correlation to proxy for monitoring effectiveness and advisory friendliness, we report empirical evidence supporting our hypotheses.

IBM is cutting off stock option grants to its board of directors but doubling their cash pay, calling the move an improvement in its governance practices. “We think it’s a sound principle of governance,” IBM spokesman John Bukovinsky said. “Less reliance on stock options is conducive to encouraging longer-term strategic decisions.”

– USA Today (December 21, 2006)

Appendix

We formally develop a model to provide theoretical support for the hypothesis. This model is a one-principal and two-agents model based on the standard principal-agent problem of Holmstrom and Milgrom (1987). The time sequence of this 2-period game is the following. At time 0, shareholders design one compensation contract $\{ {\phi_m},{\alpha_m}\}$ for the manager and another compensation contract $\{ {\phi_d},{\alpha_d}\}$ for the outside director. The sharing rules are restricted to the firm’s total final cash flow: ${\alpha_m} \in [0,1]$ and ${\alpha_d} \in [0,1]$. At time 1, the manager exerts effort ${a_m}$ to make business decisions and the outside director exerts effort ${a_d}$ to monitor the manager. At Time 2, terminal cashflow $x$ is realized and all claims are settled.

The manager (agent 1) is risk-averse and works as a CEO for a firm owned by a representative shareholder (principal) who is risk-neutral. The director (agent 2) is also risk-averse and works for the same firm. The firm’s final cash flow or profit is $x$ after deducting initial investment $I$, and it is the sum of manager’s effort ${a_m}$, the director’s effort ${a_d}$ and a noise $\varepsilon$ term which is normally distributed with mean zero and variance ${\sigma^2}$: $x = {a_m} + \rho {a_d} - I + \varepsilon$. Here, $\rho \in [0,1]$ is a measure of the monitoring effectiveness by the director, $\rho = 1$ being very effective and $\rho = 0$ having no impact on firm’s outcome. For simplification purposes, we assume zero initial investment cost: $I = 0$, the profit function then can be rewritten as: $x = {a_m} + \rho {a_d} + \varepsilon$.

The manager has an exponential utility function, which depends on the final wealth, the cost of effort and how friendly the director is to the manager: ${U_m}({w_m},{a_m},{a_d}) = - {e^{{ - {\gamma_m}\left( {{w_m} - \frac{{{c_m}}}{2}{a_m}^2 + \beta {a_d}} \right)}}}$, where ${\gamma_m}$ is risk-aversion coefficient, ${a_m}$ is manager’s effort, ${c_m} > 0$ is manager’s cost of effort, ${a_d}$ is the director’s effort, $\beta \in [ - 1,1]$ is a measure of cooperation between the manager and the director or how friendly the director is to the manager in terms of exchanging information and providing advices, and ${w_m}$ is total wealth of the manager including wage $\phi$ and equity (of both stock and option) compensation. With a linear contract as in Holmstrom and Milgrom (1987), the equity compensation can be modeled as a performance based compensation or as a profit-sharing rule ${\alpha_m}$: ${w_m} = {\phi_m} + {\alpha_m}x$. The manager receives ${\alpha_m}$ fraction of the firm’s profit. The manager’s objective function is his certainty equivalent wealth:

$$ {\phi_m} + {\alpha_m}x - \frac{{{c_m}}}{2}{a_m}^2 + \beta {a_d} - \frac{{{\gamma_m}}}{2}{\alpha_m}{\sigma^2} $$

(1)

The manager (agent 1)’s problem is to choose her effort level ${a_m}$ to maximize his certainty equivalent wealth minus the cost of effort and unfriendliness from the director:

$$ \mathop{{Max}}\limits_{{{a_m}}} \left( {{\phi_m} + {\alpha_m}x - \frac{{{c_m}}}{2}{a_m}^2 + \beta {a_d} - \frac{{{\gamma_m}}}{2}{\alpha_m}{\sigma^2}} \right) $$

(2)

The director has an exponential utility function, which depends on the final wealth and the cost of effort: ${U_d}({w_m},{a_d}) = - {e^{{ - {\gamma_d}\left( {{w_d} - \frac{{{c_d}}}{2}{a_d}^2} \right)}}}$, where ${\gamma_d}$ is risk-aversion coefficient, ${a_d}$ is the director’s effort, ${c_d} > 0$ is the director’s cost of effort, and ${w_d}$ is total wealth of the director including wage $\phi$ and equity compensations. With a linear contract the equity compensation can be modeled as: ${w_d} = {\phi_d} + {\alpha_d}x$. The director receives ${\alpha_d}$ fraction of the firm’s profit. The director’s objective function is his certainty equivalent wealth:

$$ {\phi_d} + {\alpha_d}x - \frac{{{c_d}}}{2}{a_d}^2 - \frac{{{\gamma_d}}}{2}{\alpha_d}{\sigma^2} $$

(3)

The director (agent 2’s) problem is to choose her effort level ${a_d}$ to maximize his certainty equivalent wealth minus the cost of effort:

$$ \mathop{{Max}}\limits_{{{a_d}}} \left( {{\phi_d} + {\alpha_d}x - \frac{{{c_d}}}{2}{a_d}^2 - \frac{{{\gamma_d}}}{2}{\alpha_d}{\sigma^2}} \right) $$

(4)

The representative shareholder (principal’s) problem is to choose the manager’s profit-sharing rule ${\alpha_m}$ and the director’s profit-sharing rule ${\alpha_d}$ to maximize his final payoff subject to incentive compatibility (IC) and participation constraint (PC):

$$ \mathop{{Max}}\limits_{\alpha } E\left[ {x - \left( {{\phi_m} + {\alpha_m}x + {\phi_d} + {\alpha_d}x} \right)} \right] $$

(5)

s.t. ${a_m} \in \arg \max \left( {{\phi_m} + {\alpha_m}x - \frac{{{c_m}}}{2}{a_m}^2 + \beta {a_d} - \frac{{{\gamma_m}}}{2}{\alpha_m}{\sigma^2}} \right)$ (IC1)

$$ {a_d} \in \arg \max \left( {{\phi_d} + {\alpha_d}x - \frac{{{c_d}}}{2}{a_d}^2 - \frac{{{\gamma_d}}}{2}{\alpha_d}{\sigma^2}} \right) $$

(IC2)

$$ {\phi_m} + {\alpha_m}x - \frac{{{c_m}}}{2}{a_m}^2 + \beta {a_d} - \frac{{{\gamma_m}}}{2}{\alpha_m}{\sigma^2} \ge \underline {{W_m}} $$

(PC1)

$$ {\phi_d} + {\alpha_d}x - \frac{{{c_d}}}{2}{a_d}^2 - \frac{{{\gamma_d}}}{2}{\alpha_d}{\sigma^2} \ge \underline {{W_d}} $$

(PC2)

where $\underline {{W_m}}$ and $\underline {{W_d}}$ are the minimum utility level from outside opportunity for manager and director respectively; these two participation constraints always bound such that the inequality becomes equality.

The solutions, comparative statistics and proofs can be found in Dong (2012), and the optimal contract of directors implies: (1) The board director’s equity-based compensation (modeled as profit sharing rule) is positive related to his effectiveness of monitoring and friendliness in advising the CEO; (2) The relationship between the effectiveness of monitoring and the friendliness in advising is negative and convex. This result is similar to Kumar and Sivaramakrishnan (2008) and Adams and Ferreira (2007) which conclude that shareholders can sometime be better off with a friendly board.