Managerial remuneration - The risk incentive tradeoff

The perfect incentive schemes: The classic risk / incentive models

Among the first theorists to treat the manager-stockholder conflict with mathematics where Ross [1973] and Mirrlees [1974, 1976], who studied the risk / incentive trade-off, between managers and shareholders. In their model the shareholders’ problem is to design a wage contract or mechanism that induces the manager to maximize stock value. This problem have become classic in the principal-agency literature. The insight from this theory has no practical relevance because it is ceteris paribus. However, the theory is superior with respect to structuring our thoughts and it provides a good reference for the more realistic explanations that are presented in the next section. Hart and Holmström [1987] deliver the one version of this particular theory.

Hart and Holmström consider four cases. In all cases the agents and the principals are perfectly rational and they pursue utility maximization (full opportunism). The shareholders are assumed to be risk neutral. Normally, this is a terribly unrealistic assumption, but not in this case. It is reasonable to believe that the introduction of risk averse stockholders would not change the implications of the models as long as the risk aversion by the stockholders are significantly less than the risk aversion by the manager. Furthermore, it is realistic to expect that shareholders are less risk averse than managers because they are more capable of diversifying their portfolios and/or because managers may have a large portion of their wealth in the firm they manage (risk aversion normally increases by the share of ones wealth at risk). The assumption of risk neutral shareholders is therefore unimportant for the economics of the models. However, it is necessary to simplify the mathematics. The cases may be difficult to understand by readers who are not familiar with the principal-agent literature. However, the economics of the cases is also discussed and this should be easier to follow.

CASE 1: The shareholders have full information (perfect monitoring) about management effort. This case is trivial. The shareholders can implement the profit maximizing optimum by threatening with severe punishment, should the manager not render the efficient level of effort. Furthermore, because the manager is risk averse the optimal wage contract will have to pay the manager at a fixed salary (full insurance) equal to his reservation salary evaluated at the optimal level of effort.[1]

CASE 2: Now, the manager is risk neutral, but the shareholders only observe profit. They cannot observe the manager’s effort level. This is, asymmetric information. The optimal solution is to design a wage contract that pays the manager the entire profit, less a fixed amount equal to the expected total profit, less the manager’s reservation salary. In effect, the manager is made the residual claimant of the firm’s profit, as if he was the sole owner of the firm (no insurance). On average, the manager gets his reservation salary only if he chooses the efficient level of effort. Therefore, the solution is first best like it was in case 1.

CASE 3: Now, the manager is assumed to be infinitely risk averse, and the shareholders remain unable to observe manager effort (asymmetric information). An implication of infinite risk aversion is that the manager will avoid any risk at any cost in mean return. This outlaw wage contracts that tries to induce higher effort by higher pay for higher profit. Therefore, the principal can do no better than paying the manager a constant salary (full insurance) equal to the reservation salary evaluated at the minimum effort level. Note that the agent always chooses the minimum effort level because he knows that the principal cannot observe it. The outcome of this model is clearly second best.

CASE 4: Now, the manager is assumed to be normally risk averse and the shareholders can still not observe manager effort, only profit (asymmetric information). These are very sensible assumptions why this case is the most interesting from an economic point of view. The best possible solution is to make the wage an increasing function of profit in order to induce profitable effort levels. Unfortunately, this makes the salary risky, and the agent will suffer a utility loss by not being fully insured. The wage contract will have to compensate the agent for this loss.

Comparing the models with asymmetric information (case 2,3, and 4), it can be proved that case 4 is the situation between the to extremes; case 3 (infinite risk aversion, constant salary, minimum effort) and case 2 (risk neutrality, residual payment, social efficient effort). Case 4 has medium risk aversion, a profit dependent salary, and the manager exert an effort below the socially efficient but above the minimum level. Furthermore, case 1 and 2 are first best solutions to the principal-agent problem, and case 3 and 4 are second best. However, case 4 is superior to 3 because although the manager is indifferent, the principal makes a net gain on the agent’s higher effort.

What is the economics to be learned from the above cases? One thing is that a fundamental dilemma exists between providing incentives and avoiding risk. Perfect incentives (this is full ownership or complete residual payment) can only be provided at a major cost of risk, and a complete avoidance of risk (this is no ownership or a fixed payment) leaves us with no incentives. The cases further illustrate that if there is a significant and positive correlation between the manager effort and the profit of the firm, then it is a good idea to make the salary of the manager an increasing function of the firm’s profit. The reason is that we would expect people to be in control of their own effort and to desire more money. In other words, higher effort =>higher profit =>higher salary, and this incentive scheme is efficient for both parties if 1) the manager’s loss in utility from increased effort is less than the gain in utility from increased salary, and 2) if the shareholder’s gains in profits are higher than the loss from increased salary payments.

The principal-agent theory applies the C.P. approach and this raises a lot of practical questions. For example, how does the salary become an increasing function of profit, and how is the optimal balance between risk and incentives determined? It also raises the question of how compensation schemes are designed so that they simultaneously consider not only risk and pecuniary incentives, but also other relevant factors. These questions are treated in the following subsections. The discussion ignores the issue of taxes because they differ too much between countries and because tax laws change all the time, thus making old arguments worthless.

[1] The reservation salary is the salary he could get by redeploying his resources at the best alternative use.