## Archive for December, 2009

### Incentive compensation

Friday, December 25th, 2009

Income from an asset, $X$, depends on manager decision $A$ and random factor $s$, so $X = f(A,s)$. Assume that managers are motivated by personal income $I(X)$, such that the action taken $A(I) = \arg\max_A{E_s(U(I(f(A,s)))}$ where $U$ is the manager’s utility function and $I$ is the incentive-compensation scheme.

The problem in incentive compensation (principle-agent theory) is that of finding $\arg\max_I{E_s(f(A(I),s)-I(X))}$, the incentive compensation scheme under which payoff to the owners is maximized. The inputs considered are the utility (including risk adversity) of the manager, $U$, and the relationship of effort to outcome, $f$.

By designing $I$, you want to maximize the incentive (the responsiveness of compensation to managerial effort) while minimizing the actual payoff, all while sharing risk so that the manager is not crippled by the risk involved.

Net-net, it seems to suggest that we don’t want managers that are too rich, since the manager needs to have a significant proportion of his wealth vested in the company (to align risk interests and prevent moral hazard) at the same time the owners are trying not to pay him too much, and hence limit his ownership of the company. In fact, it seems to me that an equitable arrangement always results in the manager’s percentage ownership of the company growing with time, an effect only partially offset by the growth in asset value as a whole. After all, what good reason can a manager give for not wanting to own more of the company they have control of?

The possibility of separating ownership from management is made possible by knowledge of responsiveness of managerial effort to reward (motivation, $A(I)$) and the responsiveness of asset income to managerial effort ($f$). This knowledge cannot be guaranteed to always be of a form that makes the separation possible.