Abstract: Moral hazard and adverse selection, sometimes referred to hidden actions and hidden information, have always been the focus of principal-agent theory, and also the core problem in the design of corporate compensation contract. But most study described the hidden information from the perspectives of output and cost, which were not comprehensive enough.
In this paper, the hidden information of the agent is described from the perspective of the ability to control over profit risk, and the optimal compensation contract design is also explored under a single contract situation and two contracts situation.and the explicit optimal solutions are solved. The results show that, compared with the case of a single contract, the agents with different abilities under the two contract conditions would achieve the separation equilibrium, and the shareholders get higher expect return. The incentive of the contract to the managers with low abilities would decrease, while the incentive to the managers with high abilities would increase, but the utility would be distorted and decrease. It is also found that shareholders could design a single contract for high ability managers, but this method could fail when the proportion of local ability managers is too high, and designing two contracts would become the optimal choice again.
The research results are verified through numerical simulation, and the findings of this paper would be helpful to provide important reference of the compensation contracts designing for industries that attach importance to the risk controlling ability of managers, such as private equity funds.

Key words: moral hazard, adverse selection, incentive-compatible, contract