Effort, Idiosyncratic Risk and Investment Under Uncertainty
This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.