Risk Budgeting in Financial Firms and The Value of an Expert Opinion
We derive the optimal contract of a trader who (a) must privately exert costly effort in order to collect information and (b) may request a costly second opinion from management on a trading decision. We show that a risk limit is not a mere hard constraint on the action space of a trader; rather, it is a component of the optimal contract that helps overcome agency frictions. A risk budget functions as a policy that optimally determines which decisions can be fully delegated to the trader and which ones require further approval. Second opinions deliver multiple benefits to the principal: they are a cost-effective way to encourage more informed trading decisions, they allow for more efficient agency contracting, and their use is ex-post efficient as a substitute of renegotiation. As a result, the presence of moral hazard makes risk limits relatively more restrictive. Moreover, the model predicts that risk limits will be relaxed as the cost of accessing an expert second opinion increases, but tightened as the trader’s cost of providing accurate research increases, since in that case the agency problem worsens. Overall, the model rationalizes the increasingly common practice of “risk budgeting” at the trading desk level, where risk limits allow authorities to perform cost-effective monitoring.