Risk Budgeting in Financial Firms and The Value of an Expert Opinion

We analyze the role of risk limits in the provision of incentives to acquire valuable information for efficient risk management. We study the optimal contract of a trader who (a) must privately exert costly effort in order to collect information and (b) may have access to a costly second opinion from upper management on any trading decision. We show that a risk limit is not a mere hard constraint on the action space of a trader; rather, the optimal contract includes the use of a risk budget – a policy that optimally determines which decisions can be fully delegated to the trader and which ones require further approval, akin to an expert second opinion. Risk budgeting delivers multiple benefits to the principal: a cost-effective way to pursue more informed trading decisions, more efficient agency contracting, and the ex-post efficient use of a principal's validation as a substitute of renegotiation. As a result, the model predicts that risk limits will be set tighter as the agency problem gets worse, and more relaxed as the cost of accessing an expert second opinion from the principal increases. 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