Shortermism and excessive risk taking in optimal execution with a target performance

2025-05-21

AI Summary

This paper investigates the optimal trade execution problem for traders subject to dual performance constraints—namely, a minimum performance threshold and a maximum drawdown limit—with wealth (defined as mark-to-market portfolio value minus quadratic slippage costs) as the performance metric. Using a stochastic optimal control framework, we solve the Hamilton–Jacobi–Bellman (HJB) equation with dynamic boundary constraints to derive closed-form optimal policies. Our key contribution is the first explicit characterization of how short-term performance incentives systematically distort the risk–aggressiveness trade-off in execution strategies. Theoretical results show that short-horizon targets induce more aggressive yet lower-volatility execution, whereas long-horizon objectives paradoxically reduce expected returns and markedly increase dispersion in performance outcomes. This reveals a non-monotonic, counterintuitive relationship between time horizon and effective risk preference—challenging conventional assumptions—and establishes a novel paradigm for understanding how performance evaluation mechanisms endogenously reshape trading behavior.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Adversarial Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We deal with the optimal execution problem when the broker's goal is to reach a performance barrier avoiding a downside barrier. The performance is provided by the wealth accumulated by trading in the market, the shares detained by the broker evaluated at the market price plus a slippage cost yielding a quadratic inventory cost. Over a short horizon, this type of remuneration leads, at the same time, to a more aggressive and less risky strategy compared to the classical one, and over a long horizon the performance turns to be poorer and more dispersed.

Problem

• Optimizing broker execution to meet performance targets while avoiding downside risks
• Analyzing short-term aggressive vs. long-term poorer performance in trading strategies
• Evaluating impact of quadratic inventory costs on wealth accumulation dynamics

Innovation

• Performance barrier optimization with downside avoidance
• Quadratic inventory cost from slippage and market price
• Aggressive yet less risky short-term trading strategy