Minimizing Volatility: Optimal Adjustment with Evolving Feasibility Constraints

TL;DR

This paper develops optimal decision rules for minimizing volatility and adjustment costs under evolving constraints, revealing that reference-based strategies significantly outperform heuristics in various economic settings.

Contribution

It introduces a framework for optimal adjustment with dynamic feasibility constraints, deriving explicit reference rules for different cost and constraint scenarios.

Findings

Optimal policies are reference rules minimizing distance to a target.

In the special case of random walk constraints, the target is the previous action.

Optimal rules can reduce quadratic variation and variance by 50% or more.

Abstract

Minimizing volatility and adjustment costs is of central importance in many economic environments, yet it is often complicated by evolving feasibility constraints. We study a decision maker who repeatedly selects an action from a stochastically evolving interval of feasible actions in order to minimize either average adjustment costs or variance. We show that for strictly convex adjustment costs (such as quadratic variation), the optimal decision rule is a reference rule in which the decision maker minimizes the distance to a target action. In general, the optimal target depends both on the previous action and the expectation of future constraints; but for the special case where the constraints follow a random walk, the optimal mechanism is to simply target the previous action. If the decision maker minimizes variance, the optimal policy is also a reference rule, but the target is a constant, which is not necessarily equal to the long-term average action. Compared to mid-point heuristics, these optimal rules may substantially reduce quadratic variation and variance, in natural environments by $50\%$ or more. Applied to stock market auctions, our results provide an explanation for the wide-spread use of reference price rules. We also apply our results to bilateral trade in over-the-counter markets, capacity planning in supply chains, and positioning in political agenda setting.