March 25, 2025

How Reservation Strategies Shape Optimal Trading

Introduction

When large orders hit the market, they don't just move prices — they introduce real risk. Traders must balance execution speed, price impact, and uncertainty about whether their trades will even go through as planned. In practice, brokers often don’t have full control. Clients impose reservation strategies like TWAP, VWAP, or Implementation Shortfall benchmarks, and brokers must follow them — but still want to do better.

A recent paper by Cheng, Guo, and Wang — “Optimal Order Execution Subject to Reservation Strategies under Execution Risk” (Xue Cheng, Peng Guo, Tai-Ho Wang, 2023) — explores how brokers can optimize execution under uncertainty, even when constrained by a client-imposed benchmark. The authors build on the classic Almgren–Chriss model, extending it to include order fill uncertainty — the risk that not all orders get executed as intended.

What’s the problem?

A broker receives a large order to buy or sell over a set time period. The client provides a reservation strategy — a benchmark path that the execution should follow. The broker wants to outperform this benchmark, but is exposed to:

Market impact (trading moves the price)
Execution risk (orders might partially fill)
Price volatility

The challenge is to find a strategy that manages these risks while still closely tracking the client's benchmark.

The solution: Utility Maximization

Instead of just minimizing cost or tracking error, the broker maximizes their expected utility of the difference between their execution result and the benchmark’s. This gives a more realistic goal: balancing returns with risk aversion.

The authors show that under certain conditions (e.g. constant uncertainty), there’s a closed-form solution to this problem. The optimal execution strategy depends on:

How far the broker is from the target position
How closely they follow the client’s benchmark
How friendly the market is to trading (captured by correlation ρ)
How risk-averse the broker is (parameter θ)

In simpler terms: the more uncertain or hostile the market, the more conservative the strategy should be. The more confident the fills, the more aggressively the broker can diverge from the benchmark to chase better outcomes. ## **When there’s no fill uncertainty**

When there’s no fill uncertainty

If execution risk disappears, the problem simplifies. The optimal strategy becomes deterministic — and the paper shows how any client reservation strategy can be approximated using two “building block” strategies:

Implementation Shortfall (IS): front-loaded execution, minimizes price risk
Target Close (TC): back-loaded execution, tracks closing price

Almost any reasonable benchmark can be expressed as a combination of IS and TC trajectories, which makes computation and interpretation much easier.

Key findings from simulations

Using Monte Carlo simulations, the authors compare their optimal strategy to a standard TWAP. The results are consistent:

The optimal strategy yields higher average P&L
It shows less volatility and better tail behavior (fewer extreme losses)
It holds up even in stress test conditions (high volatility, high fill risk, etc.)

Why this matters

This framework gives brokers a practical way to work within client constraints while still optimizing outcomes. It connects intuitive strategies (IS, TC) with a deeper structure, allowing brokers to design smarter execution paths — especially useful when execution risk is non-negligible.

About Axon Trade

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