Execution Allocation Objectives and Sharpe Ratio Evaluation

Summary

The document asks why an order-execution strategy should not directly maximize its Sharpe ratio when choosing child-order placements. It summarizes a paper’s objective as expected return after transaction costs minus a variance penalty, then gives an adjusted Sharpe ratio as a way to evaluate the resulting execution strategy. The question observes that optimizing the objective and optimizing the ratio may select different placements.

No answer or comparison of the two optimization problems is included, and the paper’s assumptions are not developed here. The excerpt therefore identifies a useful distinction between an objective used to choose a strategy and a metric used to assess performance, but does not establish which criterion is preferable. Resolving the issue would require considering the objective’s risk-aversion scaling, the role of the risk-free rate, and how expected net returns and variance change across candidate placements.

Key ideas

• Child-order placement can be chosen by balancing expected net returns against return variance.
• The document presents an adjusted Sharpe ratio as an execution-performance measure.
• Maximizing a mean-minus-variance objective need not produce the same choice as maximizing a ratio.
• The excerpt poses the distinction but does not resolve which objective is preferable.
• Comparing the criteria requires assumptions about risk penalties and candidate strategy returns.

Tags

# Why not to maximize Sharpe Ratio directly when computing optimal allocation of an order?


# Why not to maximize Sharpe Ratio directly when computing optimal allocation of an order?












I was reading the following paper of Engle about balancing transaction costs performance and risk: https://www.nber.org/papers/w12165.pdf

He deals with finding the optimal placement of the child orders, and he does so maximizing a term akin to $$\max_{child \, order \, placement} (\mathbb{E}[Return - Transaction Costs] - Var(Return - Transaction Costs))$$.

He goes on stating that, from this, we can evaluate the effectiveness of our placement strategy by evaluating the Adjusted Sharpe Ratio:

$$\frac{\mathbb{E}[Return - Transaction Costs] - R_f}{\sqrt{Var(Return - Transaction Costs)}}.$$

My question is: if the metric used to evaluate the execution strategy is the Sharpe, why not maximize that in the first place? It seems to me that the two maximization problems in general lead to different results.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.