Smart Predict--then--Optimize Paradigm for Portfolio Optimization in Real Markets

TL;DR

This paper addresses the gap between forecast accuracy and portfolio decision quality under realistic trading frictions. It adopts the Smart Predict--then--Optimize (SPO) paradigm with linear predictors and several objective variants, training with the SPO$+$ loss $\mathcal{L}_{\mathrm{SPO+}}$ and robust extensions (RobustSPO) to align learning with downstream decisions. Through rolling-window backtests on US ETF data from 2015–2025, the authors show decision-focused SPO methods outperform traditional PtO and other baselines in risk-adjusted metrics and display resilience during the 2020 COVID crisis. The findings support the practical value of decision-focused learning for portfolio optimization in non-stationary markets, while highlighting trade-offs between aggressiveness and downside protection.

Abstract

Improvements in return forecast accuracy do not always lead to proportional improvements in portfolio decision quality, especially under realistic trading frictions and constraints. This paper adopts the Smart Predict--then--Optimize (SPO) paradigm for portfolio optimization in real markets, which explicitly aligns the learning objective with downstream portfolio decision quality rather than pointwise prediction accuracy. Within this paradigm, predictive models are trained using an SPO-based surrogate loss that directly reflects the performance of the resulting investment decisions. To preserve interpretability and robustness, we employ linear predictors built on return-based and technical-indicator features and integrate them with portfolio optimization models that incorporate transaction costs, turnover control, and regularization. We evaluate the proposed approach on U.S. ETF data (2015--2025) using a rolling-window backtest with monthly rebalancing. Empirical results show that decision-focused training consistently improves risk-adjusted performance over predict--then--optimize baselines and classical optimization benchmarks, and yields strong robustness during adverse market regimes (e.g., the 2020 COVID-19). These findings highlight the practical value of the Smart Predict--then--Optimize paradigm for portfolio optimization in realistic and non-stationary financial environments.

Figures (6)

• Figure 1: Overview of the Smart Predict--then--Optimize (SPO) training pipeline for portfolio optimization.
• Figure 2: Architecture of the SoftmaxDFL.
• Figure 3: Rolling-window backtesting protocol with monthly rebalancing and time-series validation.
• Figure 4: Cumulative net asset value (NAV) curves of all compared strategies over the full backtest period (2016--2024).
• Figure 5: Cumulative net asset value (NAV) trajectories of selected strategies during the COVID-19 market turmoil in 2020. The inset zooms in on the early crash period from January to April 2020. During this interval, the RobustSPO ($\rho=0.1$) and SPO+ with Fee strategies produce almost overlapping NAV paths, suggesting that these models arrive at highly similar portfolio decisions when facing severe market stress. This behavior indicates that, under extreme market conditions, the SPO+ with Fee solution is already sufficiently conservative due to binding constraints and transaction cost penalties, such that additional robustness does not alter the optimal allocation.