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<p>This study evaluates the Wasserstein distance — a metric rooted in optimal transport theory — as a distribution-aware feature input to financial price forecasting and as a dissimilarity input to the Hierarchical Risk Parity (HRP) portfolio construction framework. Using thirty financial assets, comprising nineteen commodity futures and eleven sector or industry exchange-traded funds (ETFs) sponsored by State Street Global Advisors, BlackRock, and Vanguard, we compute 1- and 2-Wasserstein distances over rolling windows and compare them against Minkowski-family and correlation-based distance measures. Decision-tree forecasters of next-day log returns are tuned by Bayesian optimisation and explained with SHAP, LIME, and permutation importance; the forecasting comparison contrasts Wasserstein feature packs against the original-dataset baseline and against the canonical technical-indicator pack (moving averages, RSI, Bollinger-Band width). In the portfolio experiment, HRP portfolios driven by Wasserstein distances are compared with a strengthened benchmark suite consisting of the equal-weight 1/<i>N</i> portfolio, the covariance-based Risk-Parity portfolio, and Mean–Variance optimisation under both Sharpe and Minimum-Risk objectives, on Sharpe, Sortino, Maximum Drawdown, Ulcer Performance Index, and Outlier Win Ratio. A regime-specific robustness analysis partitions the out-of-sample window into three economically distinct sub-periods — the 2020 Pandemic Shock, the 2021 Reflation, and the 2022 – mid-2023 Quantitative Tightening cycle — to evaluate which strategies are robust to which form of market stress. The originality of the paper is the systematic empirical comparison of optimal-transport-based features and covariance-based allocations against the strengthened benchmark suite, with regime-conditional decomposition that makes the source of any performance differential explicit.</p>

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Wasserstein Distance-Based Feature Engineering for Enhancing Forecasting and Asset Allocation Insights

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  • 发表日期：

    2026年5月27日

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  • Insu Choi

摘要

This study evaluates the Wasserstein distance — a metric rooted in optimal transport theory — as a distribution-aware feature input to financial price forecasting and as a dissimilarity input to the Hierarchical Risk Parity (HRP) portfolio construction framework. Using thirty financial assets, comprising nineteen commodity futures and eleven sector or industry exchange-traded funds (ETFs) sponsored by State Street Global Advisors, BlackRock, and Vanguard, we compute 1- and 2-Wasserstein distances over rolling windows and compare them against Minkowski-family and correlation-based distance measures. Decision-tree forecasters of next-day log returns are tuned by Bayesian optimisation and explained with SHAP, LIME, and permutation importance; the forecasting comparison contrasts Wasserstein feature packs against the original-dataset baseline and against the canonical technical-indicator pack (moving averages, RSI, Bollinger-Band width). In the portfolio experiment, HRP portfolios driven by Wasserstein distances are compared with a strengthened benchmark suite consisting of the equal-weight 1/N portfolio, the covariance-based Risk-Parity portfolio, and Mean–Variance optimisation under both Sharpe and Minimum-Risk objectives, on Sharpe, Sortino, Maximum Drawdown, Ulcer Performance Index, and Outlier Win Ratio. A regime-specific robustness analysis partitions the out-of-sample window into three economically distinct sub-periods — the 2020 Pandemic Shock, the 2021 Reflation, and the 2022 – mid-2023 Quantitative Tightening cycle — to evaluate which strategies are robust to which form of market stress. The originality of the paper is the systematic empirical comparison of optimal-transport-based features and covariance-based allocations against the strengthened benchmark suite, with regime-conditional decomposition that makes the source of any performance differential explicit.