Conformal Predictive Portfolio Selection
Masahiro Kato
TL;DR
The paper tackles uncertainty in forecasting future portfolio returns by proposing Conformal Predictive Portfolio Selection (CPPS), which builds $\widehat{C}^{\bm{w}}_T(X_{T+1})$ with coverage $1-\alpha$ for each candidate portfolio return $R_{T+1}(\bm{w})$ and selects $\widehat{\bm{w}}_{T+1}$ from a finite set $\mathcal{W}$. It provides a concrete HR-LR CPPS instantiation and develops AR-based and neural-network predictive intervals, along with a theoretical validity result for dependent data under a blocking permutation. Empirical tests on US and Japanese stock data show that Conformal (AR) and Conformal (NN) approaches achieve higher cumulative returns and greater stability than baselines like mean- and AR-based strategies, highlighting the practical benefits of interval-based portfolio decisions. The framework is model-free and adaptable to various predictive models, offering robust uncertainty-aware portfolio construction with potential extensions to fully multivariate conformal prediction in future work.
Abstract
This study examines portfolio selection using predictive models for portfolio returns. Portfolio selection is a fundamental task in finance, and a variety of methods have been developed to achieve this goal. For instance, the mean-variance approach constructs portfolios by balancing the trade-off between the mean and variance of asset returns, while the quantile-based approach optimizes portfolios by considering tail risk. These methods often depend on distributional information estimated from historical data using predictive models, each of which carries its own uncertainty. To address this, we propose a framework for predictive portfolio selection via conformal prediction , called \emph{Conformal Predictive Portfolio Selection} (CPPS). Our approach forecasts future portfolio returns, computes the corresponding prediction intervals, and selects the portfolio of interest based on these intervals. The framework is flexible and can accommodate a wide range of predictive models, including autoregressive (AR) models, random forests, and neural networks. We demonstrate the effectiveness of the CPPS framework by applying it to an AR model and validate its performance through empirical studies, showing that it delivers superior returns compared to simpler strategies.