Conformal Predictive Portfolio Selection

Masahiro Kato. 2024. Presented at the JAFEE 2024 winter meeting. Preprint (arXiv:2410.16333). 日本語版

Conformal Predictive Portfolio Selection (CPPS) predicts future portfolio returns, builds a prediction interval for each candidate with conformal prediction, and picks the allocation from those intervals. A choice made from point predictions alone leaves the uncertainty of the prediction model out of the decision, and CPPS brings it in.

The problem

Many methods for portfolio selection, from the mean-variance approach to quantile-based ones, estimate features of the return distribution from past data with a prediction model and then act on the estimate. Those predictions carry error, and the size of the error differs from model to model. If the allocation is set without asking how large a loss a wrong prediction can produce, the choice is left undefended against model uncertainty.

The proposed method

For each candidate portfolio, the framework predicts the future return and computes a prediction interval with conformal prediction. The portfolio is then selected from the interval rather than from the point prediction. Conformal prediction does not look inside the prediction model, so the construction combines with autoregressive models, random forests, neural networks, and a wide range of other predictors.

Main results and conditions

An implementation built on an autoregressive model demonstrates that the framework works, and an empirical analysis examines how it behaves. The coverage guarantee of conformal prediction rests on conditions such as exchangeability of the data. Financial time series shift in distribution, so live use assumes that the validity of the intervals is checked continuously.

Relation to earlier work

The theory of portfolio selection begins with Markowitz's mean-variance analysis (1952, Portfolio Selection). Conformal prediction, which attaches a guarantee to a prediction interval without distributional assumptions, has become usable on time series whose distribution shifts, thanks to adaptive methods such as that of Gibbs and Candès (2021, Adaptive Conformal Inference Under Distribution Shift). Our contribution is to join those two lines and feed predictive uncertainty into portfolio selection as an interval that carries a guarantee.

Where it applies

The setting we have in mind is a desk that already runs a return prediction model and wants to manage how much that model's hits and misses move the allocation. Since the construction does not depend on the model, it can be fitted to an existing prediction pipeline after the fact.

Paper and materials

BibTeX

@inproceedings{conformal-predictive-portfolio-selection,
  author       = {Masahiro Kato},
  title        = {Conformal Predictive Portfolio Selection},
  year         = {2024},
  booktitle    = {JAFEE 2024 Winter Meeting},
  eprint       = {2410.16333},
  archivePrefix = {arXiv},
  url          = {https://arxiv.org/abs/2410.16333},
}