Schr\"{o}dinger Risk Diversification Portfolio

TL;DR

This paper introduces the Schrödinger risk diversification portfolio, which employs quantum mechanics-inspired Schrödinger PCA to improve risk factor estimation and portfolio diversification, outperforming traditional methods.

Contribution

It proposes a novel Schrödinger PCA method for risk diversification, enhancing factor estimation accuracy in small or unevenly spaced data samples.

Findings

Outperforms conventional risk parity portfolios

Accurately estimates risk factors with limited data

Provides efficient risk diversification

Abstract

The mean-variance portfolio that considers the trade-off between expected return and risk has been widely used in the problem of asset allocation for multi-asset portfolios. However, since it is difficult to estimate the expected return and the out-of-sample performance of the mean-variance portfolio is poor, risk-based portfolio construction methods focusing only on risk have been proposed, and are attracting attention mainly in practice. In terms of risk, asset fluctuations that make up the portfolio are thought to have common factors behind them, and principal component analysis, which is a dimension reduction method, is applied to extract the factors. In this study, we propose the Schr\"{o}dinger risk diversification portfolio as a factor risk diversifying portfolio using Schr\"{o}dinger principal component analysis that applies the Schr\"{o}dinger equation in quantum mechanics. The Schr\"{o}dinger principal component analysis can accurately estimate the factors even if the sample points are unequally spaced or in a small number, thus we can make efficient risk diversification. The proposed method was verified to outperform the conventional risk parity and other risk diversification portfolio constructions.