Portfolio optimization by price-to-earnings ratio network analysis

Abstract

This paper introduces Price-to-Earnings Ratio Network (PEN) analysis as an alternative to mean–variance analysis for portfolio optimization. The equivalence among Price-to-Earnings (P/E) ratios, node degree distribution and capital allocation distribution is established with a Havel–Hakimi network structure. Such equivalences allow network entropy to be a measure of portfolio diversification and robustness. Our empirical analysis finds a linear correlation between in-sample network entropy and out-of-sample portfolio returns. Then, a return-entropy efficient frontier is introduced to interpret the return-diversification trade-offs. Further, we compare the out-of-sample performance of portfolios optimized with PEN analysis against those optimized with mean–variance analysis, showing that PEN-optimized portfolios outperform mean–variance efficient portfolios in returns, given a low-to-medium P/E ratio level. This outcome accords with the P/E effect that stocks with low P/E ratios are undervalued and will provide increased returns in the future. In addition, regarding global financial risk events such as the financial crisis in 2008, the Euro debt crisis in 2013 and Brexit in 2016, this study finds that the PEN-optimized portfolio size increased significantly (even to more than 300 stocks) to mitigate systemic risk, while mean–variance efficient portfolios were not sufficiently diversified.