The Triumph of Mediocrity: A Case Study of Naïve Beta

Abstract

In contrast to factor-based smart beta, diversification-based smart beta assumes that, seemingly naively, all investments are the same in some dimension. The four possible dimensions—portfolio weight, expected return, risk-adjusted return, and risk contribution—lead respectively to four naïve beta portfolios: equally weighted, minimum-variance, maximum-diversification, and risk parity portfolios. In this article, the authors show how these four portfolios outperform the capitalization-weighted S&P 500 Index due to their sector differences and, especially, the index’s aggressive shifts into specific sectors. Among the three naïve beta portfolios that use risk inputs as part of their portfolio construction, both minimum-variance and maximum-diversification portfolios tend to be highly concentrated in certain sectors. The authors develop an analytic framework based on a partitioned correlation matrix, modeling sectors as two groups (mostly defensive versus cyclical). The results shed light on material differences between the risk parity and optimized portfolios in their level of diversification. Empirical examples of sector portfolios within the universe of the S&P 500 Index show the triumph of naïve beta over the index, which suffers from strong sector biases and ill-timed allocation shifts.

TOPICS: Big data/machine learning, statistical methods, manager selection