Maximizing an equity portfolio excess growth rate: a new form of smart beta strategy?

Abstract

It has been claimed that, for dynamic investment strategies, the simple act of rebalancing a portfolio can be a source of additional performance, sometimes referred to as the volatility pumping effect or the diversification bonus because volatility and diversification turn out to be key drivers of the portfolio performance. Stochastic portfolio theory suggests that the portfolio excess growth rate, defined as the difference between the portfolio expected growth rate and the weighted-average expected growth rate of the assets in the portfolio, is an important component of this additional performance (see Fernholz [Stochastic Portfolio Theory, 2002 (Springer)]). In this context, one might wonder whether maximizing a portfolio excess growth rate would lead to an improvement in the portfolio performance or risk-adjusted performance. This paper provides a thorough empirical analysis of the maximization of an equity portfolio excess growth rate in a portfolio construction context for individual stocks. In out-of-sample empirical tests conducted on individual stocks from 4 different regions (US, UK, Eurozone and Japan), we find that portfolios that maximize the excess growth rate are characterized by a strong negative exposure to the low volatility factor and a higher than 1 exposure to the market factor, implying that such portfolios are attractive alternatives to competing smart portfolios in markets where the low volatility anomaly does not hold (e.g. in the UK, or in rising interest rate scenarios) or in bull market environments.

Keywords:

• Portfolio construction
• Diversification
• Excess growth rate
• Stochastic portfolio theory

Acknowledgments

We would like to express our gratitude to two anonymous referees for their most useful comments, which have allowed us to improve the quality of our paper. We thank Vincent Milhau for fruitful discussions and Mikheil Esakia for providing us with database assistance.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 MVR stands for Maximum Volatility Return and our definition is derived from Mantilla-Garcia (2016) portfolio excess growth rate optimization problem.

2 $\parallel \cdot \parallel$ denotes the euclidian norm.

3 As for the Max $g^{\star }$ portfolio, the analytical solution of the MVR portfolio can lead to possibly negative weights, so in our long-only framework we have to compute the solution numerically.

4 Cauchy-Schwarz inequality states that for any two vectors $(x_1,\dots ,x_{n_t})$ and $(y_1,\dots ,y_{n_t})$, we have $(\sum _i{x}_i{y}_i{)}^2\le (\sum _i{x}_i^2)\times (\sum _i{y}_i^2)$. Equality is achieved if, and only if, one of the two vectors is zero or the two vectors are parallel. Here, we take $y_i=1$.

5 The data for the US region is extracted from CRSP. See www.scientificbeta.com for more details.

Additional information

Funding

This project is sponsored by BdF Gestion in the context of the “Maximizing and Harvesting the Rebalancing Premium in Equity Markets” research chair at EDHEC-Risk Institute.