Risk parity portfolio optimization under a Markov regime-switching framework

Abstract

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.

Keywords:

• Risk parity
• Asset allocation
• Factor model
• Markov regime switching
• Robust optimization
• Uncertainty

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Giorgio Costa https://orcid.org/0000-0002-2119-5295

Roy H. Kwon http://orcid.org/0000-0002-0502-1607

Notes

1 The authors note the use of the word ‘nominal’ throughout this paper in the context of the Operations Research discipline, where it serves to differentiate a basis model from its robust counterpart. It should not be taken in the context of Economics, where it serves to differentiate between real and nominal values. Thus, the basic ERC model shall be referred to as the nominal.

2 An exception was made for the Telecommunications sector, as only three stocks had sufficient historical data available for our test.

3 The sample covariance matrix is based purely on the observed asset returns, directly computing the covariance of asset i against asset $j\mathrm{\forall }i,j$ from their respective observed historical returns.

4 For a detailed proof of Lemma 1 see Goldfarb and Iyengar (2003).

Additional information

Funding

This work was supported by MITACS [501616].