The Theoretical Properties of Novel Risk-Based Asset Allocation Strategies using Portfolio Volatility and Kurtosis

The theoretical properties of novel risk-based asset allocation approaches considering the portfolio kurtosis (proxied by the fourth root of the portfolio fourth moment) exclusively or combined with volatility in the reference risk measure are developed. The properties of this mixed risk measure are analyzed and its outcomes, when implemented in the typical risk-based allocation strategies, are compared with those from the standard polynomial goal programming (PGP), either in its standard form or in a novel version, specifically designed to account for the rationale of the risk-parity allocation approach. From this, an interesting and original interpretation of the PGP as a risk-based asset allocation approach can be learnt. The novel risk-based asset allocation approaches are then applied primarily in-sample to provide validation and secondarily out-of-sample to learn their “behavioural characteristics” when they are implemented within an equity investment universe using datasets of monthly and weekly returns from July 2002 to June 2022. This paper extends the existing literature by identifying and demonstrating analytically the clear hierarchy of portfolio kurtosis that, in an increasing order, starts with the Minimum Kurtosis strategy, goes through the Kurtosis-based Risk Parity and arrives to the Equally Weighted Strategy.