The theoretical properties of novel risk-based asset allocation strategies using portfolio volatility and kurtosis

The properties of risk-based asset allocation approaches considering the portfolio kurtosis exclusively or combined with volatility in the reference risk measure are developed. This paper extends the existing literature by proving theoretically and empirically 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. The risk-based asset allocation approaches are first applied in sample to provide validation and then out-of-sample to learn their “behavioural characteristics” when they are implemented within an equity investment universe using datasets of monthly and weekly returns. In particular, the outcomes of the risk-based asset allocation strategies based on mixed risk measures are compared with those from the standard polynomial goal programming ( P G P ), 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 P G P as a risk-based asset allocation approach can be learned. • The properties of risk-based asset allocation approaches using volatility and kurtosis exclusively or combined are studied. • A novel risk measure based on a convex linear combination of both volatility and kurtosis is proposed. • The outcomes of the novel mixed risk measure are compared with those of the polynomial goal programming. • A novel version of the polynomial goal programming designed to account for the rational of the risk-based approach is proposed.