Kurtosis-based risk parity: methodology and portfolio effects

Abstract

In this paper, a risk parity strategy based on portfolio kurtosis as reference measure is introduced. This strategy allocates the asset weights in a portfolio in a manner that allows an homogeneous distribution of responsibility for portfolio returns' huge dispersion, since portfolio kurtosis puts more weight on extreme outcomes than standard deviation does. Therefore, the goal of the strategy is not the minimization of kurtosis, but rather its ‘fair diversification’ among assets. An original closed-form expression for portfolio kurtosis is devised to set up the optimization problem for this type of risk parity strategy. The latter is then compared with the one based on standard deviation by using data from a global equity investment universe and implementing an out-of-sample analysis. The kurtosis-based risk parity strategy has interesting portfolio effects, with lights and shadows. It outperforms the traditional risk parity according to main risk-adjusted performance measures. In terms of asset allocation solutions, it provides more unbalanced and more erratic portfolio weights (albeit without excluding any component) in comparison to those pertaining the traditional risk parity strategy.