Biased Risk Parity with Fractal Model of Risk

Abstract: For the past two decades investors have observed long memory and highly correlated behavior of asset classes that does not fit into the framework of Modern Portfolio Theory. Custom correlation and standard deviation estimators consider normal distribution of returns and market efficiency hypothesis. It forced investors to search more universal instruments of tail risk protection. One of the possible solutions is a naive risk parity strategy, which avoids estimation of expected returns and correlations. The authors develop the idea further and propose a fractal distribution of returns as a core. This class of distributions is more general as it does not imply strict limitations on risk evolution. The proposed model allows for modifying a rule for volatility estimation, thus, enhancing its explanatory power. It turns out that the latter improves the performance metrics of an investment portfolio over the ten year period. The fractal model of volatility plays a significant protective role during the periods of market abnormal drawdowns. Consequently, it may be useful for a wide range of asset managers which incorporate innovative risk models into globally allocated portfolios.