Risk Parity Strategies With Different Risk Measures

Risk parity has become an increasingly popular approach for portfolio con-struction within and across asset classes.In a nutshell,the goal of the method-ology is to ensure that the constituent assets have the same contribution to the overall risk of the portfolio.Risk parity is a meaningful and robust approach for building well-diversified portfolios,but it relies on historical volatility estimates,which penalises upside risk as well as downside risk and leads to a massive over-weighting of bonds versus equitries,even in a low yield environment.This article can be regarded as an attempt to address these two concerns via the introduc-tion of a.new class of risk parity strategies.We refer to them as " conditional risk parity"(CRP)strategies,in contrast to the standard "unconditional risk parity"(URP)strategies that are based upon historical volatility.In a first step,we recognize that the volatility of a bond is related to its duration,and that duration is a decreasing function of the bond yield.As a result,it is possible to construct a volatility estimate such that the bond weight in the RP portfolio is increasing in the yield.In a.second step,we define a new class of conditional RP portfolios with respect to downside risk measures such as semi-volatility,value-at-risk or expected shortfall.In this extension,the riskiness of an asset class is an explicit function of its expected return,and a lower expected return results in a higher risk,thus in a lower allocation in the risk parity portfolio.Duration-based volatility is an instantaneous and obsevable volatility bond measure that avoids the sample dependency and overweighting of bonds in a low interest rate environment,which inevitably follow from the use of historical volatility measures in the construction of risk parity portfolios.Risk parity portfolios constructed with a downside risk measure show a higher degree of sensitivity with respect to market conditions,and lead to further de-creases in bond allocation in a low yield environment compared to risk parity portfolios constructed on the basis of volatility as a risk measure.The maximum Sharpe ratio portfolio,which can be interpreted as a risk par-ity portfolio under some conditions(identical pairwise correlations and identical Sharpe ratios),is a less robust alternative to incorporating expected returns in the construction of a well-diversified policy portfolio.Overall our results show that CRP portfolios constructed from downside risk measures are more responsive to yield changes than are their URP counterparts,and also that they involve a lower allocation to bonds in a low yield environment,precisely when downside risk in bonds is higher.