Turning Tail Risks into Tailwinds

The Properties of Alpha Risk Parity Portfolios

“…The Sharpe ratio is the ratio of excess returns to annualized volatility. CVaR is the conditional value-at-risk for a quantile of [ 2 ]. Max drawdown is the maximum observed loss from peak to trough as a percentage of peak value [ 44 ].…”

“…Volatility and downside volatility are deviation measures [ 22 ]. Conditional value-at-risk [ 23 ] and the power-spectrum measure [ 2 ] are spectral risk measures [ 24 ] that can be applied to risk parity portfolios after proper centering. See [ 2 ] for a review of tail-risk measures and their application to risk parity portfolios with and without dependencies.…”

“…Minimizing volatility amounts to maximizing a quadratic von Neumann–Morgenstern expected utility function with expected returns. Minimizing a spectral risk measure amounts to maximizing an expected rank-based utility function [ 2 , 41 ].…”

“…Risk parity is a sensible choice for investors who know which assets to buy but do not wish to express views on expected returns across these assets. This approach can also be applied to baskets of systematic investment strategies [ 2 ].…”

Portfolio Optimization Constrained by Performance Attribution

“…Measures, such as VaR and CVaR, that focus on tail-risk became very popular as the result of the need to understand exposure to loss under 'extreme' market events. (See Gava et al (2021) for a recent study demonstrating that consideration of tail risk can suc-cessfully reduce sharp losses in multi-asset portfolios). However VaR has undesirable mathematical characteristics; except when the underlying random process is Gaussian, VaR is not a coherent risk measure as it lacks the properties of subadditivity and convexity (Artzner et al 1999).…”