We measure the contributions to risk of a set of factors, strategies, or investments, based on "Minimum-Torsion Bets", namely a set of uncorrelated factors, optimized to closely track the factors used to allocate the portfolio. We then introduce a novel definition of contributions to risk, which...

This book provides a comprehensive treatment of all the steps of asset allocation: detecting the market invariants; estimating the invariants' distribution; modeling the market at any horizon; defining optimality; accounting for estimation- and model-risk; including the practitioner's experience...