This chapter examines the use and merits of hierarchical clustering techniques in the context
of multi‐asset multi‐factor investing. In particular, it contrasts these techniques with several …

Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to
the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework …

This study compares a broad range of risk models for managing multi-asset portfolios. The
investment universe is extended to a range of systematic strategies with varying risk and …

We define and develop an approach for risk budgeting allocation--a risk diversification
portfolio strategy--where risk is measured using a dynamic time-consistent risk measure. For …

Risk driver contributions are key to understanding portfolio risk. Often, this is done by
decomposing portfolio volatility. This is problematic in the presence of non-elliptical …

Risk parity is an approach to investing that aims to balance risk evenly across assets within
a given universe. The aim of this study is to unify the most commonly-used approaches to …

Risk parity portfolio optimization, using expected shortfall as the risk measure, is
investigated when asset returns are fat-tailed and heteroscedastic. The conditional return …

Risk parity methods focused on volatility have gained traction in the last decade. A few
extensions have been proposed, including tail risk parity. The authors show that, at its limits …

We argue that most investable assets and strategies cluster into two broad groups:
productive and scarce. Intuitively, productive assets have high equity beta and positive carry …

What should investors do in the presence of economic regimes? Researchers and
practitioners usually address this topic from a tactical asset allocation point of view. In this …