Uncertainty in financial markets makes portfolio diversification a valuable tool to navigate difficult market conditions. Diversification is probably the only free lunch in finance. It is closely related to asset segmentation: different representations of portfolio diversification are derived depending on what is considered the atom of asset allocation (capital / risk / factor). Probably a single measurement cannot provide a comprehensive representation.
After reviewing the main metrics in the literature, we focus on entropy as a tool to represent portfolio diversification and on DAMS as representative of the so-called economic scenario methods. Then we introduce the concepts of available diversification and diversification curves, we critically analyse diversification measures through single-period optimisations, out-of-sample back-testing in multi-period investments, and Monte Carlo simulations to evaluate their robustness with respect to estimation risk of asset volatility and correlation. We introduce a framework to reconcile a fully diversified risk parity-like portfolio with a fundamental-based high-conviction strategy. The two allocations are connected by a constrained entropy-maximisation process that makes it possible to swap a portion of portfolio return with extra diversification. We finally present a new approach that is able to separate diversification in asset-idiosyncratic risk from factor diversification; while the former is quantified by the entropy in asset risk contribution, the second is reinterpreted in terms of the DAMS framework.
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