Directional Structural Concentration and Downside Risk in Multi-Asset Portfolios

This study examines whether the directional organization of predictive relationships within a multi-asset portfolio contains information about subsequent downside risk beyond conventional diversification diagnostics. Using daily returns for 15 liquid U.S.-listed exchange-traded funds from 2014 to 2025, we construct rolling directed predictive networks and use a Hodge decomposition to obtain a global transmitter–receiver hierarchy. Its concentration is summarized by the normalized range of the gradient potential, Cϕ. Under the reference 126-trading-day first-order vector autoregressive specification, high-Cϕ states are followed by maximum drawdown losses approximately 1.65 percentage points larger over the subsequent 63 trading days than matched low-Cϕ states with similar volatility, average correlation, leading correlation-eigenvalue concentration, and diversification ratio. The association is stable across tested network densities but sensitive to matching tolerance, temporal specification, downside horizon, and market regime. A simple net-flow concentration measure reproduces a similarly strong association, indicating that directional imbalance is an important part of the underlying phenomenon, while residualized tests indicate that the Hodge hierarchy retains information not captured by a linear projection on that benchmark. The result is reproduced under an alternative Granger-type edge weighting but not under generalized forecast-error variance decomposition. Overall, directional structural concentration is best interpreted as a specification-dependent portfolio risk diagnostic for monitoring, stress testing, and discretionary risk budgeting rather than as a universal early-warning or trading signal.