This paper presents a method to identify causal interactions between two time series. The largest eigenvalue follows a Tracy-Widom distribution, derived from a Coulomb gas model. This defines causal interactions as the pushing and pulling of the gas, measurable by the variability of the largest eigenvalue's explanatory power. The hypothesis that this setup applies to time series interactions was validated, with causality inferred from time lags. The standard deviation of the largest eigenvalue's explanatory power in lagged correlation matrices indicated the probability of causal interaction between time series. Contrasting with traditional methods that rely on forecasting or window-based parametric controls, this approach offers a novel definition of causality based on dynamic monitoring of tail events. Experimental validation with controlled trials and historical data shows that this method outperforms Granger's causality test in detecting structural changes in time series. Applications to stock returns and financial market data show the indicator's predictive capabilities regarding average stock return and realized volatility. Further validation with brokerage data confirms its effectiveness in inferring causal relationships in liquidity flows, highlighting its potential for market and liquidity risk management.

Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers of a portfolio in terms of its diversification dynamics. The proof relies on the Reichenbach Common Cause Principle, along with the fact that the sensitivities of portfolio constituents with respect to the common causal drivers are themselves causal. A conformal map preserves idiosyncratic diversification from the unconditional setting while optimizing systematic diversification on an embedded space of these sensitivities. Causal methodologies for combinatorial driver selection are presented, such as the use of Bayesian networks and correlation-based algorithms from Reichenbach's principle. Limitations of linear models in capturing causality are discussed, and included for completeness alongside more advanced models such as neural networks. Portfolio optimization methods are presented that map risk from the sensitivity space to other risk measures of interest. Finally, the work introduces a novel risk management framework based on Common Causal Manifolds, including both theoretical development and experimental validation. The sensitivity space is predicted along the common causal manifold, which is modeled as a causal time system. Sensitivities are forecasted using SDEs calibrated to data previously extracted from neural networks to move along the manifold via its tangent bundles. An optimization method is then proposed that accumulates information across future predicted tangent bundles on the common causal time system manifold. It aggregates sensitivity-based distance metrics along the trajectory to build a comprehensive sensitivity distance matrix. This matrix enables trajectory-wide optimal diversification, taking into account future dynamics.

Portfolio optimization is increasingly argued to require causally identified return predictors to avoid signal inversion and optimization failure. This paper reexamines this claim by studying when predictive signals yield viable efficient frontiers, even under structural misspecification. We show that causal identification is not necessary for portfolio efficiency within static mean-variance and closely related quadratic portfolio optimization frameworks. Instead, efficiency is governed by geometric sufficiency conditions on predictive signals: directional alignment, ranking preservation, and calibration. We formally decompose portfolio efficiency into these three components and show that miscalibration alone attenuates Sharpe ratios even when alignment and ranking are preserved. Robustness is characterized as smooth degradation rather than collapse, with explicit attenuation behavior and continuity of performance under increasing misspecification. The theoretical results are supported by simulations and empirical analysis. Empirical validation combines equity-based illustrations with a large global bond universe spanning multiple currencies, countries, sectors, maturities along the term structure, seniority classes, and credit ratings, together with high-dimensional stress tests, nonlinear data-generating processes, rolling-window analyses, covariance regularization, realistic portfolio constraints, and bootstrap-based statistical validation. Across these settings, optimization geometry remains well behaved whenever directional alignment is preserved. The results clarify the boundary between causality and portfolio optimization: causality may inform signal representation, but portfolio efficiency at the optimization stage is a geometric property conditional on a given representation.