High-Dimensional Monte Carlo Risk Attribution in Mean-Variance and Risk Parity Portfolios

This work presents a quantitative study of portfolio optimization under stochastic market dynamics using Monte Carlo simulation techniques. The paper investigates two widely used portfolio construction frameworks, namely classical Mean Variance Optimization and Risk Parity allocation, with an emphasis on risk attribution, robustness, and sensitivity to estimation error in high dimensional settings. Using historical daily equity return data, empirical estimates of expected returns and covariance structures are constructed and employed to generate optimized portfolios. Monte Carlo simulations based on multivariate normal return models are then used to evaluate portfolio behavior across a large ensemble of possible market realizations. This approach allows for an examination of dispersion, tail risk, and the dependence of portfolio outcomes on stochastic return paths beyond single historical backtests. The results demonstrate that while Mean Variance Optimized portfolios can achieve favorable risk adjusted performance under idealized assumptions, they exhibit significant sensitivity to estimation error and non stationarity in return generating processes. Risk Parity based allocations are discussed as a comparatively robust alternative that relies primarily on covariance structure rather than expected return forecasts. Overall, the study highlights the gap between theoretical optimality and empirical robustness in portfolio optimization and emphasizes the importance of simulation based stress testing when constructing portfolios in uncertain and evolving market environments. The work reflects an interdisciplinary perspective that draws on probabilistic modeling, linear algebra, and concepts commonly encountered in physics inspired approaches to complex systems.