Block-Structured Covariance matrix for Portfolios Construction

Accurate covariance matrix estimation is critical to portfolio construction yet classical sample estimators fail in high dimensional settings. We pro- pose a parsimonious block structured estimator that models the matrix logarithm of asset returns in disjoint blocks (within block covariances determined by two parameters and between block links captured by a low dimensional, factor-weighted cosine similarity) and ensures global positive definiteness through the matrix exponential map. This approach reduces the number of free parameters to 2 + d, where d denotes the number of block-level factors, while preserving the full block covariance structure upon exponentiation. Building on this estimator, we design a minimum variance strategy, min block, and evaluate its out of sample performance over a rolling 120-month window for 500 randomly selected A share stocks from July 2013 to June 2023. Across a range of performance measures and under several proportional trading-cost scenarios, the min-block strategy delivers a cost-free cumulative return of 566.9% and tops the Sharpe ranking at 0.235. Even after accounting for realistic trading costs, it sustains strong risk-adjusted results with only moderate turnover. These findings confirm that leveraging latent block structure through log-covariance modeling significantly enhances both estimation stability and portfolio outcomes in large-scale equity markets.