A trip into the Clusterverse: Comparing Covariance Matrix Clustering in Portfolio Optimization

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Bartel, M., & Stöckl, S. (2020). A trip into the Clusterverse: Comparing Covariance Matrix Clustering in Portfolio Optimization. Presented at the 35th Workshop of the Austrian Woring Group on Banking and Finance, Virtual Conference.

Publication type

Presentation at Scholarly Conference


Buidling on prior success of clustering approaches, we comprehensively investigate (dis-)advantages of clustering in covariance matrices. The goal is to combine distinct pioneer work in the covariance clustering literature and to close knowledge gaps in the remaining space. Instead of using few algorithms, feature dimensions and portfolio optimizations we reach a reasonable maximum of potential combinations. Additionally, we investigate whether aggregating models outperforms individual models. We comprehensively apply and compare the performance of modern machine learning clustering methodologies targeting the covariance matrix. As a first step, assets are clustered using three different clustering algorithms: affinity propagation, ward hierarchical clustering and agglomerative clustering. As a second step, the clustering is applied in popular portfolio optimization techniques. The clustering is performed on the 1/N, sample-based mean-variance, minimum variance and MacKinlay and Pastor’s (2000) missing-factor portfolios, both with and without short sale constraints. Additionally, mixtures and aggregations of the different models are investigated. The resulting portfolio performance is compared to the shrinkage benchmark. Evaluation criteria are the out-of-sample Sharpe ratio and certainty equivalent returns. Using S&P 500 returns from 1970 to 2019, we demonstrate that clustering techniques significantly stabilize the optimization process and resulting portfolios outperform out-of-sample.


Organizational Units

  • Chair in Finance