Factor Models for Futures Contracts to Improve Estimation of the Correlation Matrix

Abstract: In this paper regularization of the correlation matrix between futures contracts is examined. With starting point in the recently established HPCA framework (Avellaneda, 2019), a couple of different extensions to the one-factor model is suggested. Extensions are made in terms of adjusting the model according to different cluster structures. The data consists of futures contracts on a wide variety of underlying assets. Naturally they can be partitioned by asset class, asset sub class and/or region. The considered asset classes are equities, bonds, FX and commodities. Equities, bonds and FX are further partitioned by region - Europe, North/Latin America and Asia/Oceania. Commodities are partitioned into metals, energies and agriculturals. Metals are also divided into precious metals and industry metals, and agriculturals are divided into grains, livestock and miscellaneous agriculturals. These clusters are modelled both hierarchically and non-hierarchically where region is considered a second dimension rather than a child cluster. A completely different approach to HPCA is also presented, which is based on the assumption that sparseness in the eigenvectors is favourable. The proposed methods to modify the correlation matrix are evaluated with respect to ability of predicting eigenportfolio risk, interpretability/sparseness of eigenvectors and portfolio performance. Three different allocation methods are applied - minimum variance, mean-variance and equal risk contribution. All proposed methods turns out to predict eigenportfolio risk very well. Sparseness of the eigenvectors vary significantly between the different methods. The methods based on the sparseness-assumption turns out to perform best regarding Sharpe Ratio in portfolio performance.