Portfolio diversification using subspace factorizations

Successful investment management relies on allocating assets so as to beat the stock market. Asset classes are affected by different market dynamics or latent trends. These interactions are crucial to the successful allocation of monies. The seminal work on portfolio management by Markowitz prompts the adroit investment manager to consider the correlation between the assets in his portfolio and to vary his selection so as to optimize his riskreturn profile. The factor model, a popular model for the return generating process has been used for portfolio construction and assumes that there is a low rank representation of the stocks. In this work we contribute a new approach to portfolio diversification by comparing a recently developed clustering technique, SemiNMF, with a new sparse low-rank approximate factorization technique, Sparse-semiNMF, for clustering stocks into latent trend based groupings as opposed to the traditional sector based groupings. We evaluate these techniques using a diffusion model based on the Black-Scholes options pricing model. We conclude that Sparse-semiNMF outperforms semiNMF when applied to synthetic stocks as the contribution of each trend to each stock is more disjoint for Sparse-semiNMF than for semiNMF, in an inter-class sense, meaning that the underlying trends for each stock are more readily apparent, whilst preserving the accuracy of the factorization. We conclude that the trend-based asset classes generated by Sparse-semiNMF should be considered in the investment management process to reduce the risk in portfolio selection.