On sparsity of eigenportfolios to reduce transaction cost

Abstract

Purpose – Transaction cost becomes significant when one holds many securities in a large portfolio where capital allocations are frequently rebalanced due to variations in non-stationary statistical characteristics of the asset returns. The purpose of this paper is to employ a sparsing method to sparse the eigenportfolios, so that the transaction cost can be reduced and without any loss of its performance. Design/methodology/approach – In this paper, the authors have designed pdf-optimized mid-tread Lloyd-Max quantizers based on the distribution of each eigenportfolio, and then employed them to sparse the eigenportfolios, so those small size orders may usually be ignored (sparsed), as the result, the trading costs have been reduced. Findings – The authors find that the sparsing technique addressed in this paper is methodic, easy to implement for large size portfolios and it offers significant reduction in transaction cost without any loss of performance. Originality/value – In this paper, the authors investigated the performance the sparsed eigenportfolios of stock returns in S&P500 Index. It is shown that the sparsing method is simple to implement and it provides high levels of sparsity without causing PNL loss. Therefore, transaction cost of managing a large size portfolio is reduced by employing such an efficient sparsity method.

Keywords

• transaction cost
• principal component analysis (pca)
• sparse matrix
• eigenportfolio
• karhunen-loeve transform (klt)
• midtread (zero-zone) pdf-optimized lloyd-max quantizer
• eigen decomposition