Application of Copula Based Correlations and Mutual Information in Time Series Clustering and Enhanced Indexing by Adopting the Robust Optimization Approach

Enhanced index Tracker portfolio, as one of the investment management strategies, is trying to combine the benefits of both active and passive approaches. This research is going to provide a two-stage model that can first reproduce the index performance with a smaller number of index-forming shares and, secondly, calculate the Enhanced index tracker portfolio weights.

In the first step, using a binary mathematical programming model to create clustering of time series, an index tracker portfolio was created. Coppola-based correlation coefficients and mutual information were used as time series similarity measures at this stage. In the second stage, the weight of investment in the selected shares was determined in a way that the return on the portfolio surplus was maximized relative to the index created in the first stage. The uncertainty resulting from the estimation of the excess stock returns in the second phase was considered by using a robust optimization approach.

The results obtained by applying the out of sample test on the 50 more active companies in the Tehran Stock Exchange from the spring of the Iranian calendar year of 1394 to spring of 139, using the tracking error and market ratio, indicate that in addition to the success of the similarity criteria in time series clustering and index tracking, at a confidence level of 99%; Enhanced index Tracker portfolios based on normal, T and Clayton Copula correlation coefficients have a positive significant difference with the index.

According to this study, to develop an enhanced index tracker portfolio, it is practical to apply copula-based correlation coefficients and try a robust optimization approach to take into account the uncertainty of the parameters.