Construction and Analysis of Multi-Index Financial Model

Abstract

This paper presents an empirical study of the expansion of the single-index model into a multi-index model with a careful selection of indices. A total of 91 multi-index models were built and tested using advanced statistical methods in the range from 2015 to 2018. This narrowed down the selection to 14 quality multi-index models which needed to be tested for the balance between simplicity and goodness of fit. Using the Akaike Information Criterion it was found that a seven-factor model provided the best trade-off between the two criteria. Nevertheless, it is up to the reader to decide what is of more importance, the fit quality or simplicity. Using the chi-square test, for the case of maximising the model quality benchmarked against the single-index model, a multi-index model has seen a reduction in chi-square value from 6588 to 4678. This model consisted of the market factor, 10 and 30- Year U.S. Treasury Bond, Gold, Oil, CMA and RMW which were proven to provide the most explanation behind the stock price movements as confirmed by the cited literature. Furthermore, this model was tested for its predictive power by testing it in the year 2019 which led to the conclusion that the model was overfitted due to the over-leniency of the Akaike Information Criterion and when it comes to predictiveness, a three-factor model is recommended. The last objective was to test the models in the extreme market events, so the range of 2020-2021 was selected which had unusual market movements caused by the global pandemic. The results reveal that none of the multi-index models outperformed the single-index model during the extreme market events due to the high correlation of all stocks with the market.