Applying exogenous variables and regime switching to multifactor models on equity indices

Paweł Sakowski, Robert Ślepaczuk, Mateusz Wywiał


This article aims to extend the evaluation of classic multifactor models of Carhart (1997) for the case of global equity indices and to expand analysis performed in Sakowski, Slepaczuk, and Wywial (2015). Our intention is to test several modifications of these models to take into account different dynamics of equity excess returns between emerg-ing and developed equity indices. Proposed extensions include volatility regime switch-ing mechanism (using dummy variables and the Markov approach) and three new risk factors based on realized volatility of index returns, percentage deviation from nominal GDP trend and capitalisation relative to GDP factor. Additional modifications include introduction of common and country specific variables in order to control for global risk where fluctuations of volatility of various assets, prices of commodities, currencies and rates is really important.
Moreover, instead of using data for individual stocks (which is a common approach in the literature), we evaluate the performance of these models for weekly data of 81 world investable equity indices in the period of 2000-2015. Such approach is proposed to estimate equity risk premium for a single country.
Empirical evidence from the first part reveals important differences between results for classical models estimated on single stocks (either in international or US-only frame-work) and models evaluated for equity indices. Additionally, we observe substantial discrepancies between results for developed countries and emerging markets. The last part of this research helps us to understand results revealed in the first part. Thanks to introduction of new risk factors, and additional common and country specific variables we were able to increase explanatory power of our factor models especially in case of emerging market indices. Finally, using weekly data for the last 15 years we illustrate importance of model risk and data overfitting effects when drawing conclusions upon results of multifactor models.


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