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

Pawe? Sakowski, Robert ?lepaczuk, Mateusz Wywia?


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 modi?cations of these models to take into account di?erent 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 modi?cations include introduction of common and country speci?c variables in order to control for global risk where ?uctuations 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 ?rst part reveals important di?erences 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 ?rst part. Thanks to introduction of new risk factors, and additional common and country speci?c 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 over?tting e?ects when drawing conclusions upon results of multifactor models.


Ammann, M., and M. Verhofen (2006): The effect of market regimes on style allocation. Financial Markets and Portfolio Management, 20(3), 309-337.

Angelidis, T., and N. Tessaromatis (2014): Global portfolio management under state

dependent multiple risk premia, in Proceedings of Economics and Finance Conferences,

no. 0400966. International Institute of Social and Economic Sciences.

Arshanapalli, B. G., T. D. Coggin, and J. Doukas (1998): Multifactor Asset Pricing

Analysis of International Value Investment Strategies,The Journal of Portfolio Management, 24(757), 10-23.

Asness, C., A. Frazzini, and L. H. Pedersen (2013): Quality minus junk, Available at SSRN.

Asness, C. S. (1995): The power of past stock returns to explain future stock returns, Unpublished working paper Applied Quantitative Research.

Black, F., M. C. Jensen, and M. Scholes (1972): The Capital Asset Pricing Model: Some Empirical Tests, vol. 81.

Cakici, N., F. J. Fabozzi, and S. Tan (2013): Size, value, and momentum in emerging

market stock returns, Emerging Markets Review, 16, 46-65.

Carhart, M. M. (1997): On persistence in mutual fund performance, The Journal of Finance, 52(1), 57-82.

Chen, L., R. Novy-Marx, and L. Zhang (2011): An Alternative Three-Factor Model, SSRN Electronic Journal.

Connor, G., and S. Sehgal (2001): Tests of the Fama and French Model in India," London School of Economics and Political Science,Discussion paper, 379, 1-23.

Davis, J. L., E. F. Fama, and K. R. French (2000): Characteristics, covariances, and

average returns: 1929 to 1997, The Journal of Finance, 55(1), 389-406.

Duarte, F., C. Rosa, et al. (2015): The equity risk premium: a review of models," Discussion paper.

Fama, E. F., and K. R. French (1992): The Cross-Section of Expected Stock Returns,"

Journal of Finance, XLVII(2).

Duarte, F., C. Rosa, et al. (2012): Size, value, and momentum in international stock returns," Journal of Financial Economics, 105(3), 457-472.

Fama, E. F., and K. R. French (2015): A five-factor asset pricing model," Journal of Financial Economics, 116(1), 1-22.

Foye, J., D. Mramor, and M. Pahor (2013): A Respeci_ed Fama French Three-Factor

Model for the New European Union Member States," Journal of International Financial

Management & Accounting, 24(1), 3-25.

Frazzini, A., and L. H. Pedersen (2014): Betting against beta," Journal of Financial Economics, 111(312417), 1-25.

Griffin, J. M. (2002): Are the Fama and French Factors Global or Country Specific?," Review of Financial Studies, 15, 783-803.

Hammerschmid, R., and H. Lohre (2014): Regime Shifts and Stock Return Predictability, Available at SSRN 2445086.

Hou, K., G. A. Karolyi, and B. C. Kho (2011): What factors drive global stock returns?," Review of Financial Studies, 24, 2527-2574.

Jegadeesh, N., and S. Titman (1993): Returns to buying winners and selling losers:

Implications for stock market effciency, The Journal of Finance, 48(1), 65-91.

Lakonishok, J., A. Shleifer, and R. W. Vishny (1994): Contrarian Investment, Extrapolation, and Risk, The Journal of Finance, 49(5), 1541-1578.

Lieksnis, R. (2010): Multifactor Asset Pricing Analysis of the Baltic Stock Market," Ekonomika, 89(4), 85-95.

Lintner, J. (1965): The valuation of risk assets and the selection of risky investments in

stock portfolios and capital budgets," The Review of Economics and Statistics, 13-37.

Liu, W. (2004): Liquidity premium and a two-factor model," EFA 2004 Maastricht Meet-

ings Paper, 44(September 2003), 0-52.

Rahim, R. A., and A. H. S. M. Noor (2006): A Comparison Between Fama and French

Model and Liquidity-Based Three-Factor Models in," Asian Academy of Management

Journal and Finance, 2(2), 43-60.

Sakowski, P., R. Slepaczuk, and M. Wywial (2015): Cross-sectional returns from

diverse portfolio of equity indices with risk premia embedded," Quantitative Methods in


Sakowski, P., R. Slepaczuk, and M. Wywial (2016a): Cross-sectional returns with volatility regimes from diverse portfolio of emerging and developed equity indices," eFinanse, forthcoming.

Sakowski, P., R. Slepaczuk, and M. Wywial (2016b): Do multifactor models produce robust results? Econometric and diagnostic issues in equity risk premia study," Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach, forthcoming.

Sharpe, W. F. (1964): Capital asset prices: A theory of market equilibrium under con-

ditions of risk," The Journal of Finance, 19(3), 425-442.

Tan, M. (2013): Regime switching behaviour of the UK equity risk premium," Ph.D.

thesis, University of Birmingham.

Wu, X. (2002): A conditional multifactor analysis of return momentum," Journal of Banking and Finance, 26(February 1997), 1675-1696.



  • There are currently no refbacks.