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Factor Analysis and Independent Component Analysis in Presence of High Idiosyncratic Risks

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  • Thierry Vessereau
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    Abstract

    This paper addresses the case when stock market returns are assumed being generated through a factorial structure. High levels of idiosyncratic risk are shown to exist for most stocks on the US market, when CAPM or APT are used for the estimation of diversifiable risks. The presence of these high idiosyncratic risks may not allow a correct estimation of the generating factors when using a classic factor analysis method. The Independent Component Analysis is introduced as an adequate method for factor estimation; using neural networks, this method allows taking into account the information contained in higher moments. Through simulations of markets with various assumptions on the kind of processes followed by the generating factors, this method is shown to strongly improve the factors estimation, especially when high idiosyncratic risks are present. In the latter case, a traditional factor analysis, such as the Principal Component Analysis, may fail to estimate the generating factors. Cet article traite le cas d'un marché d'actions dont les rendements sont susceptibles d'être expliqués par une structure factorielle. Sur le marché américain, il est montré que des risques idiosyncratiques élevés existent pour la plupart des actions quelque soit le modèle d'évaluation utilisé (CAPM ou APT). La présence de ces risques idiosyncratiques élevés peut empêcher une évaluation correcte des facteurs générant les rendements, lorsqu'une méthode d'analyse factorielle classique est utilisée. Il est ici proposé d'utiliser la méthode de l'Analyse en Composantes Indépendantes (INCA), reposant sur les réseaux neuronaux, pour parvenir à une évaluation correcte des facteurs; cette méthode permet de prendre en compte la majeure partie de l'information contenue dans les distributions des rendements des actions, en utilisant les moments d'ordre élevé de ces distributions. ¸ l'aide de simulations de marchés artificiels, pour lesquels différentes hypothèses des processus de générations des rendements sont retenus, il est montré que la méthode de l'INCA permet une amélioration significative de l'estimation de la structure factorielle, en particulier lorsque des composantes idiosyncratiques élevées sont présents dans les les rendements des actions. Dans ce dernier cas, une méthode classique d'analyse factorielle, comme l'Analyse en Composantes Principales, peut échouer totalement dans l'estimation des facteurs.

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    Bibliographic Info

    Paper provided by CIRANO in its series CIRANO Working Papers with number 2000s-46.

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    Date of creation: 01 Oct 2000
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    Handle: RePEc:cir:cirwor:2000s-46

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    Keywords: Independent component analysis; principal component analysis; arbitrage pricing theory; idiosyncratic risks; Analyse en composantes indépendantes; analyse en composantes principales; modèle d'évaluation par arbitrage; risques idiosyncratiques;

    References

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    1. Chen, Nai-fu & Ingersoll, Jonathan E, Jr, 1983. " Exact Pricing in Linear Factor Models with Finitely Many Assets: A Note," Journal of Finance, American Finance Association, vol. 38(3), pages 985-88, June.
    2. Trzcinka, Charles A, 1986. " On the Number of Factors in the Arbitrage Pricing Model," Journal of Finance, American Finance Association, vol. 41(2), pages 347-68, June.
    3. Ingersoll, Jonathan E, Jr, 1984. " Some Results in the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 39(4), pages 1021-39, September.
    4. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
    5. Mei, Jianping, 1993. " A Semiautoregression Approach to the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 48(2), pages 599-620, June.
    6. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
    7. Lehmann, Bruce N. & Modest, David M., 1988. "The empirical foundations of the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 21(2), pages 213-254, September.
    8. Gary Chamberlain & Michael Rothschild, 1982. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
    9. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
    10. Grinblatt, Mark & Titman, Sheridan, 1983. "Factor pricing in a finite economy," Journal of Financial Economics, Elsevier, vol. 12(4), pages 497-507, December.
    11. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    12. Chen, Nai-fu, 1983. " Some Empirical Tests of the Theory of Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 38(5), pages 1393-1414, December.
    13. Connor, Gregory & Korajczyk, Robert A., 1986. "Performance measurement with the arbitrage pricing theory : A new framework for analysis," Journal of Financial Economics, Elsevier, vol. 15(3), pages 373-394, March.
    14. Roll, Richard & Ross, Stephen A, 1980. " An Empirical Investigation of the Arbitrage Pricing Theory," Journal of Finance, American Finance Association, vol. 35(5), pages 1073-1103, December.
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    Cited by:
    1. Maximilian Vermorken & Ariane Szafarz & Hugues Pirotte, 2010. "Sector Classification through non-Gaussian Similarity," ULB Institutional Repository 2013/95542, ULB -- Universite Libre de Bruxelles.

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