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Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model

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  • Manuel Galea

    (Pontificia Universidad Católica de Chile)

  • Patricia Giménez

    (Universidad Nacional de Mar del Plata)

Abstract

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean–variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic.

Suggested Citation

  • Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0838-8
    DOI: 10.1007/s00362-016-0838-8
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    1. Bartholdy, Jan & Peare, Paula, 2003. "Unbiased estimation of expected return using CAPM," International Review of Financial Analysis, Elsevier, vol. 12(1), pages 69-81.
    2. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    3. Miguel Angel Uribe-Opazo & Joelmir Andr� Borssoi & Manuel Galea, 2012. "Influence diagnostics in Gaussian spatial linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(3), pages 615-630, July.
    4. Sik-Yum Lee & S. Wang, 1996. "Sensitivity analysis of structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 93-108, March.
    5. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    6. Xiaoyan Shi & Hongtu Zhu & Joseph G. Ibrahim, 2009. "Local Influence for Generalized Linear Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 65(4), pages 1164-1174, December.
    7. Giménez, Patricia & Galea, Manuel, 2013. "Influence measures on corrected score estimators in functional heteroscedastic measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 1-15.
    8. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    9. Claude Broquet & Robert Cobbaut & Roland Gillet & André Van Den Berg, 2004. "Gestion de portefeuille," ULB Institutional Repository 2013/14359, ULB -- Universite Libre de Bruxelles.
    10. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    11. David Cademartori & Cecilia Romo & Ricardo Campos & Manuel Galea, 2003. "Robust estimation of systematic risk using the t distribution in the chilean stock markets," Applied Economics Letters, Taylor & Francis Journals, vol. 10(7), pages 447-453.
    12. van der Hart, Jaap & Slagter, Erica & van Dijk, Dick, 2003. "Stock selection strategies in emerging markets," Journal of Empirical Finance, Elsevier, vol. 10(1-2), pages 105-132, February.
    13. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    14. Levy,Haim, 2012. "The Capital Asset Pricing Model in the 21st Century," Cambridge Books, Cambridge University Press, number 9781107006713, January.
    15. Fukang Zhu & Shuangzhe Liu & Lei Shi, 2016. "Local influence analysis for Poisson autoregression with an application to stock transaction data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 4-25, February.
    16. Shu-Jia Wang & Sik-Yum Lee, 1996. "Sensitivity analysis of structural equation models with equality functional constraints," Computational Statistics & Data Analysis, Elsevier, vol. 23(2), pages 239-256, December.
    17. Wing K. Fung & C. W. Kwan, 1997. "A Note on Local Influence Based on Normal Curvature," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 839-843.
    18. Manuel Galea & Jose Diaz-Garcia & Filidor Vilca, 2008. "Influence diagnostics in the capital asset pricing model under elliptical distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(2), pages 179-192.
    19. N. G. Cadigan & P. J. Farrell, 2002. "Generalized local influence with applications to fish stock cohort analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 469-483, October.
    20. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    21. Levy,Haim, 2012. "The Capital Asset Pricing Model in the 21st Century," Cambridge Books, Cambridge University Press, number 9780521186513, January.
    22. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    23. Elsas, Ralf & El-Shaer, Mahmoud & Theissen, Erik, 2003. "Beta and returns revisited: Evidence from the German stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 13(1), pages 1-18, February.
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    Cited by:

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    2. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.

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