fama and macbeth revisited: A Critique

Salazar, Juan and Lambert, Annick (2010): fama and macbeth revisited: A Critique. Published in: Aestimatio. The IEB International Journal of Finance No. 1 (December 2010): pp. 1-24.

Abstract

The main conclusion of the FM study relies on the fact that the average of the slopes of 402 regressions of the monthly returns on 20 portfolios on theirs beta coefficients is positive. Considering this set of 402 slopes as a random sample drawn from the same normally distributed population, FM performed a t-test on the mean and conclude that the true mean significantly differs from zero. Then they took this result as a proof in favour of the theory that there is in the real world a perfect linear relationship between the expected return and the true beta of securities and portfolios or, in other terms, in favour of the theory that the market portfolio is efficient. In this article, we present several tests and arguments that put some shadow on these conclusions. In fact, several tests lead us to the conclusion that the 402 random observations above mentioned are not drawn from a normal (or symmetric stable) distribution, neither are they independent or identically distributed. Indeed, the most disturbing fact is that those observations are likely not independent.

• Item Type: MPRA Paper
• Language: English
• Keywords: CAPM, CAPT, Portfolio theory, Empirical tests, Hypothesis testing,Regression analysis, Spectral analysis, January anomaly
• Subjects: G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Arditti, F. D. (1967). Risk and the Required Return in Equity, Journal of Finance, 22(1), pp. 19-36.

Black, F. (1972). Capital Market Equilibrium with Restricted Borrowing, Journal of Business, 45(3), pp. 444-454.

Brock, W.A., Dechert, W. D. and Scheinkman, J.A. (1996). A Test for Independence Based on the Correlation Dimension, Econometric Reviews, 15(3), pp. 197-235.

Fama, E.F. (1976). Foundations of Finance, Basic Books, New York.

Fama, E.F. (1971). Risk, Return, and Equilibrium, Journal of Political Economy, 79(1), pp. 30-55.

Fama, E.F. and French, K.R. (1992). The Cross-Section of Expected Stock Returns, Journal of Finance, 47(2), pp. 427-465.

Fama, E.F. and MacBeth, J. (1973). Risk, Return and Equilibrium: Empirical Tests, Journal of Political Economy, 81(3), pp. 607-636.

French, K.R. (1980). Stocks Returns and the Weekend Effect, Journal of Financial Economics, 8(1), pp. 55-69.

Granger, C. W. J. (1966). The Typical Shape of an Economic Variable, Econometrica, 34(1), pp. 150-161.

Granger, C.W.J. and Hatanaka, M. (1964). Spectral Analysis of Economic Time Series, Princeton University Press, Princeton, New Jersey.

Granger, C. W. J. and Morgenstern, O. (1963). Spectral Analysis of New York Stock Prices, Kyklos, 16(1), pp. 1-27.

Harvey, A. C.(1975). Spectral Analysis in Economics, The Statistician, 24(1), pp. 1-36

Jarque, C.M. and Bera, A.K. (1987). A Test for Normality of Observations and Regression Residuals, International Statistical Review, 55(2), pp. 163-172.

Jensen, M.C. (1972). Studies in the Theory of Capital Markets, Praeger, New York.

Lilliefors, H.W. (1967). On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown, Journal of the American Statistical Association, 62(318), pp. 399-402.

Lintner, J. (1965). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, Review of Economics and Statistics, 47(1), pp. 13-37.

MacKinnon, W.J. (1964). Table for Both the Sign Test and Distribution-Free Confidence Intervals of the Median for Sample Sizes to 1,000, Journal of the American Statistical Association, 59(307), pp. 935-956.

Markowitz, H. (1952). Portfolio Selection, Journal of Finance, 7(1), pp. 77-91.

Markowitz, H. (1976). Portfolio Selection, Fourth printing, Yale University Press, New Haven.

Massey, F.J. Jr. (1951). The Kolmogorov-Smirnov Test for Goodness of Fit, Journal of the American Statistical Association, 46(253), pp. 68-78.

Miller, M.H. and Scholes, M. (1972). Rates of Return in Relation to Risk: A Re-Examination of Some Recent Findings, in Jensen, M.C. (Ed.), Studies in the Theory of Capital Markets, Praeger, New York, pp. 47-78.

Mossin, J. (1966). Equilibrium in a Capital Asset Market, Econometrica, 34(4), pp. 768-783.

Racicot, F.É. and Théoret, R. (2001). Traité d’économétrie financière, Presses de l’Université du Québec, Sainte-Foy, Québec.

Roll, R. (1977). A Critique of Asset Pricing Theory’s Tests, Journal of Financial Economics, 4(2), pp. 129-176.

Salazar Clavel, J.M. (1986). Étude de la relation entre les espérances mathématiques et les écarts types des taux de rendement des titres dans un marché financier efficient, doctoral dissertation, Université Laval, Québec.

Salazar Clavel, J.M. and Iglesias Antelo, S. (2003). Ilusiones, esperanzas, medias, betas y varianzas, in Proceedings of VI Congreso Galego de Estatística e Investigación de Operacións, Vigo, Spain.

Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance, 19(3), pp. 425-442.

Siegel, S. (1956). Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill, New York.

Tinic, S. and West, R. (1984). Risk and Return: January vs. the Rest of the Year, Journal of Financial Economics, 13(4), pp. 561-574.

Treynor, J.L. (1961). Toward a Theory of Market Value of Risk Assets, unpublished manuscript.

Wang, P. (2003). Financial Econometrics: Methods and Models, Routledge, London.