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Estimating Beta

  • Haim Shalit
  • Shlomo Yitzhaki
Article

Abstract

This paper presents evidence that Ordinary Least Squares estimators of beta coefficients of major firms and portfolios are highly sensitive to observations of extremes in market index returns. This sensitivity is rooted in the inconsistency of the quadratic loss function in financial theory. By introducing considerations of risk aversion into the estimation procedure using alternative estimators derived from Gini measures of variability one can overcome this lack of robustness and improve the reliability of the results.

OLS estimators systematic risk mean-Gini 

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References

  1. Amihud, Y., B. J. Christensen and H. Mendelson. Further Evidence on the Risk-Return Relationship. Working paper, New York University, 1992.Google Scholar
  2. Brown, S. J. and J. B. Warner, “Using Daily Stock Returns. ” Journal of Financial Economics 14, 3–31, (1985).Google Scholar
  3. Carroll, C., P. D. Thistle and K. C. John Wei, “The Robustness of Risk-Return Nonlinearities to the Normality Assumption. ” Journal of Financial and Quantitative Analysis 27(3), 419–435, (1992).Google Scholar
  4. Chan, L. K. C. and J. Lakonishok, “Robust Measurement of Beta Risk. ” Journal of Financial and Quantitative Analysis 27, 265–282, (1992).Google Scholar
  5. Durbin, J., “Errors in Variables. ” International Statistical Review 22, 23–32, (1954).Google Scholar
  6. Fama, E., “The Behavior of Stock Prices. ” Journal of Business 38, 34–105, (1965).Google Scholar
  7. Fama, E. F. and K. R. French, “The Cross-Section of Expected Stock Returns. ” Journal of Finance 47, 427–465, (1992).Google Scholar
  8. Fama, E. F. and K. R. French, “Common Risk Factors in the Returns on Stocks and Bonds. ” Journal of Financial Economics 33, 3–56, (1993).Google Scholar
  9. Fama, E. F. and K. R. French, “Size and Book-to-Market Factors in Earnings and Returns. ” Journal of Finance 50, 131–155, (1995).Google Scholar
  10. Fama, E. F. and K. R. French, “Industry Costs of Equity. ” Journal of Financial Economics 44, 153–193, (1997).Google Scholar
  11. Fama, E. F. and J. D. MacBeth, “Risk, Return, and Equilibrium: Empirical Tests. ” Journal of Political Economy 81, 607–636, (1973).Google Scholar
  12. Fisher, L. and J. H. Lorie, “Some Studies of Variability of Returns on Investments in Common Stocks. ” Journal of Business 43, 99–134, (1970).Google Scholar
  13. Gibbons, M. R., “Multivariate Tests of Financial Models: A New Approach. ” Journal of Financial Economics 10, 3–27, (1982).Google Scholar
  14. Gregory-Allen, R. B. and H. Shalit, “The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach. ” Review of Quantitative Finance and Accounting 12, 135–157, (1999).Google Scholar
  15. Hadar, J. and W. R. Russell, “Rules for Ordering Uncertain Prospects. ” American Economic Review 59, 25–34, (1969).Google Scholar
  16. Hanoch, G. and H. Levy, “The Efficiency Analysis of Choices Involving Risk. ” Review of Economic Studies 36, 335–346, (1969).Google Scholar
  17. Jagannathan, R. and Z. Wang, “The Conditional CAPM and the Cross-Section of Expected Returns. ” Journal of Finance 51, 3–53, (1996).Google Scholar
  18. Kandel, S. and R. F. Stambaugh, “Portfolio Inefficiency and the Cross-Section of Expected Returns. ” Journal of Finance 50, 157–184, (1995).Google Scholar
  19. Knez, P. J. and M. J. Ready, “On the Robustness of Size and Book-to-Market in Cross-Sectional Regressions. ” Journal of Finance 52, 1355–1382, (1997).Google Scholar
  20. Levhari D. and H. Levy “The Capital Asset Pricing Model and the Investment Horizon.” The Review of Ecomics and Statistics 59, 92–104, (1977)Google Scholar
  21. Levy, H., “Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio. ” American Economic Review 68, 643–658, (1978).Google Scholar
  22. Levy, H., “Stochastic Dominance and Expected Utility: Survey and Analysis. ” Management Science 38, 555–593, (1992).Google Scholar
  23. Levy, H., “Risk and Return: An Experimental Analysis. ” International Economic Review 38(1), 119–149, (1997).Google Scholar
  24. Levy, H. and G. Schwarz, “Correlation and the Time Interval over which Variables are Measured. ” Journal of Econometrics 76, 341–350, (1997).Google Scholar
  25. Lintner, J., “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets. ” Review of Economics and Statistics 47, 13–37, (1965).Google Scholar
  26. MacKinlay, A. C. and M. P. Richardson, “Using Generalized Methods of Moments to Test Mean-Variance Efficiency. ” Journal of Finance 46, 511–527, (1991).Google Scholar
  27. Mandelbrot, B., “The Variation of Certain Speculative Prices. ” Journal of Business 36, 394–419, (1963).Google Scholar
  28. Mantegna, R. N. and H. E. Stanley, “Scaling Behaviour in the Dynamics of an Economic Index. ” Nature 376, 46–49, (1995).Google Scholar
  29. Merton, R. C., “An Analytic Derivation of the Efficient Portfolio Frontier. ” Journal of Financial and Quantitative Analysis 7, 1851–1872, (1972).Google Scholar
  30. Merton, R. C., “On the Microeconomic Theory of Investment under Uncertainty, ” in K. J. Arrow and M. D. Intrilligator (Eds.), Handbook of Mathematical Economics Vol. II, Amsterdam: North-Holland, 1982.Google Scholar
  31. Merton, R. C., Continuous Finance, Cambridge, UK: Blackwell, 1990.Google Scholar
  32. Mossin, J., “Equilibrium in a Capital Market. ” Econometrica 34, 768–783, (1966).Google Scholar
  33. Olkin, I. and S. Yitzhaki, “Gini Regression Analysis. ” International Statistical Review 60, 185–196, (1992).Google Scholar
  34. Roll, R., “A Critique of the Asset Pricing Theory's Test: Part I, On Past and Potential Testability of the Theory. ” Journal of Financial Economics 4, 129–176, (1977).Google Scholar
  35. Rothschild, M. and J. E. Stiglitz, “Increasing Risk I: A Definition. ” Journal of Economic Theory 3, 66–84, (1970).Google Scholar
  36. Schechtman, E. and S. Yitzhaki, Asymmetric Gini Regression. Working paper, Hebrew University of Jerusalem, Department of Economics, 1998.Google Scholar
  37. Shalit, H. and S. Yitzhaki, “Mean-Gini, Portfolio Theory and the Pricing of Risky Assets. ” Journal of Finance 39(5), 1449–1468, (1984).Google Scholar
  38. Shalit, H. and S. Yitzhaki, “Evaluating the Mean-Gini Approach to Portfolio Selection. ” International Journal of Finance 1(2), 15–31, (1989).Google Scholar
  39. Shalit, H. and S. Yitzhaki, “Marginal Conditional Stochastic Dominance. ” Management Science 40, 670–674, (1994).Google Scholar
  40. Shanken, J., “On the Estimation of Beta-Pricing Models. ” Review of Financial Studies 5, 1–33, (1992).Google Scholar
  41. Sharpe, W. F., “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. ” Journal of Finance 19, 425–442, (1964).Google Scholar
  42. Sharpe, W. F., Investments, second edition. Englewood Cliffs, NJ: Prentice Hall, 1981.Google Scholar
  43. Sharpe, W. F., “Capital Asset Prices with and without Negative Holdings. ” Journal of Finance 46, 489–509, (1991).Google Scholar
  44. Stambaugh, R. F., “On the Exclusion of Assets from Tests of the Two-Parameter Model: A Sensitivity Analysis. ” Journal of Financial Economics 10, 237–268, (1982).Google Scholar
  45. Yaari, M. E., “The Dual Theory of Choice Under Risk. ” Econometrica 55, 95–115, (1987).Google Scholar
  46. Yitzhaki, S., “Stochastic Dominance, Mean-Variance, and Gini's Mean Difference. ” American Economic Review 72(1), 178–185, (1982).Google Scholar
  47. Yitzhaki, S., “On an Extension of the Gini Inequality Index. ” International Economic Review 24, 617–628, (1983).Google Scholar
  48. Yitzhaki, S., “Calculating Jackknife Variance Estimators for Parameters of the Gini Method. ” Journal of Business and Economic Statistics 9, 235–239, (1991).Google Scholar
  49. Yitzhaki, S., “On Using Linear Regression in Welfare Economics. ” Journal of Business and Economic Statistics 14, 478–486, (1996).Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Haim Shalit
    • 1
  • Shlomo Yitzhaki
    • 2
    • 3
  1. 1.Department of EconomicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of EconomicsHebrew University of JerusalemJerusalemIsrael
  3. 3.Central Bureau of StatisticsJerusalemIsrael

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