Skip to main content
SpringerLink
Log in

Estimating Beta

  • Published:
Review of Quantitative Finance and Accounting Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Amihud, Y., B. J. Christensen and H. Mendelson. Further Evidence on the Risk-Return Relationship. Working paper, New York University, 1992.

  • Brown, S. J. and J. B. Warner, “Using Daily Stock Returns. ” Journal of Financial Economics 14, 3–31, (1985).

    Google Scholar 

  • 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 

  • Chan, L. K. C. and J. Lakonishok, “Robust Measurement of Beta Risk. ” Journal of Financial and Quantitative Analysis 27, 265–282, (1992).

    Google Scholar 

  • Durbin, J., “Errors in Variables. ” International Statistical Review 22, 23–32, (1954).

    Google Scholar 

  • Fama, E., “The Behavior of Stock Prices. ” Journal of Business 38, 34–105, (1965).

    Google Scholar 

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

    Google Scholar 

  • 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 

  • 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 

  • Fama, E. F. and K. R. French, “Industry Costs of Equity. ” Journal of Financial Economics 44, 153–193, (1997).

    Google Scholar 

  • Fama, E. F. and J. D. MacBeth, “Risk, Return, and Equilibrium: Empirical Tests. ” Journal of Political Economy 81, 607–636, (1973).

    Google Scholar 

  • 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 

  • Gibbons, M. R., “Multivariate Tests of Financial Models: A New Approach. ” Journal of Financial Economics 10, 3–27, (1982).

    Google Scholar 

  • 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 

  • Hadar, J. and W. R. Russell, “Rules for Ordering Uncertain Prospects. ” American Economic Review 59, 25–34, (1969).

    Google Scholar 

  • Hanoch, G. and H. Levy, “The Efficiency Analysis of Choices Involving Risk. ” Review of Economic Studies 36, 335–346, (1969).

    Google Scholar 

  • Jagannathan, R. and Z. Wang, “The Conditional CAPM and the Cross-Section of Expected Returns. ” Journal of Finance 51, 3–53, (1996).

    Google Scholar 

  • Kandel, S. and R. F. Stambaugh, “Portfolio Inefficiency and the Cross-Section of Expected Returns. ” Journal of Finance 50, 157–184, (1995).

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • Levy, H., “Stochastic Dominance and Expected Utility: Survey and Analysis. ” Management Science 38, 555–593, (1992).

    Google Scholar 

  • Levy, H., “Risk and Return: An Experimental Analysis. ” International Economic Review 38(1), 119–149, (1997).

    Google Scholar 

  • Levy, H. and G. Schwarz, “Correlation and the Time Interval over which Variables are Measured. ” Journal of Econometrics 76, 341–350, (1997).

    Google Scholar 

  • 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 

  • 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 

  • Mandelbrot, B., “The Variation of Certain Speculative Prices. ” Journal of Business 36, 394–419, (1963).

    Google Scholar 

  • Mantegna, R. N. and H. E. Stanley, “Scaling Behaviour in the Dynamics of an Economic Index. ” Nature 376, 46–49, (1995).

    Google Scholar 

  • Merton, R. C., “An Analytic Derivation of the Efficient Portfolio Frontier. ” Journal of Financial and Quantitative Analysis 7, 1851–1872, (1972).

    Google Scholar 

  • 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 

  • Merton, R. C., Continuous Finance, Cambridge, UK: Blackwell, 1990.

    Google Scholar 

  • Mossin, J., “Equilibrium in a Capital Market. ” Econometrica 34, 768–783, (1966).

    Google Scholar 

  • Olkin, I. and S. Yitzhaki, “Gini Regression Analysis. ” International Statistical Review 60, 185–196, (1992).

    Google Scholar 

  • 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 

  • Rothschild, M. and J. E. Stiglitz, “Increasing Risk I: A Definition. ” Journal of Economic Theory 3, 66–84, (1970).

    Google Scholar 

  • Schechtman, E. and S. Yitzhaki, Asymmetric Gini Regression. Working paper, Hebrew University of Jerusalem, Department of Economics, 1998.

  • 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 

  • Shalit, H. and S. Yitzhaki, “Evaluating the Mean-Gini Approach to Portfolio Selection. ” International Journal of Finance 1(2), 15–31, (1989).

    Google Scholar 

  • Shalit, H. and S. Yitzhaki, “Marginal Conditional Stochastic Dominance. ” Management Science 40, 670–674, (1994).

    Google Scholar 

  • Shanken, J., “On the Estimation of Beta-Pricing Models. ” Review of Financial Studies 5, 1–33, (1992).

    Google Scholar 

  • Sharpe, W. F., “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. ” Journal of Finance 19, 425–442, (1964).

    Google Scholar 

  • Sharpe, W. F., Investments, second edition. Englewood Cliffs, NJ: Prentice Hall, 1981.

    Google Scholar 

  • Sharpe, W. F., “Capital Asset Prices with and without Negative Holdings. ” Journal of Finance 46, 489–509, (1991).

    Google Scholar 

  • 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 

  • Yaari, M. E., “The Dual Theory of Choice Under Risk. ” Econometrica 55, 95–115, (1987).

    Google Scholar 

  • Yitzhaki, S., “Stochastic Dominance, Mean-Variance, and Gini's Mean Difference. ” American Economic Review 72(1), 178–185, (1982).

    Google Scholar 

  • Yitzhaki, S., “On an Extension of the Gini Inequality Index. ” International Economic Review 24, 617–628, (1983).

    Google Scholar 

  • Yitzhaki, S., “Calculating Jackknife Variance Estimators for Parameters of the Gini Method. ” Journal of Business and Economic Statistics 9, 235–239, (1991).

    Google Scholar 

  • Yitzhaki, S., “On Using Linear Regression in Welfare Economics. ” Journal of Business and Economic Statistics 14, 478–486, (1996).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel

    Haim Shalit

  2. Department of Economics, Hebrew University of Jerusalem, Jerusalem, 91000, Israel

    Shlomo Yitzhaki (Director)

  3. Central Bureau of Statistics, Jerusalem, 91342, Israel

    Shlomo Yitzhaki (Director)

Authors
  1. Haim Shalit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shlomo Yitzhaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shalit, H., Yitzhaki, S. Estimating Beta. Review of Quantitative Finance and Accounting 18, 95–118 (2002). https://doi.org/10.1023/A:1014594617251

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014594617251

Search

Navigation