EstimateBeta - C Review of Quantitative Finance and...

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Review of Quantitative Finance and Accounting, 18: 95–118, 2002 ° C 2002 Kluwer Academic Publishers. Manufactured in The Netherlands . Estimating Beta HAIM SHALIT Department of Economics, Ben-Gurion University of the Negev, Beer Sheva, 84105 Israel E-mail: SHLOMO YITZHAKI Department of Economics, Hebrew University of Jerusalem, Jerusalem, 91000 Israel and Director, Central Bureau of Statistics, Jerusalem, 91342 Israel E-mail: Abstract. This paper presents evidence that Ordinary Least Squares estimators of beta coef±cients of major ±rms 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 ±nancial 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. Key words: OLS estimators, systematic risk, mean-Gini JEL Classifcation: G12 1. Introduction The valuation of risky assets is one of the major research tasks in ±nancial economics that has led to the development of several Capital Asset Pricing Models, the most popular of which is the Sharpe-Lintner-Black mean-variance CAPM . In this model, the typical measure of asset riskiness is the beta, i.e., the covariance between the asset return and the market portfolio return. The basic tenet of CAPM lies in the separation of estimating beta risk from its pricing. Indeed CAPM assumes that one can de±ne and measure systematic risk irrespective of risk aversion, which affects only the equilibrium pricing of individual assets. As is well known, this separation is valid only under the restrictive assumption of two-factor separating distributions or alternatively, if the utility function is quadratic. Empirical asset-pricing models attract massive attention in ±nance, their goal being to assert or refute whether CAPM holds true. The traditional technique used to estimate the risk-expected return relation consists of two stages. In the ±rst pass, betas are estimated from a time-series. In the second pass, the relationship between mean returns and betas is tested across ±rms or portfolios. This methodology has been the subject of much criticism that has Address correspondence to: Haim Shalit, Department of Economics, Monaster Center for Economic Re- search, Ben-Gurion University of the Negev, Beer Sheva, 84105 Israel. Tel.: +972-8-6472299; Fax +972- 8-6472941. E-mail:
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96 SHALIT AND YITZHAKI led to many attempts at improvement. Such studies were initiated by Fama and MacBeth (1973) who introduced a rolling technique, and were followed by proponents of maximum likelihood estimation, for example Gibbons (1982), Stambaugh (1982), and Shanken (1992) to name a few. MacKinlay and Richardson (1991) developed a test for mean-variance ef±ciency without assuming normally distributed asset returns. However, CAPM suffered a
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EstimateBeta - C Review of Quantitative Finance and...

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