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2023 | OriginalPaper | Chapter

4. The Market Model

Authors : James W. Kolari, Seppo Pynnönen

Published in: Investment Valuation and Asset Pricing

Publisher: Springer International Publishing

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Abstract

The famed capital asset pricing model (CAPM) of Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966) is surprisingly elegant in design. To test the CAPM, the market model was invented in the form of a simple regression equation. Early evidence did not support the CAPM. Due to these findings, researchers later proposed new forms of the CAPM and alternative models extending the CAPM to multiple factors.

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previous chapter Capital Asset Pricing Model (CAPM)

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See also Black et al. (1972).

Treasury rates were only available from 1948 to 1966. From 1925 to 1947 they used the dealer commercial paper rate for the riskless rate proxy.

See Blume (1970) and Friend and Blume (1970).

In forthcoming Sect. 4.4, we discuss the error term and other OLS assumptions in more detail.

The exact details of their data are somewhat complicated and beyond the scope of the present general discussion. See Fama and MacBeth (1973, pp. 616–617).

It is well known that this rolling FM procedure eliminates correlation between residuals, or \(e_{pt}\), in cross-sectional regressions that can bias average risk premium t-tests. Some researchers conduct the cross-sectional regressions within the sample by regressing portfolio returns in each month in the sample period on average \(\beta\) estimates for the entire period. In this case, it is necessary to make a correction to adjust the standard errors in the t-statistic. Excellent discussions of this correction can be found in Shanken (1992) and Cochrane (2005, Chapter 12).

See https://fred.stlouisfed.org/series/DGS1MO.

In the estimation of the market model and other asset pricing models with multiple factors, the authors have found that the beta coefficients are changed little if any. Nonetheless, inclusion of an intercept is more appropriate to ensure that the regression coefficients are BLUE.

The term \(Var \,(u_{it}) = \sigma _i^2 - 2\beta _i\sigma _{iM} + \beta _i^2\sigma _M^2\), where \(\sigma _i^2 = Var \,(R_{it})\), \(\sigma _M^2 = Var \,(R_{Mt})\), and \(\sigma _{iM} = Cov \,(R_{it}, R_{Mt})\). In the CAPM, \(\beta _i = \sigma _{iM} / \sigma _M^2 = \rho _{iM}(\sigma _i / \sigma _M)\), and using \(\beta _i\sigma _{iM} = \beta _i^2\sigma _M^2 = \sigma _i^2 \rho _{iM}^2\) in \(Var \,(u_{it})\) above, we get after adding up and rearranging terms \(Var \,(u_{it}) = \sigma _i^2(1 - \rho _{iM}^2)\)..

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Title: The Market Model
Authors: James W. Kolari
Seppo Pynnönen
Publisher: Springer International Publishing
Book: Investment Valuation and Asset Pricing
Print ISBN: 978-3-031-16783-6

Electronic ISBN: 978-3-031-16784-3

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-3-031-16784-3_4