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2023 | OriginalPaper | Chapter

8. Multifactor Models

Authors : James W. Kolari, Seppo Pynnönen

Published in: Investment Valuation and Asset Pricing

Publisher: Springer International Publishing

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Abstract

In 1990 William Sharpe was awarded the Nobel Prize in Economics for the CAPM along with Harry Markowitz for portfolio diversification and Merton Miller for corporate valuation. Unfortunately, studies by Fama and French (1992, 1993, 1995, 1996) showed that the CAPM did not work in the real world. They proposed the three-factor model containing the market factor plus two new factors—namely, size and value factors. The new factors are long/short portfolios that improved the goodness-of-fit of the CAPM to stock returns. The three-factor model sparked some controversy that continues today.

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See their original works, especially Sharpe (1964), Markowitz (1959), and Modigliani and Miller (1958, 1963). With respect to the CAPM, both Lintner (1965) and Mossin (1966) had died by 1990 and Treynor (1961, 1962) had not never published his CAPM papers, such that these authors were not eligible for the prize.

See Basu (1977), Lakonishok and Shapiro (1986), and Bhandari (1988). Fama and French (2004) have provided an excellent survey of the CAPM and these contradictory studies.

We cannot visualize four-dimensional objects as humans, but a multivariate regression model enables a mathematical realization of N dimensions corresponding to N variables including both the dependent and independent variables. Interestingly, Einstein’s theory of General Relativity argued that a space-time continuum exists with 3 dimensions of space and 1 dimension of time. He thought that there is curvature in space-time due to gravity. Could the return-risk space be curved also? Is there a unifying force like gravity that links returns and risk in financial markets? Perhaps it can bend return-risk space much as gravity can bend light as it travels through space.

In Chapter 10 we cover the ZCAPM of Kolari et al. (2021), which is based on Black’s (1972) zero-beta CAPM. Consistent with Black’s (1995) comments about a large second factor, empirical tests of the ZCAPM have revealed a highly significant, large second factor (viz.,cross-sectional returncross-sectional return dispersion in the market).

See also Hsia et al. (2000), who used annual returns to compute moving-average betas and better take into market anomalies. Their results supported a positive relation between average returns and beta risk also. Additionally, a study of U.K. stock market returns by Clare et al. (1998) found that the beta was not dead. Using a somewhat different method of estimating the cross-sectional relation between expected returns and factor loadings, market beta risk was significantly priced in their tests. However, their study only employed 100 U.K. stocks with data available from 1980 to 1993. Thus, their results were somewhat limited in scope.

In time-series regressions of the three-factor model, information in the size and value test asset portfolios (and even residual errors for these portfolios) will naturally have information related to the size and value factors. In this respect, recall from Chapter 4’s discussion of the market model and underlying statistical assumptions, the error terms should be uncorrelated with the independent variables.

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Title: Multifactor Models
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_8