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A New Model of Capital Asset PricesSynopsis of Asset Pricing and the ZCAPM

A New Model of Capital Asset Prices: Synopsis of Asset Pricing and the ZCAPM [During the period from the 1960s to early 1990s, the Capital Asset Pricing Model (CAPM) of John Lintner, Jan Mossin, William Sharpe, and Jack Treynor developed into the main branch of asset pricing. A pathbreaking theoretical masterpiece, the CAPM was derived from equilibrium pricing conditions as well as seminal portfolio theory by Harry Markowitz. However, early empirical evidence suggested that CAPM relation between beta risk associated with the market portfolio and stock returns was weaker than predicted. In an effort to take into account this evidence, Fischer Black proposed the zero-beta CAPM. Extending the CAPM to continuous time, Robert Merton advanced the intertemporal CAPM (ICAPM). Other forms of the CAPM were derived also. In recognition of the CAPM’s worldwide prominence, Professors Markowitz and Sharpe shared the Nobel Prize in Economics in 1990. Immediately thereafter in the early 1990s, Eugene Fama and Kenneth French published a series of papers that overturned the CAPM. Using U.S. stock returns over many years, they documented evidence against the relation between beta risk and the cross section of U.S. stock returns. Creating a new branch of asset pricing, they proposed a three-factor model comprised of market, size, and value factors to better fit stock return data. The latter so-called multifactors are zero-investment portfolios based on stocks with different firm characteristics. This long-minus-short portfolio method of specifying factors motivated many researchers to propose new multifactors based on other firm characteristics and stock return anomalies. A growing number of contender models evolved with different zero-investment factors. The resultant multifactor model competition has raised questions about the most important factors and models to use. A major problem with this branch of literature is that there is little or no theoretical foundation for zero-investment factors. In defense, some researchers loosely tie multifactor models to the Arbitrage Pricing Theory (APT) of Stephen Ross or the ICAPM of Robert Merton. In this book we developed a new theoretical CAPM that is a special case of Black’s zero-beta CAPM dubbed the ZCAPM. Our new asset pricing model departs from the multifactor model branch of literature by returning to the main CAPM branch. Based on the same mean-variance portfolio theory and equilibrium conditions of the CAPM and zero-beta CAPM, the ZCAPM hypothesizes that expected returns are a function of beta risk associated with average market returns and zeta risk related to return dispersion. Unlike previous asset pricing models, assets can have asymmetric positive and negative sensitivity to return dispersion (RD) in any given time period (e.g., one day). To estimate the theoretical ZCAPM with stock return data, we specified the empirical ZCAPM as a novel regression model containing a dummy signal variable to capture positive versus negative sensitivity to RD. The probability that this latent (or hidden) signal variable is positive or negative was estimated using the well-known expectation–maximization (EM) algorithm. This marginal form of the ZCAPM is a probabilistic mixture of two-factor models that take into account positive versus negative sensitivity to RD. Using over 50 years of U.S. common stock returns, comparative graphical analyses and batteries of cross-sectional tests strongly favored the empirical ZCAPM over popular multifactor models. In repeated out-of-sample cross-sectional tests with different portfolios, individual stocks, and sample periods, the ZCAPM dominated popular multifactor models. Also, we found that a number of prominent anomalies, including size, value, momentum, profit, and capital investment, are explained by the empirical ZCAPM. It is important to recognize that zero-investment portfolios themselves are rough measures of return dispersion that capture slices of the total dispersion. Taken together, they proxy total return dispersion. In this sense, multifactor models bear some relation to the ZCAPM and thereby the CAPM.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A New Model of Capital Asset PricesSynopsis of Asset Pricing and the ZCAPM

Kolari, James W.; Liu, Wei; Huang, Jianhua Z.
Springer Journals — Mar 2, 2021
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24 pages

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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-65196-1
Pages
261 –285
DOI
10.1007/978-3-030-65197-8_10
Publisher site
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Abstract

[During the period from the 1960s to early 1990s, the Capital Asset Pricing Model (CAPM) of John Lintner, Jan Mossin, William Sharpe, and Jack Treynor developed into the main branch of asset pricing. A pathbreaking theoretical masterpiece, the CAPM was derived from equilibrium pricing conditions as well as seminal portfolio theory by Harry Markowitz. However, early empirical evidence suggested that CAPM relation between beta risk associated with the market portfolio and stock returns was weaker than predicted. In an effort to take into account this evidence, Fischer Black proposed the zero-beta CAPM. Extending the CAPM to continuous time, Robert Merton advanced the intertemporal CAPM (ICAPM). Other forms of the CAPM were derived also. In recognition of the CAPM’s worldwide prominence, Professors Markowitz and Sharpe shared the Nobel Prize in Economics in 1990. Immediately thereafter in the early 1990s, Eugene Fama and Kenneth French published a series of papers that overturned the CAPM. Using U.S. stock returns over many years, they documented evidence against the relation between beta risk and the cross section of U.S. stock returns. Creating a new branch of asset pricing, they proposed a three-factor model comprised of market, size, and value factors to better fit stock return data. The latter so-called multifactors are zero-investment portfolios based on stocks with different firm characteristics. This long-minus-short portfolio method of specifying factors motivated many researchers to propose new multifactors based on other firm characteristics and stock return anomalies. A growing number of contender models evolved with different zero-investment factors. The resultant multifactor model competition has raised questions about the most important factors and models to use. A major problem with this branch of literature is that there is little or no theoretical foundation for zero-investment factors. In defense, some researchers loosely tie multifactor models to the Arbitrage Pricing Theory (APT) of Stephen Ross or the ICAPM of Robert Merton. In this book we developed a new theoretical CAPM that is a special case of Black’s zero-beta CAPM dubbed the ZCAPM. Our new asset pricing model departs from the multifactor model branch of literature by returning to the main CAPM branch. Based on the same mean-variance portfolio theory and equilibrium conditions of the CAPM and zero-beta CAPM, the ZCAPM hypothesizes that expected returns are a function of beta risk associated with average market returns and zeta risk related to return dispersion. Unlike previous asset pricing models, assets can have asymmetric positive and negative sensitivity to return dispersion (RD) in any given time period (e.g., one day). To estimate the theoretical ZCAPM with stock return data, we specified the empirical ZCAPM as a novel regression model containing a dummy signal variable to capture positive versus negative sensitivity to RD. The probability that this latent (or hidden) signal variable is positive or negative was estimated using the well-known expectation–maximization (EM) algorithm. This marginal form of the ZCAPM is a probabilistic mixture of two-factor models that take into account positive versus negative sensitivity to RD. Using over 50 years of U.S. common stock returns, comparative graphical analyses and batteries of cross-sectional tests strongly favored the empirical ZCAPM over popular multifactor models. In repeated out-of-sample cross-sectional tests with different portfolios, individual stocks, and sample periods, the ZCAPM dominated popular multifactor models. Also, we found that a number of prominent anomalies, including size, value, momentum, profit, and capital investment, are explained by the empirical ZCAPM. It is important to recognize that zero-investment portfolios themselves are rough measures of return dispersion that capture slices of the total dispersion. Taken together, they proxy total return dispersion. In this sense, multifactor models bear some relation to the ZCAPM and thereby the CAPM.]

Published: Mar 2, 2021

Keywords: Arbitrage pricing theory (APT); Asset pricing; Beta risk; CAPM; Cross-sectional regression tests; Dualism; Empirical ZCAPM; Expectation-maximization (EM) algorithm; Eugene Fama; Fischer Black; Kenneth French; Harry Markowitz; Industry portfolios; Multifactor models; Out-of-sample returns; Return dispersion; Securities investment; Signal variable; Stock market; Test assets; Theoretial ZCAPM; William Sharpe; ZCAPM; Zero-beta CAPM; Zeta risk

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