Abstract
This paper presents an extension of the Capital Assets Pricing Model (hereafter CAPM) where various utility functions are applied. Specifically, we propose an overall CAPM beta that accounts for the higher order moments and reflects the investor preferences and attitudes toward risk. We particularly develop CAPM betas for different classes of utility function: the negative exponential utility function, power utility function or “Constant Relative Risk Aversion (CRRA) Utilities” and hyperbolic utility function or “HARA Utilities” (hyperbolic absolute risk aversion). In order to validate our theoretical results, we analyze the impact of investors’ preferences on the valuation equation. Applying the International CAPM, the results indicate that our utilities-based betas differ largely from the traditional CAPM betas. Moreover, the results confirm the importance of higher order moments on the pricing equation. Finally, the results both empirically and theoretically post to the consistent effect of the risk av...
Highlights
The traditional version of the CAPM of Sharpe (1964) and Lintner (1965) assumes that assets’ returns are a linear function of their equivalent systematic risk measured by CAPM, the slope from the regression of securities’returns on the market risk premium.The CAPM relies on several restrictive assumptions
We propose risk measures for the negative exponential utility function, power utility function or “Constant Relative Risk Aversion (CRRA) Utilities”, and hyperbolic utility function or “HARA Utilities”
The aim of this paper is to develop a new CAPM extracted from various utility functions
Summary
The traditional version of the CAPM of Sharpe (1964) and Lintner (1965) assumes that assets’ returns are a linear function of their equivalent systematic risk measured by CAPM, the slope from the regression of securities’returns on the market risk premium.The CAPM relies on several restrictive assumptions. Shah, Abdullah, Khan, and Khan (2011) compare the performance of the CAPM and the Fama and French (1993) three factor model Their results favor the use of the CAPM model to estimate expected returns. Markowtiz (1952) proposes the variance as a measure of risk (see Bouchaud & Potters, 1997; Duffie & Richardson, 1991) and the “mean-variance” approach to determine the optimal portfolio, minimizing the variance or maximizing returns This model is valid only on a quadratic utility function framework and supposes that returns follow a normal distribution. To solve this problem, Markowitz (1959) suggests the semi-variance to account for the downside risk. Other risk measures are proposed, such as the partial order moments and the value-at-risk (see Bouchaud & Selmi, 2001; Coombs & Lehner, 1981, 1984; Fishburn, 1982, 1984; Luce, 1980; Pollatsek & Tversky, 1970; Sarin, 1987; Stone, 1973)
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