Capital asset pricing model under distribution uncertainty

Abstract

<p style='text-indent:20px;'>In this paper, we investigate and demonstrate the capital asset pricing model (CAPM) based on distribution uncertainty (or ambiguity, defined as uncertainty about unknown probability).</p><p style='text-indent:20px;'>We first achieve directly capital asset pricing model based on spectral risk measures (abbreviated as SCAPM) in the case of normal distributions; Then we can characterize SCAPM under the condition of uncertain distributions of returns by solving a robust optimal portfolio model based on spectral measures. Specifically, we do it in the following two folds: 1) Completing first the corresponding effective frontier fitting; 2) Getting the valuation of the market portfolio return <inline-formula><tex-math id="M1">\begin{document}$ r_m $\end{document}</tex-math></inline-formula> and the risk parameters of <inline-formula><tex-math id="M2">\begin{document}$ \beta_\phi $\end{document}</tex-math></inline-formula> in use of the kernel density estimation under the distribution uncertainty of returns.</p><p style='text-indent:20px;'>Finally, by selecting 10 stocks from the constituent stocks of the HS300 Index, and comparing the valuation results from the SCAPM formula with the actual yield in the market, we verify the model proposed in the present paper is reasonable and effective.</p>