Capital asset pricing model under distribution uncertainty

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