Fractional-moment CAPM with loss aversion q

In this paper, we present a new fractional-order value function which generalizes the value function of Kahneman and Tversky [Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica 1979;47:263–91; Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 1992;4:297–323], and give the corresponding fractional-moment versions of CAPM in the cases of both the prospect theory [Kahneman D, Tversky A. Prospect theory: an analysis of decision under risk. Econometrica 1979;47:263–91; Tversky A, Kahneman D. Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 1992;4:297–323] and the expected utility model. The models that we obtain can be used to price assets when asset return distributions are likely to be asymmetric stable Levy distribution during panics and stampedes in worldwide security markets in 2008. In particular, from the prospect theory we get the following fractional-moment CAPM with loss aversion: EðRi R0Þ¼ E½ðW W0Þ 0:12 þ ðRi R0Þ þ2:25E½ðW0 WÞ 0:12 þ ðRi R0Þ E½ðW W0Þ 0:12 þ ðW R0Þ þ2:25E½ðW0 WÞ 0:12 þ ðW R0Þ EðW R0Þ; where W0 is a fixed reference point distinguishing between losses and gains.