Study On The Validity Of Capital Asset Pricing Model Subject To A Skewness Constraint In Stock Market

The traditional CAPM assumption returning on asset is normal distribution, so investors only consider two factors which contain the mean and variance when they pricing.However, the returns on financial assets are not well described by variance for the existence of higher order skewness is generally acknowledged in literatures.In order to guide investors to allocate their resources rationally, this thesis attempts to use skewness to improve the explanation of traditional CAPM in the capital markets.Firstly, this thesis expounds the traditional CAPM theory by analyzing its assumptions. And then, the thesis discuss its deficiency when explains the real world; secondly,this thesis explains the basis for the existence of skewness by analyzing the asset yield’s non-normal distribution characteristics. In this way, the thesis demonstrates that the skewness plays an important role in the process of pricing; besides, in order to keep the variance minimization, this thesis uses the method of Lagrange multipliers in the process of improvement. In particular, it introduces conditions of mean, skewness and unit weight to solve the model, and then obtains optimal weight and new CAPM which includes the constraint of skewness. It is important that there are two ways to solve portfolio optimization problems under the constraint of skewness in academia, direct and indirect method.In direct method, it puts the function of skewness directly as a constraint so as to realize the minimizing variance; the indirect one spreads out the expected utility function through Taylor series. In this way, the utility maximization can be converted to how to achieve asset portfolio optimization under the condition of higher moments. Generally, investors’ utility function is expressed as the exponential in the indirect method. For this reason,the real situation cannot be fully described, so the thesis adopts the direct one; finally,this thesis tests the performance of the new skewness CAPM based on real data, and then draws the conclusion that the skewness CAPM reflects market conditions better.On the basis of the framework of mean-variance, the skewness CAPM has rigorous mathematical derivation. Comparing with adding skewness factors to traditional CAMP directly. This thesis is more normative and persuasive, which contributes to reasonable pricing of capital assets.