A Study On Portfolio Selection Model On Condition Of Non-normal Distributions

As an important branch of finance theory, portfolio theory studies how optimally allocates wealth of individuals or institutions in all kinds of assets such as stocks, bonds, derivative securities and so on.Mean-variance model that Harry M. Markowitz has put forward in 1952 indicates the naissance of modern portfolio theory. So far, studies on portfolio theory are done in two main frameworks: reward-risk dominance and expected utility maximization. Regardless using reward-risk dominance or using expected utility maximization, mean-variance model is logic origin of all researches and all reaserches can be regarded as improvements to mean-variance model.Normal distribution hypothesis is very important to mean-variance model. In framework of reward-risk dominance, only when returns of risky assets are normally distributed, variance is the best risk measurement. In framework of expected utility maximization, only when utility function of investor is quadratic or returns of risky assets are normally distributed, mean-variance model accords with expected utility hypothesis.However, many empirical researches have shown that distributions of returns of risky assets are skew and leptokurtic and are not normal. So studying portfolio theory on condition of non-normal distributions is very necessary and has both high theoretical value and high applied value.This article studies portfolio theory on condition of non-normal distributions in framework of reward-risk dominance. Main contents of this thesis are as follows.Chapter one analyzes the research actuality of portfolio theory from aspect of four research methods and puts forward studying portfolio model on condition of non-normal distributions because returns of risky assets are not normally distributed.Chapter two does an empirical test to study the non-normal distributional characters of returns of stock in China. The result shows that returns of stock in China stock market are not normally distributed obviously. So, we must modify normal distribution hypothesis and study portfolio model on condition of non-normal distributions.Chapter three firstly analyzes the relation between EMH and normal distribution hypothesis and points out that EMH is not a sufficient condition but a necessary condition of normal distribution hypothesis firstly; then uses behavioral finance theory and complex science theory to analyze why market is inefficient and points out even the necessary condition of normal distribution hypothesis doesn't exist. So non-normal distributions is normal state of returns of risk securities.Chapter four studies risk measurement and correlation measurement on condition of non-normal distributions; analyzes risk and its essential properties and advances to measure risk by distribution of result of uncertain events and references; proposes to select risk measurement according to purpose of measuring risk; puts forward the properties risk measurement of portfolio should possess: convexity, downside risk and riskless condition; proposes to replace linear correlation coefficient by Kendall's r and proves using Kendall'sr to measure correlation between risky securities do improve effect of risk reduction of diversified investment by empirical analysis.Chapter five studies mean-LPM model. Puts forward a new CLPM arithmetic that adapts LPM to measure risk on condition of non-normal distributions better; using this new CLPM arithmetic, deduces the portfolio frontier equation of Mean-LPM model and proves that portfolio frontier of Mean-LPM model satisfies two funds separation theorem; finds that portfolio frontier of Mean-LPM model satisfies two funds separation theorem in Shanghai stock market by empirical analysis.Chapter six studies portfolio model on condition of non-normal stable distributions. Finds the fitness of returns of stock in China to non-normal stable distributions is very good; puts a portfolio model on condition of stable distributions: mean-scale parameter model; finds mean-scale parameter model can better explain actual investment behavior by empirically analyzing.Chapter seven is summarization and prospect. Summarizes whole article and puts forward some viewpoints for further researches.The innovations of this article include:Firstly, puts forward a new viewpoint studying portfolio model on condition of non-normal distributions.Secondly, proposes to replace linear correlation coefficient by Kendall's t andproves using Kendall'st to measure correlation between risky securities do improve effect of risk reduction of diversified investment by empirical analysis.Thirdly, advances a new CLPM arithmetic; using this CLPM arithmetic, deduces the portfolio frontier equation of Mean-LPM model; proves that portfolio frontier of Mean-LPM model satisfies two funds separation theorem theoretically and empirically.Fourthly, puts forward a portfolio model on condition of stable distributions: mean-scale parameter model.