| In the year of 1952, Harry M. Markowitz published his famous paper "Portfolio Selection" in the Journal of Finance. In this paper, he firstly studied the selection of portfolio by using the method based on mean-variance analysis. Markowitz's studies started the research of relationship between return and risk of financial asset based on quantitative analysis method, his studies also became the methodical basis of modern portfolio theoretical analysis. Based on the about 50 years development of mean-variance portfolio theory, this paper analyzes and discusses the relationship between return and risk of portfolios by using theoretical analysis and empirical study.In the part of theoretical analysis, the author reviews the research results of portfolio theory roundly. Based on systematically analyzing to the single-period portfolio theory, which is static portfolio theory, the author makes a deep analysis on the theoretical basis, the presupposition, and the proving about models, moreover, the author makes a general evaluation of the models. The author considers that portfolio selection theory mostly study the relationship between return and risk of optimal portfolios, its essential is return maximization or risk minimization, however, asset pricing theory mostly study the relationship between return and some influence factors of assets or portfolios when the capital market is in equilibrium. On the one hand, the author discusses Markowitz's mean-variance portfolio selection model, single-index portfolio selection model, and simplified model of optimal portfolio selection. At the same time, based on the rules of optimal portfolio selection and other risk-metric indices, the author also discusses mean-absolute deviation model, mean-semivariance model and mean-value at risk model. On the other hand, the author discusses the asset pricing model, including the capital asset pricing model (CAPM), the multi-factor asset pricing model, and the arbitrage pricing model (APT). Specially, based on risk-metric and factor variables, the author discusses multi-factor asset pricing model.In theoretical analysis, the author attempts to release the assumption of index's random walk, proves a portfolio selection model suitable for the linear index level Moreover, based on assets un-exchangeable, the author brings forward asset pricing models for B-shares, H-shares and non-circulated-shares. The author also bringsforward multi-factor asset pricing model based on risk-metric indices, such as coefficient of beta, standard variance, standard semi-variance, average absolute deviation, value at risk, and factor variables, such as circulated market equity, exchange ratio, short-term historical return.In the part of empirical study, the author systematically introduces some empirical research methods and results made by China's and overseas scholars. Especially, the author summarizes and evaluates some classical researches made by scholars abroad. Based on these, the author studies the relationship between return and risk of portfolio, respectively taking A-shares traded in Shanghai Security Exchange and security investment funds as analysis object.In empirical study, the author takes 417 A-shares from Shanghai Security Exchange as analysis sample, and takes the weekly returns from February 18th, 2000 to June 8th, 2001 as sample data. The author constructs 30 portfolios by classifying method. The author not only studies the relationship between return and 6 risk-metric indices of portfolios, the relationship between return and 3 factor variables of portfolios, but also studies the relationship between return and 4 risk factors (1 risk-metric index and 3 factor variables) of portfolios. Based on this, the author establishes corresponding asset pricing model. The empirical results show: it is weak to explain the portfolios' return for 6 risk-metric indices, however, the two factor variables, the natural logarithm of average circulated market equity and the average of short-term (one year) historical return, are able to expla...
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