The Application Of Financial Market Risk Measurement And Modern Portfolio Theory Based An Copula And EVT

â… .Main Train of Thought and Structure of the ThesisAs an important branch of Finance, portfolio theory is mainly used to optimize the collocation of personal or collective fortune in forms of assets such as shares, bond, and other derivatives and so on.In 1952, Markowitz brought forward mean-variance Model,emblematizing that modern portfolio theory came into being. However, the normal distribution hypothesis is very important for mean-variance model. In framework of reward-risk dominance,variance can be taken as the best measurement for risk only when the returns of risk assets is normally distributed. And in framework of expected utility maximization,the mean-variance model accords with the expected utility hypothesis only provided the utility function is quadratic or the returns of risky assets are normally distributed.Nevertheless, many empirical researches have shown that distributions of returns of risky assets are skew and leptokurtic. In addition, if the return of risky assets no longer accord with normal distribution, variance is not the best risk measurement.The main train of thought and the structure of the thesis is: in order to study portfolio theory, in the first place we should study normal distribution hypothesis, the key hypothesis of mean- variance model. Then, under the return-risk research framework, loose this hypothesis and testify that variance is not suitable to be taken as the measurement tool for risk. And then ES is introduced to build mean-ES model. Finally, considering the dynamic feature of returns of risky assets, extreme value theory and Copula function will be used to build a combination distribution of portfolio return, and study portfolio theory under this distribution.â…¡. Main ContentThis thesis studies portfolio management models under non-normal distribution. There are mainly three key questions will be studied. Firstly, marginal distribution of financial assets return will be studied via application of extreme value theory and GARCH model. Secondly, the thesis will figure out whether we should choose appropriate risk measurement methods in accordance with different aims of portfolio management, and further study whether this chosen measurement can be in the frame work of Economics,and accord with the principle of expectation utility maximization.The thesis is consisted of seven sections:Chapter one is the Introduction, which gives a brief general review of the relevant studies.In Chapter Two, there is a in-depth study on two aspects in according to the purpose of portfolio management, namely, how to describe the marginal distribution of financial assets return and how to choose measurement tool for risk. Under common circumstances, financial assets return dose not accord with normal distribution, but presents certain features of"leptokurtic"and"heavy tail". Extreme value theory can be applied directly to study the tail of financial assets return distribution, and describe the"heavy tail"feature of financial assets return. However, it neglects the fact that the distribution of financial assets return is time variant. The extreme value theory based upon conditional distribution can not only describe the feature of"heavy tail", but also depict the phenomenon of return cluster. Thus, it can also be applied to the description of marginal distribution of return variable. With the spread of portfolio theory to non-normal distribution condition, variance is no longer suitable for the purpose of portfolio management. Consequently, it is necessary to study the choice of risk measurement tool in accordance with the purpose of portfolio management under non-normal distribution condition.Chapter Three analyzes the advantages of ES from the perspective of tail risk and expected utility. Through analysis of the stochastic dominance theory, the thesis holds the opinion that ES accords with second order stochastic dominance. If the sequencing of risk assets can be able to be arranged by second order stochastic dominance, it testifies that there is no tail risk in ES. When the utility function is quadratic, ES accords with the maximization of expected utility. Put it in other words, when choosing risk assets, the investor achieve the maximization of individual expected utility via choosing the risk assets have less ES value.Via applying some relevant theories, Chapter Four analyzes the possibility of combining the extreme value theory and the GARCH model via to describe and forecast extreme changing condition and time series features of financial assets return. The demonstration research of this thesis proves that the AR(1) can be used to measure the condition average of financial assets return; GARCH(1,1) can be used to measure the condition variance of financial assets return; and then the GPD in extreme value theory can be applied to describe the tail; at last, a empirical research will be given to analyze the dynamic features of Shanghai stock market 180 index.On the basis of Chapter Four, Chapter Five combines marginal distribution function via copula function and get the combined distribution function of portfolio return. Considering common function can not be used to figure out the ES value of portfolio, the thesis put forwards a estimation method based upon Monte Carlo simulation.Chapter Six does a empirical research on the built mean-ES model. Six shares in the Shenzhen and Shanghai stock market are stochastically chosen as random samples to form a portfolio. The built mean-ES model is used to seek for the efficient frontier of securities portfolio, which is compared with the efficient frontier gained by mean-variance and mean-ES models.In the last chapter the thesis comes to conclusion and prospect. Summarizing all the work done in this thesis, this chapter gives expectation of further study in future.