Correlation And Risk Analysis Of Portfolio

In 1952, Markowitz proposed the selection of portfolio. It symboled the beginning of modern portfolio theory. Markowitz used expectation of the return to describe the expected return, and used variance of the return to describe the risk of portfolio. He proved the smaller linear correlation was, the smaller the risk of portfolio was. With the fast development of finance market and the invention of new financial products, modern financial market becomes more and more complicated. The traditional method of risk measurement can't meet the need of us. At the beginning of 90's of the 20th century, the significant financial disaster caused the development of VaR which was a new method of risk measurement. VaR is widely used in risk measurement recent years, such as calculation of the Capital Adequacy Ratio of banks, estimation the risk of portfolio and so on. Therefore, VaR is very important in modern risk management.Dependence plays an important role in risk management. In the past, people only used linear correlation to measure dependence. Moreover, portfolio theory of Markowitz only considered linear correlation. However, with the risk management getting more and more complicated, modern risk management sets a higher request to the risk superintendent. In modern risk management, the study of dependence with linear correlation alone is far away from the risk superintendent's satisfaction. They must go deep into understanding other dependence concepts, such as tail dependence.Based on portfolio theory of Markowitz, we want to consider the influence on VaR by dependence when we use VaR to measure risk. If market data has Gaussian distribution, we can prove the smaller linear correlation is, the smaller VaR, of portfolio is. However, masses of market data hasn't Gaussian distribution, and it is fat-tailed. We focus on finding the influence on VaR by linear correlation and tail dependence in this paper. The result indicates the tail dependence has an important influence on VaR of portfolio. Therefore, we must consider the dependence completely when we use VaR to measure risk.