Measurement Of Portfolio Risk Investments

Affected by the financial crisis, the downturn in the global stock markets and bond markets, the international price of gold is rising sharply and has a eye-catching performance in the gold market. Gold has become a very important investment tool as well as stocks and bonds. In recent years, institutional investors continue to grow and develop and the influence is also growing. Since institutional investors generally make diversified investment, gold has become a very important part of the investment portfolio. Most of the bank’s private banking assets report suggest that its asset portfolio include five categories:stocks, bonds, gold, foreign exchange and real estate. The trend of the gold assets remain optimistic. As the institutional investors use a diversified investment strategy, We should choose a more accurate and fast method when portfolio VaR is calculated. There are many ways to calculate the portfolio VaR now, including historical simulation method, parameter method and Monte Carlo simulation method. According to the current literature, institutional investors would like to use more traditional methods, such as the internal model approach to calculate the portfolio VaR.The traditional VaR calculation methods have some obvious shortcomings, such as the normal distribution assumption, the assumption of linearity, the lack of consideration of extreme events and financial assets between the end of correlation and so on. These factors will affect the effectiveness and risk of the portfolio. Thus they may have a significant impact on the accuracy of the VaR calculation. Compared with the traditional methods. Copula theory has theoretical advantages. the copula function can connect a few marginal distribution together into a joint distribution. And it does not assume that the marginal distribution is normal. The consistency and the measure for relating exported from copula function have a wider application and are more practical, which can capture the variable non-linear or non-symmetrical relationship. In particular, it is easy to catch the distribution of the correlation in the tail.This paper is based on the traditional method first to measure gold, stocks and bonds portfolio risk. Then it uses copula functions and GARCH models to build the Copula-GARCH-t model. After that, it uses historical simulation method, parameter method and Monte Carlo simulation to make empirical study of gold, stocks and bonds’ portfolio risk analysis. Finally, in the case of minimal risk, the investment ratio of the three assets is given. The results show that the T distribution can better describe the data than the normal distribution. So that the results are relatively more accurate. Copula-GARCH (1,1)-t model fits the datas very well, so the random number simulated by the copula model is closer to the real rate of return, and it is more accurate in the calculation of the risk of the portfolio. What’s more, it is higher in reliability. From calculation results of KuPiec test, the Monte Carlo simulation is superior to the several traditional methods. While the historical simulation method and Risk Metrics method may underestimate the risk. On the contrary, the GARCH-T model may overestimate the risk. Copula model can solve the shortcomings of the Monte Carlo simulation approach. The use of Monte Carlo simulation method to calculate VaR model is essential to choose. T-copula model is significantly better than the normal copula model and the calculated results are slightly larger than normal copula model. This is because the T-copula model is fully taking the assets of the thick-tailed distribution into account. And thus the calculations are more conservative. When the amount of the investment is700.6yuan, and when the risk is minimum, with the95%confidence level, the portfolio VaR of16.54yuan. It means that the maximum loss of the portfolio is16.54yuan. We can also say it is2.36%of the investment amount. In comparison, when in99%confidence level, VaR is18.95yuan, and the amount of the investment is2.70%. From the results, the expected loss of the proportion of total investment amount is very small, so it has a better hedge against inflation. The conclusion of the article shows:When institutional investors calculate the portfolio VaR, they can use Copula-GARCH (1,1)-t model to calculate for it is not only fast but also the results are more accurate than traditional methods. This is of great value for institutional investors to determine the investment strategy.