Spectrum Functions In Financial Risk Measurement

Since the Asian financial crisis, the problem of how to avoid the financial risks has become an important issue of public concern. Spectrum function is a new, great potential function of financial risk measurement. It can constitute spectral risk measure by leading investor’s risk preference attitude into the financial risk measurement. By using the spectrum functions, the results of the spectral measures of risk can be improved and get a more reasonable attitude reflects investors’ true risk. So, the results which derived from risk measurements can meet more current financial institutions and investors needs. Therefore, the spectrum function has good prospects for the development of financial risk measure. This paper starting from the preference relations, utility function and risk aversion coefficient to construct kinds of spectrum functions which can satisfy the conditions of tolerance spectrum of conditions, and study each property of different spectrum functions. Then, we combined financial data of stocks with different spectrum functions to analysis the effect on spectral measure of risk and portfolio optimization results. The main work is as follows:1Introduce the basic concepts and calculation methods of spectral measure of risk, then list several common risk measures in financial risk measurement; 2Detailed explain the concept of utility function and risk aversion coefficient, and then we will give some common utility functions’expressions and analyze their respective properties. Construct mixed utility function which can reflect the attitude of a particular investor preference;3Combining different utility functions and risk aversion coefficients to construct five different spectrum functions-exponent spectrum function, power spectrum function, logarithm spectrum function, hyperbolic spectrum function and mixed spectrum function. Then we will study of property of each spectrum function in detail;4Combined with the financial market stock data, we will calculate the values of spectral measures of risk of different spectrum functions, then create portfolio optimization model includes spectrum function. Next, analyze the impact of different spectral measure of risk generated by the model. The results show that the value of spectral measure of risk can meet the property of spectrum function. At the same time, the results of spectral measure of risk are better than the others’. At last, we will analyze the performance evaluation results between different risk measures, the result shows that the risk measure outcome derived from mixed spectrum function is the best.