Multi-scale Analysis Of Systematic Risk, Based On Wavelet Method

Measure of risk is concerned by the traders in financial markets, asthese traders have different investment time horizon and risk preferences,making measure of risk on one scale cannot meet the demand of thetraders，thus, it is necessary to analyze the systematic risk in the financialmarkets on a scale-to-scale basis. Although traditional methods canconduct a multi-scale analysis by building several models, waveletanalysis is obviously better than traditional methods when it comes tomulti-scale analysis. So this paper conduct a multi-scale analysis on thesystematic risk of the financial market by integrating the wavelet methodand traditional market model, expecting to provide more targetedinformation for the investment decisions of traders in the financialmarkets.The wavelet analysis used in this paper is completed by the softwareMATLAB. The first studied of this paper is the impact of differenttime-scales on the systematic risk of individual stock and of a givenportfolio in Shanghai Stock Market by applying the wavelet analysis.Then, to investigate the scaling properties of stock market returns atdifferent scales, wavelet variance analyses are used. An approximatelinear relationship can be observed between wavelet variance and waveletscale. The analysis by using wavelet cross-correlation analysis of therelationship between SSE180Index and the selected portfolio on a scale to scale basis shows that the co-movements between them changes withdifferent time-scales. Especially, the longer the time-scale, the strongerthe relationship. The wavelet analysis of systematic risk shows that allindividual assets and the diversified portfolio have a multi-scale behavior,which indicates that the systematic risk measured by β in the marketmodel is not stable over time. The analysis of Value-at-Risk at differenttime scales shows that risk is more concentrated at higher frequenciesdynamics(lower time scales)of the data. Finally, the analysis is extended,the performance of the portfolio is evaluated by computing the SharpeRatio and the modified Sharpe Ratio.Although the conclusions of the article is useful for traders in thefinancial markets, there is still room for improvement of the method ofconducting a multi-scale analysis. This improvement can be the point ofview of mathematical methods: using wavelet packet transform or liftingwavelet transform, it also can come from the perspective of economictheory: improving the market model according to the relevant economictheory, and so on. These will also be the direction of further study in thefuture.