Risk Measurement Of High Dimensional Portfolio And Its Application On Portfolio Selection

Over recent years, more and more studies focus on quantitative risk management, among which the risk measurement of high-dimensional data is of special difficulty. The paper aims to present an efficient and feasible method, which integrates the Independent Component Analysis, Local Adaptive Weights Smoothing and Generalized Hyperbolic Distribution, to solve the problem.After retrieving Independent Components (ICs) out of the observed high-dimensional time series, the problem of estimating the covariance of high-dimensional time series can be converted to the estimation of variance of ICs. Then the volatility of ICs is fitted individually and adaptively under the assumption of Generalized Hyperbolic (GH) distribution. For the volatility estimation of each IC, the Local Adaptive Weights Smoothing technique is used to achieve the best possibly accurate estimation. Under given trading strategies, Monte Carlo simulation is used to approximate the VaR and the expectation of the portfolio returns. At last, the optimum trading strategies are found in the light of the idea of Markovitz portfolio theory.In the paper, the VaR of 20-dimensional stock data with the equal weights in China is estimated. Besides, the optimum of trading strategies of these stocks is determined. It is found that the cumulative returns of the portfolio outperform that of Shanghai Stock Index.