Portfolio Strategies With Correlation Risk

The asset allocation strategies play an important role in financial theoriesand practice. However, classical financial models without taking into accountthe correlation risks always assume the financial markets to be perfect and thecorrelation coefficient to be fixed or a function of time, while, in fact, thecorrelation of markets is variable, and the correlation structure has asymmetriccharacter, that is to say, returns appear to be more highly correlated duringmarket downturns than during market upturns. Especially, the correlation ofmarkets will reach a peak during the financial crisis, which will significantlyraise the risks of portfolio, so we can not bring the functions of diversificationinto play. Therefore, the asset allocation strategies without taking into accountthe correlation risks are suboptimum, and if we bring the changes of correlationinto the asset allocation strategies, the portfolio will contain the position tohedge the correlation unexpected changes. Different from portfolio choice oftraditional finance theories keeping a complete market setup, we study theportfolio strategies with correlation risk.We reproduce the asymmetric tail correlation of financial markets usingCopula functions that incorporate dependence in the left or the right tail, applyGARCH models to analyze the fluctuation of markets, and apply GEDdistribution to depict the leptokurtosis and fat-tail of returns distribution. On thebasis of what we have done, we introduce the CVaR as optimized goal,combine the realistic data and Monte Carlo simulation to analyze the situationsof returns in the future, and make use of linear programming to solve theportfolio strategies with correlation risk. Farther, in order to study how thecorrelation risk effect the portfolio efficient frontiers, to analyze if the portfoliostrategies with correlation risk will improve the performance of portfolio, and todiscuss the connection between correlation and strategies, we select thelogarithmic return rates of the Hang Seng Index and Shanghai CompositeIndex between31st, October2007and30th, June2010to implement positiveanalysis. We discover that when the expect return rate is fixed, ignoring uppertail correlation will overestimate the risk of portfolio; when the expect returnrate is low, ignoring lower tail correlation will underestimate the risks of portfolio, while the expect return rate is high, ignoring lower tail correlation willoverestimate the risks of portfolio; quantify and control the asymmetric tailcorrelation will improve the performance of portfolio; compare with thestrategies without correlation risk, the strategies with correlation risk willincrease the proportion of Shanghai stock market if the lower tail correlationincrease and upper tail correlation decrease, vice versa.