International Equity Markets Portfolio Downside Risk Measured By Extreme Value Theory Methods

Studies have shown international financial market have strong downsideco-movement, which induce the most financial crisis. This is because time series datafrom financial markets are fat tailed and clustered when downside extremal events occur.In order to measure the degree of downside co-movement of international financialmarket portfolio, below-mean semi-variance or below-target semi-variance or lowerpartial moment or value-at-risk have been proposed since the 1970s and some importantresults have been obtained but these method are very limited due to lack of efficientmodel used in their application to financial extremal events.In this dissertation, some downside risk measures of international equity portfolioand exchange rate exposure of international equity portfolio are proposed and a methodof computing downside risk of a portfolio of dimension n are proposed by usingmultivariate maxima of moving maxima processes. The first series of proposed methodsare for a single portfolio downside risk management. It is designed for the time series of asingle portfolio for different holding period, which can be regarded as a clustering intime. It gives true downside risk measure if the model is correct. The second proposedmethod is a two-dimension portfolio downside measure method. It is based of theconditional correlation, which is better than the unconditional correlation method. Inchapter 2, we plot bivariate portfolio return against it Value-at-Risk. Plots can be used asthe investor utility curve for investment plan. The third proposed method is a generalizedversion of the first one in the case of multivariate portfolio. It is practically applicable todownside measure of a portfolio of dimension n. A comparison with the second methodwas carried out and it seems to be more efficient. Under the constraint the thirdValue-at-Risk computing method, we optimized the portfolio using the probabilisticmethod, which seems to be more efficient than traditional variance-covariance methodapproach.All the three methods consider the exceedances over threshold approach, which usesa generalized Pareto distribution (GPD). Assuming the sample distribution belongs to thedomains of attraction of multivariate extreme value distributions, we estimate theparameters of multivariate maxima of moving maxima processes from the observed datastandardized and transformed.How to manage a portfolio downside risk efficiently, with the highest expectedreturn for a given level of risk, or equivalently, the least risk for a given level of expectedreturn, is a key to the success or failure of a financial system. Our financial analysis ofMorgan and Staley Capital International equity index prices negative returns and ChinaState Administration of Foreign Exchange rate negative return,using the three precededdescribed methods, shows, that the best modeling of standardized financial data, isthe modeling under the assumption of stationarity, with short-range dependence withindata. We find that the best way to compute market portfolio Value-at-Risk is to expresslosses as ((, where VLt = V0 1 ? exp? R))( t )0 is market value at time t = 0, computeValue-at-Risk by the quantile method and then use the result to compute a newValue-at-Risk by the expected shortfall method.In the case of bivariate analysis of downside market portfolio analysis, we find thatconditional correlation of extreme returns increase in bear market as suggested recentfinancial academicians, but there are still differences between developed and emergingmarkets downside co-movements, for a bivariate portfolio selection when Chinese equityindex was already choose. When the second stock market is a developed market thebehavior of conditional correlation is similar to what was funded by recent academicresearches. The behavior of conditional correlation is more difficult to understandbetween two emerging stock markets. The reason is because it changes with marketsintegration.For a portfolio of dimension five, we also investigate the downside co-movement ofinternational equity markets and the exchange rate exposure of an Asian equity markets.The method we used is to compute portfolio Value-at-Risk and marginal Value-at-Risksimultaneously. Under these Value-at-Risk, we optimized the portfolio (China equityindex, Germany equity index, Hong Kong equity index, Japan equity index and USequity index) return and compare the result with the result obtained from another methoddeveloped from our second Value-at-Risk computation method. We find that the portfolioreturn decreases when the risk increase, which is opposite, of the general portfolio theoryhypothesis: return increase when risk increase. We find also that exchange rate of RMBand Yen in US dollar affect our portfolio return (portfolio composed of China equityindex, RMB exchange rate, Hong Kong equity index, Japan equity index and Yenexchange rate) because those currencies are pegged to US dollar. Comparing our methodof optimization with conditional correlation method of optimization, we find thatportfolio return decrease over Value-at-Risk is always true for our method but not alwaystrue for conditional correlation method.