Extremes, dependence and asset allocation

This thesis focuses on the quantification of financial risk and dependence. Historically, the risk of a financial asset has been measured by the standard deviation of the asset's return distribution and the dependence by the linear correlation between assets. Such measures are appropriate only under certain circumstances, namely when returns are normally distributed. There is now growing empirical evidence that the distribution of returns of financial assets is heavy-tailed. Additionally, it is conjectured that financial markets are more dependent during times of stress than they are normally found to be. In a heavy-tailed return distribution the likelihood that one encounters large losses, relative to the mean return, is much greater than in the case of the normal distribution. If markets are more dependent during time of stress, the benefits of diversification may be mitigated exactly when they are needed most.; This thesis is divided into four parts. First, in Chapter 1, we examine how heavy tails of financial returns affect several aspects of financial portfolio theory and risk management. We describe several of the methods, including techniques from extreme value theory, which can be used to deal with heavy tails. We illustrate their use with the NASDAQ composite index. In Chapter 2, we investigate the portfolio construction problem for risk-averse investors seeking to minimize quantile-based measures of risk. Using dependence measures from extreme value theory, we find that most international equity markets are asymptotically independent. This form of extremal dependence could result in a greater benefit to diversification when guarding against the rarest events. The optimal allocation is, however, also a function of the marginal risks. We examine the roles of extremal dependence and marginal risk in the asset allocation problem. In Chapter 3, we revisit the asset allocation problem using a full multivariate approach to portfolio construction. This method is much more computationally expensive than the method of Chapter 2. Lastly, in Chapter 4, we use an alternative definition of contagion between financial markets and propose a relevant test. The test is based on a measure of local correlation. Using our test, we find evidence of contagion between developed and U.S. equity markets and evidence of flight to quality from the U.S. equity market to the U.S. government bond market. The appendices contain the proofs and information related to the use of the software, which was written in support of this thesis.