Generalized Gaussian Covariance Analysis in Multi-Market Risk Assessment

In this thesis, I propose and implement a generalized Gaussian methodology to accomodate the asymmetry and kurtosis of financial returns data, features not captured by standard Gaussian methods. The methodology extends from Gaussian methods with one variance-covariance matrix by estimating different variance-covariance matrices to characterize the differential risk exposures in long and short positions across portfolios of multiple assets. Estimation of the different variance-covariance matrices involves non-linear optimization in the variable space of positive definite matrices. Separate portfolio risk assessments are proposed for "normal" and "stressful" market conditions. An individual portfolio's conditional expected return under "stressful" market conditions is estimated using best linear unbiased estimators for the location and scale parameters of a univariate Gaussian distribution with censored data. Applications to market risk measurement in multinational currency and equity markets are provided. Thesis Supervisor: Prof. Roy Welsch Title: Leaders for Manufacturing Professor of Management Science and Statistics Thesis Supervisor: Dr. Peter Kempthorne Title: Principal Research Scientist