Portfolio risk diversification, coherent risk measures and risk mapping, risk contribution analysis and the setting of risk limits : a thesis presented in partial fulfillment of the requirements for the degree of Master of Business Studies in Finance at Massey University

Abstract

This study aims to investigate the nature and sources of portfolio risks during normal as well as abnormal market conditions. The benefits of portfolio diversification will be studied first. Portfolio risk as measured by the volatility and beta will be calculated as the number of the positions is increased until the marginal diversification benefits obtained are at its optimal. Other measures based on statistical measures such as quantiles, quantile differences and quantile ratios for central tendency and asymmetry presence and significance of extreme events of skewness and kurtosis will also be used. This study is conducted on the daily data for the period August 9, 1998 to June 30, 2003, for 25 stock markets worldwide: Australia, Brazil, Chile, France, Germany, Hong Kong, Japan, India, Indonesia, Ireland, Israel, Italy, Mexico, New Zealand, Singapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, Turkey, United Kingdom and United States. Based on the theory of central limit theorem (CLT) and hence jointly normal distributions, the relationship between portfolio diversification and value at risk (VaR) as a coherent risk measure is examined. Diversification benefits based on two simulation models namely: the geometric Brownian motion (GBM) and Fréchet random walk (FRW) which serve as the ideal models are also investigated. The second part of the study focuses on the main sources of risk or risk hot spots in a portfolio using component VaR (VaR c ), incremental VaR (IVaR), and delta or marginal (DVaR). Finally, the portfolio risk will be monitored using a risk mapping or risk decomposition method. The risk of a given position is mapped onto a much smaller number of primary risk factors. In this study, individual country's stock index will be used as proxy for equities, government bond index and risk free rate for fixed interest, spot foreign exchange rate and forward one month, three month and one year exchange rale and gold and crude oil for commodities. In general, the results for the tail-risk measures are similar to what has been found for the center of the portfolio risk measures and covariance plays a significant role in the assessment of the risk inherent to real portfolios based on the greater diversification benefits gained from the two simulated models, whose log-returns were generated independently. Diversification "works" well under normal market conditions.