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    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
    (Massey University, 2003) Yuen, Mui Kuen
    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.
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    Portfolio selection by homogeneous programming : a New Zealand case study : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Economics
    (Massey University, 1985) Young, Martin
    For investment managers through to the individual the task of solving their particular portfolio problems remains a principal objective. It has been shown that an efficient portfolio can be specified in terms of its expected return and profit variance, (risk), that is the first two moments of the investor's subjective yield distribution. Selection of an efficient portfolio can always be achieved by quadratic or homogeneous programming. An integral part of the efficient portfolio selection process by homogeneous programming lies in the use of the truncated minimax criterion which gives a measure of risk preference, m. Varying m will give the complete set of efficient portfolios from all possible ones. This is detailed in chapter one where it is also shown that an optimal portfolio which allocates the budget with maximal caution can be selected from among the efficient ones under the additional criterion that the marginal value of the investment dollar is not exceeded by its marginal cost. Using a specified algorithm an optimal portfolio is selected from stocks qualifying as Trustee Investments under the Trustee Amendment Act 1974 listed on tho New Zealand Stock Exchange. Chapter two details the manner in which a five year data base of weekly observations, 1979 to 1983 inclusive, was developed for this operation and gives the preliminary results of expected return and profit variance for the stocks selected. A printout of the complete data file is included in the appendix. Chapter three of this thesis shows in detail the manner in which the algorithm is applied and gives a final result using weekly data over the four year period, 1980 - 1983 inclusive. The characteristics of this optimal portfolio are shown together with details of its performance over the twelve month period Jan - Dec 1984. Finally consideration is given to the robust nature of the portfolio selection system by looking both at a range of efficient portfolios selected from the four year data and also an optimal result from the full five year data.
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    Do cross listed securities in the face of extreme events present any risk return benefits for New Zealand investors? : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey University
    (Massey University, 2005) Browning, Rebecca
    Many investors are looking for alternative investment options in todays market as correlations among markets have increased, causing diversification benefits once gained to be diminished. This thesis examines what risk return benefits can be gained by investors from international diversification, especially cross listed securities, and how these benefits may enhance the risk return relationship in the face of extreme events. Extreme events being researched are Russian Ruble Crisis in 1998, September 11 2001, and Argentina Financial Crisis in 2002. It was found that cross listed securities held within a portfolio provided diversification benefits for investors with an improvement in the risk return relationship of lower risk and higher returns. Tested under extreme events it was found that holding cross listed securities within a portfolio mitigated some of the affects demonstrated.
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    Assessing tail-related risk for heteroscedastic return series of Asian emerging equity markets : a thesis presented in partial fulfillment of the requirements for Master of Business Studies at Massey University
    (Massey University, 2003) Xu, Qing
    High degrees of leptokurtosis, heteroscedasticity and asymmetries in return series are the common features of Asian emerging equity markets, especially during the financial crisis. Thus, strengthening risk management with improved risk measures becomes increasingly important. According to the Basle Committee on Banking Supervision, the value at risk (VaR) should be calculated at the 99% confidence level or above with daily data. In the context of Asian equity markets, the use of the estimated conditional variance of market returns as the sole measure of market risk may result in serious underestimation of the true risk caused by tail events. Therefore, this research focuses on the tail-related risk measure of nine Asian index returns within the framework of extreme value theory. It employs the generalized extreme value (GEV) and the generalized Pareto distribution (GPD) approaches combined with AR(l)-GARCH(m, s) filtering of the return data. The VaR performances under different distributions with different volatility filtering are compared, and the estimated conditional and unconditional expected shortfalls based on the GPD are reported. The important findings include the following. (1) The nine heteroscedastic index returns indeed follow heavy-tailed distributions rather than the normal distribution. (2) Both the GPD and GEV distributions of daily returns are asymmetric between local maxima (right tail) and local minima (left tail). (3) The results of the GEV approach are somewhat sensitive to the block length chosen, while the GPD approach, with the thresholds determined much less arbitrarily, can avoid equivocalness with the GEV method. (4) The reported results indicate that the VaR based on the extreme value theory at high quantiles (above 99%) is more accurate than the VaR based on the normal distribution.
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    An analysis of the gains from Asia-Pacific portfolio diversification : an Indonesian perspective : a thesis presented in partial fulfilment of the requirements for the degree of Master of Business Studies in Finance at Massey University
    (Massey University, 1996) Syarif, Agus
    This study examines the level of gains for Indonesian investors who diversify their portfolios into Asia-Pacific stock markets compared to purely domestic diversification. The study covers the national stock markets of Australia, Hongkong, India, Japan, Malaysia, New Zealand, Philippines, Singapore, South Korea, Taiwan, and Thailand over the period 1990-1994 and 1992-1994. The two overlapping periods were chosen because there was an improved performance of both the Indonesian market and the Asia-Pacific markets for the latter period, in terms of both increased return and reduced risk. Potential gains from Asia-Pacific diversification are shown to exist for the period 1990-1994. In contrast, the period 1992-1994 indicates that the Indonesian investors cannot significantly benefit from the Asia-Pacific diversification. Thus this study indicates that the Indonesian investors should diversify their portfolios within the Indonesian stock market instead of diversifying into Asia-Pacific portfolios.
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    Estimating and evaluating the Archimedean-copula-based models in financial risk management : a dissertation submitted in fulfillment of the requirements for the degree of Doctor of Philosophy in Financial Economics, Massey University, Auckland, New Zealand
    (Massey University, 2008) Xu, Qing
    Copula is used to model multivariate data, as it accounts for the dependence structure and provides a flexible representation of the multivariate distribution. Recently a large number of Archimedean copulas have been proposed to deal with various dependence aspects in financial risk management, which invokes several new questions in some important yet under-researched areas. These questions, therefore, need further investigation. This dissertation comprises three essays and probes into three untouched questions all involving the Archimedean-copula-based models. The first essay studies whether the Archimedean-copula-based portfolio value-at-risk (PVaR) model outperforms the Gaussian-copula-based PVaR model in out-of-sample forecasting. My empirical findings in this essay show that the Archimedean-copula-based PVaR model, especially the Clayton copula-based model, has better forecasting performance than the Gaussian-copula-based PVaR model in most cases m both the in-sample and out-of-sample periods. In addition, the data snooping problem (i.e., model risk) associated with the copula-based PVaR model is also explored. The second essay examines the question of how to evaluate the non-Gaussian multivariate density forecasts. In this essay, I propose a test procedure, by using the likelihood ratio test based on the Kullback-Leibler information criterion, to evaluate the Archimedean-copula-based multivariate density forecasts, and apply the procedure to foreign exchange markets. The test procedure is not only conducive to fully ranking competing sophisticated models with the non-Gaussian-distributed multivariate densities, but also allows for model misspecification in both marginal and copula functions under the null and the alternative hypothesis. The third essay focuses on this question: Will the PVaR estimation be improved if the Archimedean copula model takes into account conditional asymmetric tail dependence and time-varying investors' heterogeneous beliefs? I use the conditional skewed-t distribution (as the marginal function) to represent time-varying investors' heterogeneous beliefs, and employ three two-parameter Archimedean copulas to investigate dynamic asymmetric tail dependence between two of three Asian developed futures markets. My results provide strong evidence that such conditional copula models can improve the PVaR estimation and so a greater amount of diversification benefits can be reaped at a higher confidence level.