Risk measurement of mortgage-backed security portfolios presents a very involved task for analysts and portfolio managers of such investments. A strong predictive econometric model that can account for the variability of these securities in the future would prove a very useful tool for anyone in this financial market sector due to the difficulty of evaluating the risk of mortgage cash flows and prepayment options at the same time. This project presents two linear regression methods that attempt to explain the risk within these portfolios. The first study involves a principal components analysis on absolute changes in market data to form new sets of uncorrelated variables based on the variability of original data. These principal components then serve as the predictor variables in a principal components regression, where the response variables are the day-to-day changes in the net asset values of three agency mortgage-backed security mutual funds. The independence of each principal component would allow an analyst to reduce the number of observable sets in capturing the risk of these portfolios of fixed income instruments. The second idea revolves around a simple ordinary least squares regression of the three mortgage funds on the sets of the changes in original daily, weekly and monthly variables. While the correlation among such predictor variables may be very high, the simplicity of utilizing observable market variables is a clear advantage. The goal of either method was to capture the largest amount of variance in the mortgage-backed portfolios through these econometric models. The main purpose was to reduce the residual variance to less than 10 percent, or to produce at least 90 percent explanatory power of the original fund variances. The remaining risk could then be attributed to the nonlinear dependence in the changes in these net asset values on the explanatory variables. The primary cause of this nonlinearity is due to the prepayment put option inherent in these securities.

The main objective of this thesis is to summarize and possibly interconnect the existing methodology on principal components analysis, hierarchical clustering and topological organization in the financial and economic networks, linear regression and GARCH modeling. In the thesis the clustering ability of PCA is compared with the more conventional approaches on a set of world stock market indices returns in different time periods where the time division is represented by The World Financial Crisis of 2007-2009. It is also observed whether the clustering of DJIA index components is underlied by the industry sector to which the individual stocks belong. Joining together PCA with classical linear regression creates principal components regression which is further in the thesis applied to the German DAX 30 index logarithmic returns forecasting using various macroeconomic and financial predictors. The correlation between two energy stocks returns - Chevron and ExxonMobil is forecasted using orthogonal (or PCA) GARCH. The constructed forecast is then compared with the predictions constructed by the conventional multivariate volatility models - EWMA and DCC GARCH.

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)