Document Type thesis Author Name Motyka, Matt Email Address motykams at yahoo.com URN etd-0429103-231210 Title Risk Measurement of Mortgage-Backed Security Portfolios via Principal Components and Regression Analyses Degree MS Department Mathematical Sciences Advisors Professor Domokos Vermes, Advisor Keywords portfolio risk decomposition principal components regression principal components analysis mortgage-backed securities Date of Presentation/Defense 2003-04-28 Availability unrestricted
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.
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