Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Dr. Mark Reesor


According to Canadian tax law the interest payments on loans used for investment purposes are tax deductible while interest on personal mortgage loans is not. One way of transforming from non-tax deductible to tax deductible interest expenses is to borrow against home equity to make investments. This can be achieved through a re-advanceable mortgage and has been promoted by personal financial planners as a way of significantly decreasing the time required to pay off a mortgage and the associated total interest cost. However, the notion of risk associated with the investment holdings is not emphasized. Using simulation we study the risk associated with the re-advanceable mortgage strategy to provide a better description of the mortgagor's position. We assume that the mortgagor invests the entire proceeds from the line of credit into a single risky asset (e.g., stock or mutual fund) whose evolution is described by geometric Brownian motion (GBM). We find that this strategy reduces both the average mortgage payoff time and the total interest cost. However, there is considerable variation in the payoff times with a significant probability of a payoff time exceeding the mortgage term. Furthermore the higher the marginal tax rate, the more the average payoff time and interest cost are reduced implying that this strategy is more beneficial to high-wage earners. Using a simple stochastic model for job status we also investigate the effect of job loss on the payoff time distribution. In the event of job loss, the investment portfolio protects the homeowner from default as part of the investment portfolio can be sold to fund mortgage payments.

Variable rate mortgages are also considered in our study. The mortgage rate models we consider are the mean reverting rate model without a diffusion term and the CIR process. There is not a big difference compared with the fixed-rate mortgage in the average payoff time for the mean reverting rate model with no diffusion. However, once the diffusion term is included, the average payoff time and the volatility of payoff time increase according to the volatility of CIR process. We also incorporate a housing price model in the re-advanceable scheme and see that it can decrease the average payoff time and average total cost, however, this comes at the cost of increased standard deviations of the payoff time and total cost distributions.

Results of this study could be of interest to policy makers as they continue to adjust mortgage rules to induce desired behavior, such as reducing personal debt burdens. The modelling framework provided here can be adjusted to analyze the effect of potential policy actions on homeowners who borrow against home equity to invest.