The Influences of Foreclosure Factors on the Value, Yield, Duration and Convexity of a Mortgage

This article presents a theoretical model that considers the influence of foreclosure factors, including foreclosure lag, foreclosure costs and the ratio of the auction price to the unpaid balance of a mortgage (APUPB ratio), on that mortgage's value, yield, duration and convexity. We used data obtained by the Federal Housing Administration (FHA) to perform the numerical analyses. The results indicate that the average default period and the average foreclosure lag are 2.5 years and 1.9 years, respectively. For each percentage increase in the APUPB ratio, the foreclosure lag decreases by about 4.6 days as we specify a linear relationship between the foreclosure lag and APUPB. The lender's opportunity cost is greater than the foreclosure settlement costs, and the total foreclosure costs are 25% of the house's auction price. Moreover, the foreclosure lag, foreclosure costs and the discounted auction price (i.e., 1‐ APUPB ratio) are negatively correlated with the mortgage's value, duration and convexity, but they are positively correlated with the yield. In addition, a change in the default probability has the greatest influence on mortgage's convexity and the next greatest on the yield. Our study provides a useful tool for portfolio managers and lenders to more appropriately measure the yield, duration and convexity of a mortgage.