II. Problem - You have to show your work. No credit without an explanation (60 marks). 1. The two most-used forms of mortgages are fixed-rate mortgages and adjustable-rate mortgages: . If a borrower chooses a fixed-rate mortgage, the interest rate that she pays is fixed over the life of the loan. . If a borrower chooses an adjustable-rate mortgage, the interest rate that she pays is calculated as the rate of short-term government bonds plus a risk premium and is adjusted up or down (following the changes in the rate of government bonds) during the life of the loan. . Since adjustable-rate mortgages carry a risk of higher rates in the long run, they usually have a lower initial interest rate than do fixed-rate mortgages. In order to evaluate the factors influencing the choice between adjustable and fixed-rate mortgage loans, we have run a Linear Probability Model (LPM) and Logit Model the results of which (estimated beta coefficients) appear below, based on 78 observations: LPM Logit F (t-ratio) 0.226 (2.980) 1.185 (2.700) M (t-ratio) -0.127 (-2.600) -0.660 (-2.317) Y (t-ratio) -0.799 (-2.567) -4.030 (-2.353) Constant (t-ratio) -1.018 (-0.810) 8.192 (-1.190) where: the dependent variable is a binary (dummy) variable taking the values of D, = 1 if the i-th borrower chose an adjustable-rate mortgage and D. = 0 if the i-th borrower chose a fixed-rate mortgage. . Fi = The fixed interest rate available to the i-th borrower, in %. . Mi = The interest premium (difference) over the Treasury bills rate (that is included on the adjustable rate) that is available to the i-th borrower, in %. . Yi= The difference between the interest rate on long-term and short-term government bonds available on the day of the i-th loan, in %. The interest rate on long-term bonds is normally higher than the short-term rate to account for the unknown risks of the future. (d) Using the two models calculate the probability of choosing an adjustable rate mortgage if F = 13%, M = 2% and Y = 2% . (12 points) (e) Using the two models, what is the probability of choosing an adjustable rate mortgage if the fixed interest available now increases to 14%, with M and Y staying the same as in (c)? (12 points)