QUESTION 4. In this question, assume that a parallel shift in interest rates is the same thing as an identical shift in each of the yields to maturity and ignore the initial cashflow (that is, ignore the fact that the mortgagee receives the initial principal). Consider three fixed rate mortgages, M,,M2 and M3, all as above except that the "fixed" rates may vary in parallel. The details of the mortgages are Interest Mortgage Principal Maturity Rates M $ 500,000.00 10 years 6.00% M2 $ 300,000.00 5 years 4.50% M3 $ 200,000.00 2 years 3.00% where all interest is compounded monthly. a Find the yields to maturity of the mortgages, from the bank's point of view. b. C. d. Find the Macaulay and modified duration and convexity of the mortgages (again, from the bank's point of view). If the bank wishes to hedge one 10 year mortgage against parallel shifts in the interest rates using the 5 year mortgage, how many of the 5 year mortgages does it require? How might it achieve this? If the bank wishes to hedge one 10 year mortgage against parallel shifts in the interest rates using both 5 and 2 year mortgages, how many of the latter two must it hold?