Consider three fixed rate mortgages, M1 ,M2 and M3 , and assume that the “fixed” rates may vary in parallel. The details of the mortgages are

Mortgage Principal Maturity Interest

M1 $ 400,000.00 10 years 8.00%

M2 $ 250,000.00 5 years 6.0%

M3 $ 150,000.00 3 years 5.0%

where all interest is compounded monthly. Mortgage repayments are assumed to be monthly.

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)

a. Find the yields to maturity of the mortgages, from the bank’s point of view.

b. Find the Macaulay, modified duration and convexity of the mortgages (again, from the bank’s point of view).

c. 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 the bank achieve this?