1. [15 pts] The average life τ of a bond is defined as
where PCFt is the principal cash flow at time t, and T is the maturity of the bond.
a. [1 pt.] What is the average life of a zero-coupon bond? Show work
b. [1 pt.] What is the average life of an interest only bond? Show work
c. [2 pts] Consider a fully amortizing level-payment fixed-rate mortgage that does not default, nor is it ever curtailed or prepaid. Show that
where c is the mortgage contract rate.
d. [11 pts] Compute the realized average life of a 30 yr., 5/1 ARM with initial rate of 4%, and a margin of 2%. The underlying index is (date in yrs., index in %): (0,2), (1,3), (2,3), (3,2.5), (4,3), (5,5), (6,5), and (7-30,6). The loan is never prepaid, nor curtailed, nor defaults. There are no rate or payment caps. Annotate any excel and show all work.
2. [6 pts] A borrower is faced with choosing between two fully amortizing level-payment loans. Loan A is available for $75,000 at 10% MEY for 30 years, with 6 points included in the closing costs. Loan B would be made for the same amount, but at 11% MEY for 30 years, with 2 points included in the closing costs. Neither loan defaults/is curtailed.
a.  If the loan is to be repaid after 15 years, which is the better choice?
b.  If the loan is repaid after 5 years, which is the better choice?
Hint: Use the effective cost of borrowing to make the decision. Show work.
3. [14 pts]
A.  Describe the model of firm equity as a call option on assets of the firm. What does it mean for this option to be “out-the-money?”
B.  Why were many thrifts insolvent by the early 1980’s?
C.  Using the equity model in A, and the concept of forbearance, describe and explain the behavior of thrifts, both insolvent and solvent, in the early 1980’s.
D.  How does securitization help mitigate the problem described in B?
E.  Describe how securitization eventually played a role in the creation of the “RE bubble” of the early- to mid-2000’s.