Jun 23, 2018
Due: Jun 28, in class
HW 1
FRL 383
40 points. Show all work for full credit (annotate relevant formulae in excel). Make sure your presentation is clear. Excel table rules apply (show no more than 1 page of repeated rows, i.e., hide repeated rows so that the table fits on one page in landscape format. Make sure the font is not too small).
1. [10 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?
b. [1 pt.] What is the average life of an interest only bond?
c. Consider a fully amortizing level-payment mortgage that does not default, nor is it ever curtailed or prepaid.
i. [2 pts] Show that
where c is the mortgage contract rate.
ii. [6 pts] Make a graph of the average life vs the contract rate c, where 0 ≤ c ≤ 100% and T=30y. In you submission, show the amortization table for c=5% (and make sure it fits on one page and is annotated)
2. [10 pts] Consider a $100,000 fully amortizing 30-year 5/1 ARM with a margin of 2.5%. The note rate for the fixed period is 4%, and suppose that the underlying index has values of (date in years, rate as MEY): (0, 2%), (1,2.5%), (2,2.5%), (3,2%), (4,2%), (5,2%), (6,4.5%), and (7-30,5%). Rate caps are 1/3 (periodic/lifetime), but the fixed to floating cap is 2%. The is also a payment cap of 10%, with a negative amortization cap of 120%.
If the fees for the loan are 2% and $3,000, what is the loan’s APR?
3. [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. [4] If the loan is to be repaid after 15 years, which is the better choice?
b. [2] If the loan is repaid after 5 years, which is the better choice?
Hint: Use the effective cost of borrowing to make the decision.
4. [14 pts]
A. [2] 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. [3] Why were many thrifts insolvent by the early 1980’s?
C. [4] 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. [2] How does securitization help mitigate the problem described in B?
E. [3] Describe how securitization eventually played a role in the creation of the “RE bubble” of the early- to mid-2000’s.
