What is the average life of a zero-coupon bond

Assignment

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).

The average life τ of a bond is defined as

τ= (∑_(t=1)^T t×PCF_t) / (∑_(t=1)^T PCF_t)

where PCFt is the principal cash flow at time t, and T is the maturity of the bond.

a. What is the average life of a zero-coupon bond?

b. 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. Show that

lim-(c→0)?τ= (T+1)/2

where c is the mortgage contract rate.

ii. Make a graph of the average life vs the contract ratec, 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)

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?

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.

4.

i. 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?"

iii. Why were many thrifts insolvent by the early 1980's?

iii. 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.

iv. How does securitization help mitigate the problem described in B?

v. Describe how securitization eventually played a role in the creation of the "RE bubble" of the early- to mid-2000's.

Format your assignment according to the following formatting requirements:

1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.

2. The response also include a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.

3. Also Include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.