Question 1

Suppose that the term structure of interest rates for the next five years is as given in the chart and table below.

Use Excel to determine the swap rate for a five-year swap where payments are made every six months. In order to do this, you should follow the steps given below:

1)Calculate the continuously compounded forward rates for each six-month period in the five-year term structure.

2)Convert the continuously compounded forward rates to semi-annually compounded rates, and use these to find the floating-rate cash flows to be received at the end of each six-month period.

3)Assume that the fixed-rate cash flow to be paid is a constant percentage of the face value of some notional amount, and assume that all these payments will remain the same throughout the tenor of the swap.

4)Calculate the net cash flow for each payment period, and discount these using the appropriate continuously compounded zero rate.

5)Use Goal Seek or Solver in Excel to set the initial value of the swap to zero, by changing the swap rate in your spreadsheet.

6)Include a screenshot of your Excel calculations in your homework submission.

Question 2

A currency swap has a remaining life of 27 months. It involves exchanging interest at 10% on 20 million for interest at 6% on $30 million twice a year. The term structure of interest rates in both the United Kingdom and the United States is currently flat, and if the swap were negotiated today the interest rates exchanged would be 4% in dollars and 6% in sterling. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound sterling) is $1.4300/. What is the value of the swap to the party paying sterling?

Question 3

Empower Federal Credit Union is a mortgage originator that has recently decided to pool 4,000 of its mortgages into a portfolio. The average value of each mortgage in the pool is $125,000, and the average interest rate is 3.25%. The credit union plans to sell the mortgages to Morgan Stanley (NYSE: MS), but it will continue to service the mortgages for a small fee (0.05% per year).

The cash flows from the assets will be allocated to tranches. The investment bank plans to create a mortgage-backed security (MBS) with only three tranches: a senior tranche, a mezzanine tranche, and an equity tranche. The principal from the portfolio of mortgages will be allocated as follows: 70% will go to the senior tranche (rated AAA and earning 2.14%), 20% will go to the mezzanine tranche (rated A and earning 2.51%), and the remainder will go to the equity tranche (rated CCC). The investment bank plans to keep 0.20% per year as its share for the administration of the securitization process.

Additionally, Morgan Stanley plans to create a collateralized mortgage obligation (CMO) from the mezzanine tranche of the MBS. The principal assigned to the senior, mezzanine, and equity tranches of the CMO is in the same proportions as for the MBS; the credit ratings and coupon rates for the CMO are the same as for the MBS. All of this information is represented in the diagram below.

(a)If an investor purchased all of the equity tranche of the MBS, what annual return will be expected on the investment?

(b)Suppose that the economy experiences a real estate crisis, prices drop, and many of the original borrowers (14% of them) decide to default on their mortgages and abandon their homes. In dollar terms, how much would the loss of principal be for investors in the senior tranche of the CMO?

Time 0.0 0.5 1.0 Zero Rates (cc) Structure of Interest Rates Term 7.0% 6.006 5.0% 4.006 3.0% 2.0% 1.0% 0.0% 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.50% 3.35% 3.90% 4.35% 4.70% 5.00% 5.25% 5.45% 5.60% 5.75% 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Time (years)