In: Finance

FNMA has direct holdings of 30-year fixed-rate mortgages
financed by three- to five-year agency securities sold to the
public.

What kind of interest rate option could FNMA use to limit the
interest rate risk? Explain how this would work. Explain how a
collar could also be used.

The problem FNMA will face is that of asset liability maturity (or duration) mismatch. The mortgages have maturity of 30 years while liabilities have maturity between three to five years.

If the interest rate rises, the cost of funds will increase for FNMA however the interest income from the mortgages will remain the same. FNMA needs protection against this risk.

**Interest rate
Caps** are the popular derivatives that generate
income for the buyer or holder of the cap if interest rate rises.
Thus FNMA, will receive payments at the end of each period when
interest rate is higher than the strike price of the Cap. Caps,
practically are, a series of call options on the index with
floating rate. The payoff from the cap to the buyer will be:

Nominal Principal x (Index Level – Strike Price) x n / 360 where "n" is the number of days.

Hence, FNMA should buy interest rate caps for protection against rising interest rate risk.

**Explain how a collar could also be used.**

However, there is one problem with Caps. They are costly. FNMA may have to spend a significant amount as upfront as commission, or fees or premium to buy the Caps. IN such a situation, sources of funds can be Interest Rate Floors. So, FNMA can sell Floors to get the cash flows to buy the Caps. Such a situation where a borrower is long on Caps and short on Floor with the same underlying and same strike price, is called Collar. Thus, Collar position will:

- Help get the initial cash flows to buy the Caps
- Limit the interest rate risk

A savings institution (SI) has funded $12 million of
30-year fixed-rate mortgages with an average interest rate of 5.75
percent. These assets are funded with time deposits with an average
maturity of six months. The deposits are currently paying 3.5
percent. In six months time, however, the Fed has raised interest
rates twice and the depositors now must be paid 4.25 percent. What
will happen to the SI's ROA and NIM? How would your answer change
if the SI normally...

You want to buy a house financed with a 15-year fixed-rate
mortgage. The best interest rate you could find is 7% APR. Payments
are made monthly, so the APR should be assumed to be a simple
interest rate (i.e. a stupid interest rate) added up over 12
months.
What is the most you can borrow if you can only afford to pay
$1,800 per month?

- What is the effective rate of a 4.25%, $250,000 30
year fixed rate mortgage with 1.5 discount points, if the mortgage
is held for 10 years?
- What is the effective rate of a 4.25%, $250,000 30
year fixed rate mortgage with 1.5 discount points, if the mortgage
is held for 1 year?

FreddieMac reports that the average rate on a 30-year fixed rate
mortgage is 3.92% as of January 2012. This is down from 4.76% in
January 2011 and 5.03% in January 2010. If you have a $216,000, 5%,
30-year mortgage, how much interest will you save if you refinance
your loan at 3.5% for 20 years?
Joe Levi bought a home in Arlington, Texas, for $130,000. He put
down 25% and obtained a mortgage for 30 years at 8%. What is...

- What is the effective rate of a 4.25%, $250,000 30
year fixed rate mortgage with 1.5 discount points, if the mortgage
is held for 10 years?
- What is the effective rate of a 4.25%, $250,000 30
year fixed rate mortgage with 1.5 discount points, if the mortgage
is held for 1 year?
- You have two options for a 30 year fixed rate
mortgage:
$500,000 mortgage, 5% rate
$500,000 mortgage, 4.50% rate, 2 discount
points
For how long...

On a 30-year, fixed-rate loan with a monthly payment of $1,000
and an interest rate of 9%, what is the outstanding balance due on
the loan with after the borrower has made 18 years of payments?

Crystal Ball has a 30 year, fully amortizing fixed rate
mortgage, with monthly payments, for a $200,000 loan at 7%. In 5
years, interest rates fall and Crystal can get a 25 year, fully
amortizing fix rate mortgage with monthly payments at 6%. However,
to get this new loan, Crystal needs to pay 2 points and $2,500 in
fees. What is the return on investment (from refinancing)? Assume
Crystal stays in the property for the next 25 years – the...

A
homeowner can obtain a 250,000, 30 year fixed rate mortgage at a
rate of 6.0% with zero points or at a rate of 5.5% with 2.25
points. How long must the owner stay in the house to make it
worthwhile to pay the points if the payment saving is not
invested?

At the same interest rate, which of the following five-year
securities will have the lowest duration
A Treasury note.
A Treasury bond.
A car loan.
A simple load.
A zero-coupon bond.

Rachael has a 100,000, 30 year, fixed mortgage with a 12%
nominal interest rate convertible monthly.
She has made payments at the end of each month for ten
years.
Now she will begin making twice the payment each month.
How many years will she be able to take off the original 30
years assuming a balloon payment for the final fractional
payment?
A. 12
B. 13
C. 14
D. 15
E. 16

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