Final Exam
FIN 525 FixedIncome Securities
Philip H. Dybvig
Washington University in Saint Louis
December, 2000
This is a closedbook examination. Answer all questions as
directed. Mark your answers directly on the examination. There
are no trick questions on the exam. There are some formulas
from the course (including some you will not need) at the end
of the exam. All cash flows and interest rates are annual.
Good luck!
A. General Concepts Short Anwer: 20 points (Answer
each question in no more than one sentence of ordinary
length.)

Name three examples of fixedincome securities.

Which is a better asset for a shortterm fund to be used to pay
salaries and other expenses, Treasury Bonds or AAA corporate bonds?
Why? Assume the bonds have the same maturity and similar risk
characteristics.

Which is more sensitive to interest rate risk, a standard coupon
bond or an inverse floater of the same maturity?

What are i.o.'s in the world of mortgagebacked securities?

Why might smoothing the forward rate curve be a good idea?
B. Basic rates and arbitrage 30 points

implied forward rate Suppose a twoyear
Treasury STRIP costs $92 per $100 of
face value and the oneyear Treasury STRIP costs $96.25
per $100 of face value. What is the implied forward rate
for borrowing and lending from one year out to two years
out?

implied forward arb Suppose a twoyear
Treasury STRIP costs $80 per $100 of face value and the
oneyear Treasury STRIP costs $88 per $100 of face value.
Then the implied forward rate for borrowing and lending
from one year out to two years out is 10%. If we can also
borrow and lend forward from one year to two years at 12%,
what is the arbitrage?

replication with coupon bonds A
oneyear coupon bond with face of $100 and coupon rate of
5% is trading at par. A twoyear coupon bond with
face of $200 and a coupon rate of 4.5% is also trading
at par. A company would like to pay you $880,000 to
assume a pension liability that is expected to cost
$418,000 in two years and $543,000 in one year. Is
this a good deal? (The first coupon of each coupon
bond will be paid one year from now.)
C. Duration 20 points
A portfolio includes three discount bonds: one paying
$3 million 5 years from now, one paying $2.5 million
10 years from now, and one paying $2 million 15 years
from now.

What is the duration of the portfolio when the term
structure of forward rates is flat at 6%?

What is the duration of the portfolio when the term
structure of forward rates is flat at 7%?

How does duration change with interest rates? Explain why.
D. Binomial Option Pricing 30 points
Assume that the interest rate starts at 6% and in each period
and either increases by 2% or decreases by 2% (from 6% up to 8% or
down to 4%). The riskneutral probabilities of ups and downs are
1/2.

What is the price now of a discount bond with face of $100
maturing one year from now?

What is the price now of a discount bond with face of $100
maturing two years from now?

What is the price today of an interest rate floor with a
strike of 7% and two periods to maturity? The underlying
notional is $100 (so the cash flow is 2 if the rate is 5%).