Score:
01 NAME & STUDENT NUMBER: (IN FULL, USE PRINT WRITING)
FIXED INCOME SECURITIES
Sitting: 1
Date of exam: June 17, 2011
Time: 2.00 PM
Duration: 4 hours
READ THESE INSTRUCTIONS FIRST
1. The exam takes place in a computer room where computers have internet connection. You can
prepare your answers to the questions asked on these computers or on your own laptop if you
prefer to do so.
2. As explained before, time pressure is real during the exam. The exam schedule is as follows:
 1.45pm: Students enter the exam room, student ID’s are checked.
 1.55pm: Students ready for exam, computers logged on.
 2.00pm: Students receive multiple choice questions.
 2.30pm: Deadline for handing in multiple choice questions and receiving open questions.
 3.00pm: Deadline for handing in open questions and receiving a problem set.
 5.55pm: Students finalise their work on the problem set in a single Excel-file.
 6.00pm: End of exam.
3. You are allowed to use all means at your disposition during the exam, the only condition being that
you do not communicate with any other person inside or outside the exam room, i.e. your exam
must be an individual effort. If you break this rule your exam will be voided.
4. Mobile phones should be switched off and must not be kept on the desk at any time.
5. Take into account that no two students have identical question sets. Minor and major, subtle and
less subtle, obvious and not so obvious differences between exam sets will make any attempt to
exchange answers or answer sets traceable. Although question sets are non-identical they are
equivalent.
6. You will receive - in the order explained above - the following question sets:
 Four multiple choice questions with five alternatives:
i. Each correct answer is worth one point (out of twenty). There is no correction for
guessing.
ii. Clearly indicate the alternative of your choice with an arrow pointing at the alternative.
iii. Only one of the alternatives is correct.
 Two open questions:
iv. Each correct answer is worth two points (out of twenty).
v. The answer to an open question is a structured and original text. It is not merely a
reference to or a copy of one or a number of slides.
 A problem set consisting of three problems:
vi. The total weight of the problem set is seven points (out of twenty). The value of each
correctly solved problem is indicated in the problem set.
vii. Write your answers to the problems in the reserved area on the problem set pages.
viii. A numerically correct answer to the exercises is a priori considered 100% correct. In order
to prevent fraud you must show in detail how you obtained these answers. Do this by
mailing your self made solution file named “your full name.xls” or “your full name.xlsx” to
bart.vinck@hubrussel.be before 6.00pm today (and before leaving the exam room).
ix. Avoid disaster and save your intermediate results regularly.
x. Do not round off intermediate results.
7. All paper used during the exam must be handed in before leaving the exam room.
GOOD LUCK!
01 NAME & STUDENT NUMBER: (IN FULL, USE PRINT WRITING)
MULTIPLE CHOICE QUESTIONS (4 points)
The four questions underneath are multiple choice questions. Indicate your choice by an
arrow () in front of the option of your choice. No points will be subtracted for a wrong
answer. Only one of the alternatives is 100% correct.
MPC 01 (1 point)
When the yield on 30 year government bonds goes up, most likely
a. the yield on commercial paper also goes up.
b. the yield on corporate bonds close to maturity also goes up.
c. the perceived credit quality of the 30 year government bonds goes down.
d. the duration of the 30 year government bonds goes up.
e. the yield on corporate bonds with comparable maturity also goes up.
MPC 15 (1 point)
The spot curve obtained from coupon bearing government bonds through a
bootstrapping procedure or one of several estimation procedures represents
a. the theoretical yields to maturity on government zero bonds of different
maturities.
b. the yields on tradable government zero bonds of different maturities.
c. the (approximate) yield upon issue of coupon bearing government bonds of
different maturities.
d. the model based discount factors for different maturities related to
government issues.
e. an estimate of what the yields on government bonds should be if this
asset class were arbitrage free.
MPC 07 (1 point)
When setting up a curvature trade the trader most likely expects
a. the short end of the rate curve to steepen and the long end to flatten without
any shift.
b. the short end of the rate curve to flatten and the long end to steepen without
any shift.
c. the short end of the rate curve to shift up and the long end to shift down by
more or less the same amount.
d. the short end of the rate curve to steepen and the long end to flatten (or
vice versa) possibly accompanied by an overall shift.
e. the short end of the rate curve to flatten and the long end to flatten as well
accompanied by a moderate overall shift.
MPC 21 (1 point)
Consider a CMO-structure consisting of a single PAC-tranche protected by a single
support tranche with no extra structure. Which of the following statements is correct?
a. The effective protection offered by the support tranche is fixed for the whole
lifetime of the CMO.
b. The support tranche protects the PAC tranche against extension risk but not
against contraction risk.
c. As long as prepayments stay within the initial PAC-collar, the average life of
the PAC-tranche is fixed.
d. The expected repayment curve for the PAC-tranche is an average of the one
related to the lower prepayment speed of the collar and the one related to the
upper prepayment speed of the collar.
e. The support tranche protects the PAC-tranche against the unexpected:
if prepayments are higher than initially anticipated the support tranche
absorbs the prepayments.
01 NAME & STUDENT NUMBER: (IN FULL, USE PRINT WRITING)
HOME WORKS (5 points)
Please leave this section blank:
I : …………………
II : ……………………
OPEN QUESTIONS (4 points)
Please do NOT use numerical examples to make your point.
OQ 07 (2 points)
Using the duration balance, explain qualitatively why the duration of a 50 year low
coupon bond can be below the duration of a 20 year coupon bond with equal coupon
rate if the yield to maturity of these bonds is very high.
Coupon is low => low influence; BUT yield is high => price is low
Duration balance: total = 100%
Discount factors go down very quickly => (relative) value of the last payment of
the 20y is much (10x) higher than the one of the 50y bond.
 Relative value of the coupon payments in the first years is higher for the
50y bond than the 20y bond
OQ 19 (2 points)
In most CMO-structures, a structured interest only tranche will receive a significantly
higher interest rate than sequential pay tranches and even accrual tranches. Does
this make sense?
Yes, because their ‘risk’ is higher. The value of a protected interest only stream
usually increases if rates decline slowly and moderately, but the holder of a
companion or support IO tranche may receive interest payments only until
repayments reach a certain fraction of the face value of the pool. Rapid repayment of
mortgage principal in a sharply lower-rate environment reduces the total value of a
pool's interest payments. If a specific IO tranche is designed to be affected first by
prepayments, the interest payments available for that tranche can disappear quickly.
The mortgage prepayment option and payments dependent on its exercise or nonexercise have proven to be difficult to predict, and consequently to evaluate.
01 NAME & STUDENT NUMBER: (IN FULL, USE PRINT WRITING)
PROBLEM SET (7 points)
BP 01 (3 points)
Today is June 17, 2011.
Consider the portfolio of option free straight bullet bonds underneath.
number nominal
1
€ 50,000
2
€ 35,000
3
€ 40,000
4
€ 70,000
5
€ 65,000
maturity
next
coupon
21/02/201 21/02/2012
3
25/11/201 25/11/2011
5
23/07/201 23/07/2011
8
07/05/202 07/05/2012
0
14/09/202 14/09/2011
2
coupon price
rate
5.375% 104.46
7.500% 114.77
5.125% 108.86
5.750% 113.91
5.000% 102.46
All bonds are denominated in euro, pay annual coupons and are redeemed at par.
a. (1 point) Compute market value, yield to maturity, modified duration and
convexity of this portfolio.
289.356,96 €
market value
4,0732%
yield to maturity
5,683
modified
duration
49,383
convexity
Consider the following government bonds
number maturity
A
B
next
coupon
28/09/201 28/09/2011
2
28/03/202 28/03/2012
6
coupon price
rate
5.000% 108.87
4.500% 100.23
b. (2 points) Use these two bonds to construct a duration and convexity hedge
for the bond portfolio.
nominal position in A
nominal position in B
4.5
? not possible  solver not working correctly ???
MI 01 (2 points)
Consider the portfolio of liabilities underneath.
number
size
1
€ 60,000
2
3
due
two years from
now
€ 25,000 three years from
now
€ 80,000 four years from
now
promised
yield
1.75%
2.50%
2.75%
Consider the following zero bonds available in the market.
number
A
B
C
maturity
18 months
42 months
60 months
YTM
1.500%
2.600%
3.250%
Immunise the portfolio of liabilities using the zero bonds. Do this in such a way that
the initial profit of the financial institution is maximal but without creating net short
positions.
nominal position in A
nominal position in B
nominal position in C
net profit for the
financial institution
TS 01 (2 points)
Use a mean reverting interest rate tree (0r1 = 4.00%,  = 3.5%,  = 0.75%, k = 2) to
compute the price of a risk free instrument with the following pay off structure:
o 6 at time 1 if the spot rate is between 2% and 5%, and 0 otherwise,
o 7 at time 2 if the spot rate is between 2% and 5%, and 0 otherwise,
o 8 at time 3 if the spot rate is between 2% and 5%, and 0 otherwise,
o 109 at time 4 if the spot rate is between 2% and 5%, and 100 otherwise.
price of the instrument
109,993