2
N1D025-E1
The University of Nottingham
BUSINESS SCHOOL
A LEVEL D MODULE, SPRING SEMESTER 2002-2003
FIXED INTEREST INVESTMENT EXAM PAPER
Time allowed TWO Hours
______
Candidates must NOT start writing their answers until told to do so
Answer THREE questions
Only silent, self-contained calculators with a Single-line Display are permitted in this examination.
Dictionaries are not allowed with one exception. Those whose first language is not English may use a dictionary to translate between that language and English provided that neither language is the subject of this examination. No electronic devices capable of storing and retrieving text may be used.
DO NOT turn examination paper over until instructed to do so
N1D025-E1 Turn Over
2
N1D025-E1
1. A large UK corporation issued a UK pound-denominated note maturing on March 27, 2006, with annual coupons of 4%. Its quoted price for settlement on June 5, 2003, is 98.27.
(a) What is the accrued interest for this bond?
(b) What is the invoice price?
(c) Estimate the yield to maturity.
(d) Estimate the modified and Macaulay durations.
(e) How much is the price of the bond likely to fall if interest rates rise by1%?
(f) How would an estimate of the bond’s convexity enable you to improve the accuracy of your answer to (e)?
2. Consider the following prices of UK gilts:
Bond Maturity (years) Coupon rate Price
A 0.5 6 100.49
B 1.0 6 99.23
C 1.0 4 97.17
D 1.0 8 100.99
(a) Use the prices of A and B to compute the first two discount factors.
(b) Repeat this exercise using bonds A and C. Comment on the significance of your results.
(c) Suppose you own a portfolio consisting of 10 units each of bonds A and B. Explain precisely how you could modify your portfolio to generate the same cashflows for less money.
(d) What profit could a bond trader make with this information?
3. A large corporation issued a euro-denominated note maturing on January 31, 2007, making annual interest payments at a rate set by the formula
Rate = 18% - 2 x 12-month euro LIBOR
(a) Explain how you might replicate the cash flows of this note with simpler components.
(b) If the euro spot rate (computed with the usual semi-annual compounding) is flat at 7.5%, what should the note be worth?
(c) How do the interest-rates risks of inverse-floaters differ from the interest-risk risks of more conventional fixed-interest securities?
N1D025-E1 Turn Over
2
N1D025-E1
4. Compare the relative strengths and limitations of (a) PV01, (b) duration, (c) duration-convexity, and (d) value-at-risk approaches to the measurement of interest-rate risk.
5. (a) Explain why a swaption can be regarded as a type of bond option.
(b) Suppose the LIBOR yield curve is flat at 10% with annual compounding. A swaption gives the holder the right to receive 8% in a five-year swap starting in four years. Payments are made annually. The volatility measure for the swap is 30% per annum and the principal value is £1 million. What is the price of the swaption?
6. Compare a vanilla (fixed-for-floating) interest rate swap to a portfolio consisting of a long position in a fixed-coupon bond and a short position in a floating-rate bond (or floating-rate note), where the long and short bonds involve the same maturity and same counterparty as the swap.
N1D025-E1 Turn Over