Download 1a)Define redemption yield, spot rate and forward rate

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The University of Nottingham
BUSINESS SCHOOL
A LEVEL 4 MODULE, SPRING SEMESTER 2010-2011
FIXED INTEREST INVESTMENT
Time allowed TWO Hours
Candidates may complete the front cover of their answer book and sign their desk card but must
NOT write anything else until the start of the examination period is announced.
Answer any 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 standard translation dictionary to translate between that language and English provided
that neither language is the subject of this examination. Subject specific translation dictionaries
are not permitted.
No electronic devices capable of storing and retrieving text, including electronic dictionaries, may
be used.
DO NOT turn examination paper over until instructed to do so
ADDITIONAL MATERIAL: Normal Distribution Table and Blacks Formula
INFORMATION FOR INVIGILATORS: NONE
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a)
Define the spot rate, forward rate and the redemption yield. What are the main
weaknesses of the redemption yield and how can they be overcome using the spot
rate?
[30 marks]
b)
Explain why the forward rate so is important in the investment making process.
[20 marks]
c)
Define the yield curve and discuss the factors that drive it. Discuss the main theories
that have proposed to explain the observed shapes of the term structure of interest
rates.
[50 marks]
a)
Discuss the differences between Dollar duration, Macaulay duration, modified duration
and convexity.
[25 marks]
b)
Estimate the Macaulay and modified duration and convexity using a suitable
approximation or otherwise of a 20 year bond paying 7% coupons annually. The
initial yield is 7% per annum and the par value is £1000.
[35 marks]
c)
Using the estimated values of duration and convexity calculate the new bond price
when the yield is increased firstly to 8% and then to 12% using both the duration and
the duration with convexity rule. Explain your results.
[40 marks]
a)
Explain the main differences between interest rate forwards and interest rate futures
[25 marks]
b)
Discuss what you understand by the term, “ Price Factor”, and how it leads to the
term, “Cheapest to Deliver Bond”.
[25 marks]
c)
How would you hedge a portfolio of fixed interest securities under the following
circumstances:
i. You own a large position in relatively illiquid bond you want to sell
ii. You have a large gain on one of your Treasuries and want to sell it, but you
would like to defer the gain until the next tax year.
iii. You will receive your annual bonus next month that you hope to invest in
long-term corporate bonds. You believe that bond today are selling at quite
attractive yields, and are concerned that bond prices will rise over the next
few weeks.
[25 marks]
d)
As a fixed interest portfolio manager you have estimated that the yield on 30-year
bonds changes by 10 basis points for every 15-basis point move in the yield on 10year bonds. You hold a $100 million portfolio of 10-year maturity bonds with modified
duration 8 years and desire to hedge your interest rate exposure with T-bond futures,
which currently has modified duration 13 years and sell at F0 = $93. How many
futures contract should you buy or sell?
[25 marks]
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a)
Discuss the main characteristics of a plain vanilla interest rate swap. Your explanation
should include the main risks associated with such swaps.
[25 marks]
b)
Discuss the alternative methods that can be used to value swaps.
c)
Companies A and B have been offered the following rates per annum on a $60 million
20-year investment:
[20 marks]
Company A
Company B
Fixed rate
2.0%
3.8%
[25 marks]
Floating rate
LIBOR + 1%
LIBOR +2%
Company A requires fixed-rate investment; company B requires a floating-rate investment.
Construct a swap that will net a bank, acting as intermediary, 0.2% per annum and will
appear equally attractive to A and B.
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d)
The U.S. yield curve is flat at 1% and the euro yield curve is flat at 2%. The current
exchange rate is $0.95 per euro. What will be the swap rate on an agreement to
exchange currency over a 3-year period? The swap will call for the exchange of 1
million euros for a given number of dollars in each year
[30 marks]
a)
Discuss why standard equity models cannot be used to value interest rate options.
[30 marks]
b)
Discuss ways in which the Black-Scholes model adapted to value interest rate options?
[20 marks]
c)
Prove that an interest rate cap can be interpreted as a portfolio of put options on zero
coupon bonds.
[20 marks]
d)
Is the modified duration of options positive? Discuss
a)
Discuss why credit risk modelling is more difficult than interest rate modelling.
[25 marks]
b)
Explain what you understand by the following terms related to credit risk.
(i) expected default frequency.
(ii) market implied rating.
(iii) distance-to-default index measure.
[30 marks]
[75 marks]
End
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