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Lecture 2 Questions
1.
What’s coupon stripping? How can it create arbitrage opportunities?
Answer:
Coupon stripping entails taking a conventional bond and selling each of the
cash payments as a separate security.
To have an arbitrage opportunity with coupon stripping, one needs to be able to sell the
pieces for more than the whole. To have an arbitrage opportunity with reconstituting
(which is the reverse of stripping), one needs to be able to sell the bond for more than
the strips. In other words, buying strips and selling bonds should leave you with profit.
2.
Can arbitrage opportunities such as coupon stripping, etc. be exploited as easily? What
other considerations should be taken into account when we think about these arbitrage
opportunities?
Answer:
There’s not necessarily an arbitrage opportunity from either stripping or
reconstituting. This might be due to transaction costs (in the form of dealers’ bidask
spreads) that doesn’t allow the exploitation of small price differentials (between strip and
bond prices) in either direction. A trader should also be careful about transaction costs
other than the dealers’ bidask spreads. In addition, one should be careful about using
prices that are only newspaper quotations rather than actual contemporaneous dealer
quotes, since the dealers are not committed to trade at these prices.
3.
Show the derivation of Macaulay duration expression using P=
C
y
F
y
t
t
n
n
(
)
(
)
1
1
1
+
+
+
=
∑
.
Answer:
First, rewrite P. Then take the derivative of P with respect to (1+y). Then
multiply the whole expression by 1. Factor out (1/(1+y)). Multiply the whole expression
by ((1+y)/P) to arrive at the solution, which is the Macaulay duration expression.
4.
Go back to the three bonds discussed in class 1) a perpetuity with an annual coupon
rate of 10%, 2) a zerocoupon bond, maturing in 15 years, 3) a bond maturing in 15
years that pays a 15% annual coupon. Calculate their durations using the Macaulay
expression. Which one has the longest duration? What’s the interpretation of this?
(Hint: y=10% as in the lecture notes and you don’t need to know F.)
Answer:
Using the second formula for Macaulay expression in lecture 2 notes,
find that
for a perpetuity, duration = (1+y)/y, since n is infinite. Therefore
D
M
a c
for the first bond is
equal to 11 years.
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This note was uploaded on 11/18/2011 for the course FIN 353 taught by Professor Cobus during the Fall '08 term at S.F. State.
 Fall '08
 cobus
 Arbitrage

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