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MGCR 341: Finance 1
Summer 2010
Vadim di Pietro
Assignment 2: Solutions
Due date:
Friday July 23
rd
, by 9:00pm. You may slide the assignment under my office door (Room
504). If you can’t make it in to school on Friday, you may email your assignment to me, provided that
I receive it by 9:00pm on Friday. Of course, you can also hand in your assignment in class on
Thursday. Late assignments will not be accepted. Solutions will be posted online on Saturday July
24
th
.
Groups:
You may work in groups of up to 3 students.
Grading:
You must show your work in order to receive credit for solutions, except where noted
otherwise.
1)
Topic: Bond Pricing
Below are the prices of zero coupon bonds with face value of $1,000.
Maturity
Price
1yr
$950
2yr
$875
3yr
$820
4yr
$780
5yr
$600
a)
Today is
t = 0
. You know that you will want to borrow
$50,000 at t = 2
, and borrow
$20,000 at t = 4
, and pay back both these loans at
t = 5
. Using only the above zero
coupon bonds, how could you generate the desired cash flows (and zero cash flows at
all other dates)? Specify how many units (fractional units are OK) of which of the
above bonds will you buy/sell at
t = 0
in order to lock in an amount of money you
will owe at
t = 5
? (Note: You can only buy/sell bonds at t = 0.)
You need to buy 50 2yr bonds, and 20 4yr bonds. These will generate cash flows of 50,000 and
20,000 at t = 2 and t = 4, respectively. The cost of buying these bonds is 50*875 + 20 *780 =
59,350. Since you don’t want to have any net cash flow at t = 0, you will fund the purchase of the
2yr and 4yr bonds by shorting 5yr bonds. Each unit you short will raise 600. Thus you need to
short 59,350/600 = 98.917 units of the 5yr bonds in order to raise 59,350.
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View Full Documentb)
How much money will you owe at
t = 5
?
At t = 5, you will have to cover your short position in the 5yr bonds. This will cost you
98.917*1000 = 98,917.
2)
Topic: Bond Pricing
You are given the following information: r
0,3
= 3%; f
3,2
= 5%; the price of a 10yr zerocoupon
bond with face value $1000 is $500.
a)
What is f
5,5
if there is no arbitrage?
There are two ways you can transfer $1 from t = 0 to t = 10. The first strategy is buying $1
worth of the 10yr zero coupon bond. The cost of the 10yr bond is $500, for $1000 face value.
That means $500 invested in the bond at t = 0 turns into $1000 at t = 10. Thus, $1 invested in the
10yr bond turns into $2 at t = 10.
The second way of transferring $1 from t = 0 to t = 10 is buy investing $1 at r
0,3
= 3% for 3 years,
investing that money at f
3,2
= 5% for 2 years, and then investing that amount of money at f
5,5
for
5 years. The amount of money you will have at t = 10 from this strategy is
(1+ 0.03)
3
(1+ 0.05)
2
(1 + f
5,5
)
5
And since both strategies have to give you the same amount at t = 10 if there is no arbitrage we
get that
2 = (1+ 0.03)
3
(1+ 0.05)
2
(1 + f
5,5
)
5
f
5,5
= 10.67%
b)
If a bank were to quote you a forward interest rate of f
5,5
= 12%, explain how would
you construct an arbitrage opportunity using only r
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 Summer '09
 Jassim

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