HEC Paris Professor Ioanid Rosu MBA Financial Markets Fall 2012 ...

HEC Paris
Professor Ioanid Rosu
MBA Financial Markets
Fall 2012
Case/Assignment #3
Bonds; Forwards and Futures
The assignment should be typed (or written legibly) and is The assignment should be
typed (or written legibly) and is due at the beginning of class on November 26/27/28
(Week 9). No late assignments will be accepted. You may discuss the assignment only
with members of your group. Please, hand in one solution per group. When printing your
assignment, include only the relevant tables and numbers, not all the Excel data you are
using.
Problem 1. You are in charge of the bond trading department of a large investment bank.
The yield curve for years 1, 2 and 3 is displayed on your computer terminal as follows:
Maturity 1 2 3
YTM 5% 7% 6%
A new summer intern from HEC has just observed that the 3-year Treasury note with face
value $1000 and annual coupon rate 8% trades at $1023.00.
(a) Is the price of the bond consistent with the given list of yields?
(b) If the price of the coupon bond is not consistent with the given list of yields, what would
you do to in order to take advantage of this situation? Be explicit in describing your
strategy. You are allowed to invest in the given coupon bond, and in 1-year, 2-year, and
3-year strips.
Problem 2. Suppose it is February 22, 2006 and you have the following data for the S&P
500 and the FTSE 100. Since the index futures expire on the 3rd Friday of the month, there
are approximately 4 months until the expiration of the June contract, and 7 months until the
expiration of the September contract. Fill in the missing numbers in this table of stock index
futures prices.
Country Index Index Dividend Spot interest Futures Futures Price
Name Value Yield rate Term (same unit as
(annualized) (annualized) (months) index value)
US S&P 500 1292.67 1.70% 4.68 % 4 ???
UK FTSE 100 5872.40 ??? 4.29 % 7 5850.5
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Case 1. You are analyzing Treasury bond data on August 9, 2010. You have the following
table of yields to maturity
(a) From the Wall Street Journal you get also the following information about the 3-year
Treasury note:
Ask
Date Maturity Coupon Bid Ask Yield
2010 Aug 09 2013 Aug 15 4.250 110:11 110:13 0.7539
Note here that the face value of the bond is considered to be F = 100, and the coupon
rate is 4.250%. The bid and ask prices are quoted in 32-nds, which means for example
that P ask = 110:13 = 110 + 13
32 = 110.4063.
For now, let’s assume that the coupon is paid annually. Are then these quoted prices
consistent with the given list of yields to maturity on August 9? By being consistent
here I mean whether the fair price of the bond given the yield curve is between the
quoted bid and ask prices.
(b) August 9, 2010 is in fact a little more than 3 years away from August 15, 2013 (it is
3.0164 years away). If you write the present value formula for the bond using the exact
time until cash flows occur, does that change the price significantly? (Again, we assume
that the bond pays annual coupons.)
(c) In reality, coupons are paid semi-annually. Every 6 months, the owner of the bond gets
4.250%
half the coupon: = 2.125% of face value. How does that change the fair price of
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the 3-year Treasury note? For simplicity, assume that the coupons are paid after 0.5, 1,
1.5, 2, 2.5, and 3 years. (That is, forget about the extra 6 days from Aug 9 to Aug 15.)
Hint: The yield to maturity, e.g., for 2.5 years cannot be found in the table, but you
can take YTM 2.5 = YTM 2+YTM 3
= 0.54%+0.81% = 0.675%.
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(d) By just looking at the shape of the U.S. Treasury yield curve on August 9, 2010 below,
which of the four types of yield curve is it?
(e) Normally, what type of economy does such a shape of the yield curve predict? Do you
think it should work in this particular case? Why or why not? (Hint: Consider both
the short end and the long end of the curve in your analysis.)
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