THEORETICAL PROBLEMS
1. Suppose that the price of discount (zero coupon) bonds maturing in years 1, 2, 3, 4, and 5 are given (respectively) by

Price Time to Maturity
940 1
870 2
800 3
715 4
630 5

Consider the following risk-free investments. Which is best?
T=0 1 2 3 4 5
Investment A -40 20 15 10 5 1
Investment B -10 1 5 10 15 20
2. Three zero coupon risk-free discount bonds of one, two and three year term to maturity are selling for, respectively, $950, $890 and $800. What would be the selling price today of a 10% coupon bond of 3 year maturity (maturity value $1,000)?
3. Consider a coupon bond, period t = 0 price $900, with payments:
t=0 1 2 3
50 50 1050
Discount (zero coupon) bonds of 1, 2 and 3 years maturity (all with maturity value of $1000) sell for respectively, 960, 900, 820 dollars. Is this coupon bond properly priced? If not, design an arbitrage argument to profit by the mispricing.
4. Assume that you have calculated the following annual discount factors:
DF1=0.935
DF2 = 0.857
DF3= 0.772
(a) If inflation is expected to prevail throughout the next five years at a rate of 3% per year, what are the real spot rates observed in the financial markets?
(b) What would be the price of a bond paying 6% (annually) with a face value of $1,000 and 2 years to maturity?
(c) What would be the yield of maturity of this bond (Part b)?
(d) If a three-year bond has a price $1,284.80, what is its annual coupon rate?

5. The prices of discount bonds (all with maturity value of $1,000) maturing in years 1, 2, 3, 4, 5 are given below.

Price Time to Maturity
920 1
860 2
790 3
700 4
600 5

What is the yield to maturity on a risk-free 5% bond due in 5 years (also with maturity value of $1,000)?

PART 2: EMPIRICAL PROBLEM

INQUIRY INTO THE TERM STRUCTURE OF INTEREST RATES USING US GOVERNMENT BOND DATA
1. Download the data on prices and coupon rates for 6 government bonds maturing in consecutive six-month intervals. The first payment of each of these bonds should come in approximately 6 months. For example, if today’s date is March 2nd, the first bond should mature on August 31st, the second on February 28th of the following year and so on.
2. Convert price quotes into the actual prices (multiply by 10).
3. Convert annual coupon rates into the actual semi-annual coupons, expressed in dollars.
4. Show the cash flow table (time line) for your bonds. This table should organize each payment of each bond according to the time when it will be paid.
5. Using the same bootstrapping method as in the example on page 11 of your Bonds Lecture, calculate the first six rates of the term structure of interest rates.

a. Show equations which you used to find each of the six rates with the data plugged into them.
b. Present annualized rates.

6. Using Excel Chart menu, “draw” the graph of the term structure: time on the horizontal axis, corresponding term structure rates on the vertical axis. Is it increasing or decreasing?

7. Briefly explain your findings: Comment on the implications of the observed term structure for the economic conditions as perceived by market participants.
In the report for the second empirical part of this LE, show price conversion, coupon calculations, cash flow table, all your calculations for the term structure rates, graph and explanations.
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