## (solution) Suppose that the price of discount (zero coupon) bonds maturing

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?

 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:

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.

• 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

• 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, 2016, the first bond should mature on August 31st, 2016, the second on February 28th of 2017, and so on. 

http://www.wsj.com/mdc/public/page/2_3020-treasury.html

• Convert price quotes into the actual prices (multiply by 10).
• Convert annual coupon rates into the actual semi-annual coupons, expressed in dollars.
• 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.
• Using the same bootstrapping method as in the example on pages 8--10 of your Review of Bond Concepts handout, calculate the first six rates of the term structure of interest rates.
• Show equations which you used to find each of the six rates with the data plugged into them (use Insert ? Equation in Word to type your equations).
• Present annualized rates.

• 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?

1. 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 (the actual price of the bond for the actual \$1000 of face value), coupon calculations (i.e. from the coupon rate to the dollar amount), cash flow table (i.e time line), all your calculations for the term structure rates, graph of the term structure and explanations. Report (including all equations) should be typed.

 Notice that bonds that mature on March 15th and September 15th of any year are not a good choice here since all of them will pay coupons on March 15th 2016 (i.e. 13 days from now and not six months).

1. PART 1: THEORETICAL PROBLEMS

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

870

800

715

630 1

2

3

4

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 50 50 3

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. 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

860

790

700

600 1

2

3

4

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, 2016, the first bond should mature on August 31st, 2016, the second on

February 28th of 2017, and so on. 1

http://www.wsj.com/mdc/public/page/2_3020-treasury.html

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 pages 8--10 of your

Review of Bond Concepts handout, calculate the first six rates of the term

structure of interest rates.

1 Notice that bonds that mature on March 15th and September 15th of any year are not a

good choice here since all of them will pay coupons on March 15th 2016 (i.e. 13 days

from now and not six months). a. Show equations which you used to find each of the six rates with

the data plugged into them (use Insert ? Equation in Word to type

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 (the actual

price of the bond for the actual \$1000 of face value), coupon calculations (i.e. from the

coupon rate to the dollar amount), cash flow table (i.e time line), all your calculations for

the term structure rates, graph of the term structure and explanations. Report (including

all equations) should be typed.

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