Question Details
(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 2^{nd}, 2016, the first bond should mature on August 31^{st}, 2016, the second on February 28^{th} of 2017, and so on. [1]
Use WSJ website to download bond quotes:
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?
- 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.
[1] Notice that bonds that mature on March 15^{th} and September 15^{th} of any year are not a good choice here since all of them will pay coupons on March 15^{th} 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
Use WSJ website to download bond quotes:
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
your equations).
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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