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. In a recent trading session, the benchmark 30-year Treasury bond’s market price went up 8.62 dollars per \$1000 face value to 1032.38 dollars, while its yield fell from .07 to .068. The bond’s market price then went up another 7.62 dollars per \$1000 face value as the yield fell further to .0665 from .068. Report answers for the following (using average of latest two bond prices for duration and average of latest three bond prices for convexity): 1. Convexity, using the average of all three market prices of the bond in the denominator of the formula. 2. First modified duration, using average of first two market prices of the bond in the denominator of the formula. 3. Second modified duration, using average of second and third prices of the bond. 4. The expected rise in bond price if the interest rate were to fall another 20 basis points (.002) from .0665, using the average of two modified durations and convexity. B. Estimate term structure of discount factors, spot rates and forward rates by using data on five semi-annual coupon paying bonds with \$100 face value each: The bonds, respectively, have 1.25, 5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at annual rates of 4.62, 5.62, 6.62, 7.62, and 8.62 percent of face value; and are trading at quoted spot market prices in dollars of 98.62, 99.62, 100.62, 101.62 and 102.62. Specify the discount factor function d(t) by a third degree polynomial with unknown parameters a, b, and c, as done in class. Using estimated d(t) function, determine spot rate and forward rate functions by assuming half-year compounding. Then write the values of the following based on your estimation. 5. Coefficient of parameter a in first bond price equation. 6. Coefficient of parameter b in first bond price equation. 7. Coefficient of parameter c in first bond price equation. 8. Coefficient of parameter a in second bond price equation. 9. Coefficient of parameter b in second bond price equation. 10.Coefficient of parameter c in second bond price equation. 11.Coefficient of parameter a in third bond price equation. 12.Coefficient of parameter b in third bond price equation. 13.Coefficient of parameter c in third bond price equation. 14.Coefficient of parameter a in fourth bond price equation. 15.Coefficient of parameter b in fourth bond price equation. 16.Coefficient of parameter c in fourth bond price equation. 17.Coefficient of parameter a in fifth bond price equation. 18.Coefficient of parameter b in fifth bond price equation. 19.Coefficient of parameter c in fifth bond price equation. 20.Parameter a. 21.Parameter b. 22.Parameter c. 23.Current price of a dollar at 5th year. 24.Current price of a dollar at 7th year. 25.Current price of a dollar at 10th year. 26.Current price of a dollar at 15th year. 27.Spot rate for term 2 year. 28.Spot rate for term 5 year. 29.Spot rate for term 10 year. 30.Spot rate for term 17 year. 31.Forward rate for half year period 2.5 to 3.0 years. 32.Forward rate for half year period 5.5 to 6.0 years. 33.Forward rate for half year period 10.5 to 11.0 years. 34.Forward rate for half year period 15.5 to 16.0 years. C. Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a coupon of 8.6 percent on face value \$100 paid semi-annually. The given term structure starts with 3.1 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%) per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to calculate the key rate durations by the method done in class and given in textbook. Report answers for the following: 35. Current fair price of the bond with the given term structure. 36. Price change needed to calculate 2-year key rate duration. 37. Price change needed to calculate 5-year key rate duration. 38. Price change needed to calculate 10-year key rate duration. 39. 2-year key rate duration. 40. 5-year key rate duration. 41. 10-year key rate duration. D. Using the following data on the price of a bond and the corresponding interest rate (assuming a flat term structure) and regression method, estimate convexity and duration of the bond: Price Interest Rate 99 .06 100 .057 101.5 .052 102 .049 105 .044 106.5 .038 108 .033 108.5 .031 110.1 .028 42. What is the estimated value of Duration? 43. What is the estimated value of Convexity?
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Interest rates are expressed as annualized rates for the term specified. Report your
interest rate answers as fractional numbers like 0.11 for 11% per year.
A. In a recent trading session, the benchmark 30-year Treasury bond’s market price went up
8.62 dollars per \$1000 face value to 1032.38 dollars, while its yield fell from .07 to .068. The
bond’s market price then went up another 7.62 dollars per \$1000 face value as the yield
fell further to .0665 from .068. Report answers for the following (using average of latest
two bond prices for duration and average of latest three bond prices for convexity):
1. Convexity, using the average of all three market prices of the bond in the denominator
of the formula.
2. First modified duration, using average of first two market prices of the bond in the
denominator of the formula.
3. Second modified duration, using average of second and third prices of the bond.
4. The expected rise in bond price if the interest rate were to fall another 20 basis points
(.002) from .0665, using the average of two modified durations and convexity.
B. Estimate term structure of discount factors, spot rates and forward rates by using data
on five semi-annual coupon paying bonds with \$100 face value each: The bonds,
respectively, have 1.25, 5.35, 10.4, 15.15 and 20.2 years to maturity; pay coupon at
annual rates of 4.62, 5.62, 6.62, 7.62, and 8.62 percent of face value; and are trading at quoted
spot market prices in dollars of 98.62, 99.62, 100.62, 101.62 and 102.62. Specify the discount factor
function d(t) by a third degree polynomial with unknown parameters a, b, and c, as
done in class. Using estimated d(t) function, determine spot rate and forward rate
functions by assuming half-year compounding. Then write the values of the following
5. Coefficient of parameter a in first bond price equation.
6. Coefficient of parameter b in first bond price equation.
7. Coefficient of parameter c in first bond price equation.
8. Coefficient of parameter a in second bond price equation.
9. Coefficient of parameter b in second bond price equation.
10.Coefficient of parameter c in second bond price equation.
11.Coefficient of parameter a in third bond price equation.
12.Coefficient of parameter b in third bond price equation.
13.Coefficient of parameter c in third bond price equation.
14.Coefficient of parameter a in fourth bond price equation.
15.Coefficient of parameter b in fourth bond price equation.
16.Coefficient of parameter c in fourth bond price equation.
17.Coefficient of parameter a in fifth bond price equation.
18.Coefficient of parameter b in fifth bond price equation.
19.Coefficient of parameter c in fifth bond price equation.
20.Parameter a.
21.Parameter b.
22.Parameter c.
23.Current price of a dollar at 5th year.
24.Current price of a dollar at 7th year.
25.Current price of a dollar at 10th year.
26.Current price of a dollar at 15th year.
27.Spot rate for term 2 year.
28.Spot rate for term 5 year.
29.Spot rate for term 10 year.
30.Spot rate for term 17 year.
31.Forward rate for half year period 2.5 to 3.0 years.
32.Forward rate for half year period 5.5 to 6.0 years.
33.Forward rate for half year period 10.5 to 11.0 years.
34.Forward rate for half year period 15.5 to 16.0 years.
C. Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a
coupon of 8.6 percent on face value \$100 paid semi-annually. The given term structure
starts with 3.1 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%)
per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to
calculate the key rate durations by the method done in class and given in textbook.
35. Current fair price of the bond with the given term structure.
36. Price change needed to calculate 2-year key rate duration.
37. Price change needed to calculate 5-year key rate duration.
38. Price change needed to calculate 10-year key rate duration.
39. 2-year key rate duration.
40. 5-year key rate duration.
41. 10-year key rate duration.
D. Using the following data on the price of a bond and the corresponding interest rate
(assuming a flat term structure) and regression method, estimate convexity and duration of
the bond:
Price Interest Rate
99 .06
100 .057
101.5 .052
102 .049
105 .044
106.5 .038
108 .033
108.5 .031
110.1 .028
42. What is the estimated value of Duration?
43. What is the estimated value of Convexity?