Problem A

Attached are the values. Please use the values for UIN 663120209 (highlighted portion)

FIN415 Exam-2 Due by 5:30 p.m., March 21, 2016 Read the following paragraph before proceeding. Late Submissions Carry No Credit It is required that you submit in plain text, within the body of the email sent to sacharya@uic.edu, your UIN and then only two columns of numbers: (a) question serial number and (b) the corresponding numerical answer. Write 999999 for all blank answers. You are also required to attach to the email detailed works (scanned, pdf or doc or excel files) to your email; do not attach the answers which must be in plain text within the email itself. Non-numerical characters or explanations for answers within the body of the email will not be accepted. Each question carries equal weight. If you believe that more data are necessary to solve, assume whatever you think is necessary to answer the questions. All questions are required to be answered independently without any consultation with other students or professors. Email submissions with works attached are due by the deadline. Answers submitted by any other means, after the deadline or without matching work will be treated as missing with zero credit. Take the data from the attached page corresponding to your UIN on A1, A2, A3, B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, C1 and C2. 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 A1 dollars per $1000 face value to A2 dollars, while its yield fell from .07 to .068. The bond's market price then went up another A3 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 B1, B2, B3, B4, and B5 percent of face value; and are trading at quoted spot market prices in dollars of B6, B7, B8, B9 and B10. 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 C1 percent on face value $100 paid semi-annually. The given term structure starts with C2 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. 36. 37. 38. 39. 40. 41. Current fair price of the bond with the given term structure. Price change needed to calculate 2-year key rate duration. Price change needed to calculate 5-year key rate duration. Price change needed to calculate 10-year key rate duration. 2-year key rate duration. 5-year key rate duration. 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 99 100 101.5 102 105 106.5 108 108.5 110.1 42. 43. Interest Rate .06 .057 .052 .049 .044 .038 .033 .031 .028 What is the estimated value of Duration? What is the estimated value of Convexity? uin A1 A2 A3 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 C1 C2 659877652 6.56 1034.44 5.56 2.56 3.56 4.56 5.56 6.56 96.56 97.56 98.56 99.56 100.56 6.6 0.7 676281115 7.12 1033.88 6.12 3.12 4.12 5.12 6.12 7.12 97.12 98.12 99.12 100.12 101.12 7.1 1.3 665281264 7.69 1033.31 6.69 3.69 4.69 5.69 6.69 7.69 97.69 98.69 99.69 100.69 101.69 7.7 2 663029376 8.25 1032.75 7.25 4.25 5.25 6.25 7.25 8.25 98.25 99.25 100.25 101.25 102.25 8.2 2.7 664226312 8.81 1032.19 7.81 4.81 5.81 6.81 7.81 8.81 98.81 99.81 100.81 101.81 102.81 8.8 3.4 678145458 9.38 1031.62 8.38 5.38 6.38 7.38 8.38 9.38 99.38 100.38 101.38 102.38 103.38 9.4 4 679952915 9.94 1031.06 8.94 5.94 6.94 7.94 8.94 9.94 99.94 100.94 101.94 102.94 103.94 9.9 4.7 662099840 10.5 1030.5 9.5 6.5 7.5 8.5 9.5 10.5 100.5 101.5 102.5 103.5 104.5 10.5 5.4 663120209 11.06 1029.94 10.06 7.06 8.06 9.06 10.06 11.06 101.06 102.06 103.06 104.06 105.06 11.1 6.1 672638903 11.62 1029.38 10.62 7.62 8.62 9.62 10.62 11.62 101.62 102.62 103.62 104.62 105.62 11.6 6.8 672451979 12.19 1028.81 11.19 8.19 9.19 10.19 11.19 12.19 102.19 103.19 104.19 105.19 106.19 12.2 7.4 659853598 12.75 1028.25 11.75 8.75 9.75 10.75 11.75 12.75 102.75 103.75 104.75 105.75 106.75 12.8 8.1 663274474 13.31 1027.69 12.31 9.31 10.31 11.31 12.31 13.31 103.31 104.31 105.31 106.31 107.31 13.3 8.8 652821886 13.88 1027.12 12.88 9.88 10.88 11.88 12.88 13.88 103.88 104.88 105.88 106.88 107.88 13.9 9.4 671395344 14.44 1026.56 13.44 10.44 11.44 12.44 13.44 14.44 104.44 105.44 106.44 107.44 108.44 14.4 10.1 651382511 15 1026 14 11 12 13 14 15 105 106 107 108 109 15