I need the work done for questions 13-20, I have majority of the answers but i don't know exactly how to obtain the results. Also I could use help for questions 21 to 35. Everything I highlighted i should have the answers to

Assignment 1 FINA 455F Please show your work for numerical questions from 1 to 20. 1. Is LIBOR generally higher, lower, or the same as the repo rate? A. Higher B. Lower C. Same 2. What is the 1-month return on capital for a trader who entered into a one-month repo where , repo rate = 5%, and haircut = 2.00? Pt 98.5, PT 99.01 A. B. C. D. E. 4.60% 4.80% 5.10% 5.40% 6.20% 3. What is the profit for a trader who entered into a one-week reverse repo where PT 99.48, A. B. C. D. E. and repo rate = 6%? 0.0339 0.0341 0.0343 0.0355 0.0359 4. Discount factors depend on compounding frequency? A. True B. False Pt 99.40, 5. The higher the inflation, the __________ the discount factors. A. higher B. lower C. cannot say 6. Answer questions 6 to 10 using the following information: a. the price of zero coupon bond maturing in 6 months is PZ (0, 0.5) 99.20, b. the price of a coupon bond paying 3% quarterly and maturing in 3 months is P (0, 0.25) 100.5485, c. the price of a coupon bond paying 6% quarterly and maturing in 9 months is P (0, 0.75) 103.1655, d. and the price of a coupon bond paying 5% semiannually and maturing in 1 year is . P(0,1) 103.0325 What is A. B. C. D. E. ? 0.9900 0.9910 0.9920 0.9930 0.9940 7. What is A. B. C. D. E. Z (0, 0.50) Z (0, 0.75) ? 0.9850 0.9860 0.9870 0.9880 0.9890 8. What is Z (0,1) ? A. 0.9780 B. 0.9790 C. 0.9800 D. 0.9810 E. 0.9820 9. What is the price of a 1-year coupon bond paying 4% quarterly? A. 102.0580 B. 102.8530 C. 103.1100 D. 103.0410 E. 104.2200 10. What is the price of a 9-month coupon bond paying 5% semiannually? A. 101.9315 B. 102.6120 C. 102.9800 D. 103.6625 E. 103.8315 11. What is the price of a 5.75-year floating rate bond that pays a semiannual coupon (no spread). Use the following information: (i) The price of a 3% quarterly coupon with 3 months to maturity is , (ii) 3 months ago the 6-month LIBOR was 3%. P (0, 0.25) 100.0448 A. B. C. D. E. 99.7641 100.1244 100.3217 100.5198 100.7895 12. What is the price of a 0.5-year floating rate bond that pays a quarterly coupon equal to the floating rate plus 1% spread. Use the following information: (i) (ii) The PZ (0.0.25) 99.80, price of a 2% quarterly bond with 6 months to maturity is A. B. C. D. E. 100.1875 100.2270 100.3315 100.4980 100.5625 P(0, 0.5) 100.3960 . 13. What is the price of a 0.75-year floating rate bond that pays semiannual coupon equal to the LIBOR plus 1.50% spread? Use the following information: (i) (ii) PZ (0, 0.25) 99.70, PZ (0, 0.50) 99.20, (iii) There is a coupon bond paying 3% quarterly P (0, 0.75) 101.7380, (iv) the 6-month LIBOR 3 months ago was 5% A. 103.69 B. 103.83 C. 103.98 D. 104.11 E. 104.47 For the remaining questions, use the following discount factors when necessary. t Z(0,t) t Z(0,t) 0.25 0.9840 2.25 0.8587 0.50 0.9680 2.50 0.8445 0.75 0.9520 2.75 0.8308 1.00 0.9360 3.00 0.8175 1.25 0.9190 3.25 0.8047 1.50 0.9040 3.50 0.7924 1.75 0.8880 3.75 0.7806 2.00 0.8730 4.00 0.7691 14. What is the duration of 2-year bond paying a fixed coupon of 5% quarterly? A. 1.91 B. 1.98 C. 2.27 D. 2.83 E. 2.94 15. What is the duration of a 1.25-year floating rate bond that pays LIBOR + 50 bps semiannually? You know that the last quarter semiannual rate was 6.4%. A. 0.2411 B. 0.2469 C. 0.2532 D. 0.2574 E. 0.2633 16. What is the duration of the following portfolio? i. 5 units of a 2-year fixed rate bond paying 6% quarterly. ii. 2 units of a 1.75-year floating rate bond paying LIBOR + 80 bps semiannually. You know that the LIBOR was 6.5% three months ago. iii. 6 units of a 1-year zero coupon bond iv. A. B. C. D. E. 5 units of a 1.5-year floating rate bond with no spread paid semiannually. 0.98 (0.88??) 1.02 1.06 1.10 1.14 17. What is the dollar duration of the following portfolio? i. Long 1.5-year zero coupon bond ii. Short 2-year fixed coupon bond paying 1% quarterly A. 39.15 B. -39.45 C. 39.75 D. -41.05 E. 41.85 18. What is the dollar duration of the following portfolio? i. Long 1-year fixed coupon bond paying 4% quarterly. ii. Long 1.75-year floating rate bond paying LIBOR plus 80 bps semiannually. You know that the reference rate was set at 6% six months ago. iii. Short a 2-year zero coupon bond. A. -49.73 B. 50.05 C. -50.26 D. 51.47 E. -51.82 19. What is the convexity of a 3-year fixed rate bond paying 4% coupon semiannually? A. 8.11 B. 8.20 C. 8.38 D. 8.73 E. 8.85 20. What is the convexity of a 3-year floating rate bond with no spread paid quarterly? A. 0.25 B. 0.0625 C. Neither of the above 21. Calculate the convexity of the following portfolio. i. ii. iii. iv. A. B. C. D. E. 2 units of a 1.5-year fixed rate bond paying 6% quarterly. 4 units of a 1.75-year floating rate bond paying LIBOR + 80 bps semiannually. You know that the reference rate was 7% three months ago. 6 units of a 2-year zero coupon bond. 1 unit of a 1.5-year floating rate bond with no spread paid semiannually. 1.50 1.62 1.87 1.92 2.07 22. Consider the 5-year inverse floater 18% r1 (t 1). This inverse floater is equivalent to a portfolio of A. 1 long 5-year floating rate bond plus 1 short 5-year zero coupon bond plus 1 short 5-year 18% coupon fixed rate bond B. 1 long 5-year zero coupon bond plus 1 long 5-year 18% coupon bond plus 1 short 5-year floating rate bond C. 1 long 5-year 18% coupon bond plus 1 short 5-year zero coupon bond plus 1 short 5-year floating rate bond D. 1 long 5-year 18% coupon bond plus 1 long 5-year floating rate bond plus 1 short 5-year zero coupon bond E. None of the above 23. Consider the 4-year inverse floater 12% r1 (t 1). The coupons are paid annually. What is the duration of this inverse floater? A. 5.82 B. 6.08 C. 6.27 D. 6.49 E. 6.63 24. Consider the 4-year leveraged inverse floater 30% 3 r1 (t 1). What is the duration of this leveraged inverse floater? A. 10.454 B. 10.653 C. 10.746 D. 10.852 The coupons are paid annually. E. 10.957 25. Consider the Nelson-Sigel model for modeling the continuously compounded spot rates. r (0, T ) T T 1 exp( ) 1 exp( ) T 0 1 exp( ) 2 T T T 1 exp( ) T 0 (1 2 ) 2 exp( ) T Which of the following statements is true? i. The short-term spot rate is given by ii. A. B. C. D. The long-term spot rate is given by 0 1 . . i only ii only Both of the above None of the above 26. Assume annual coupons for the following bonds. Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Annual Coupon(%) 8 7 5 8 7 Maturity (Years) 1 2 3 4 5 Price 105 103 101 108 100 Derive the spot curve until 5-year maturity. Use matrix multiplication and matrix inverse in Excel. What is the 1-year discount factor? (Knowing the discount factors is just like knowing the spot rates; one can be converted to the other very easily) A. B. C. D. E. 0.9841 0.9722 0.9665 0.9438 None of the above 27. What is the 3-year discount factor? A. 0.8216 B. 0.8553 C. 0.8727 D. 0.8938 E. None of the above 28. What is the 5-year discount factor? A. 0.7209 B. 0.7167 C. 0.7029 D. 0.6914 E. None of the above 29. A semi-annual 7% coupon bond has 3 years to maturity. The price of the bond is $943.31, the duration is 2.75, and the convexity is 7.96. What is the drop in the bond price when there is a parallel shift in the yield curve by 75 bps? A. $19.24 B. $20.31 C. $21.06 D. $22.80 E. $23.12 30. Calculate the annualized expected returns for a 30-year zero coupon bond when E[dr] = 0 and E[dr2] = 7 x 10-7 (on a daily basis) . A. 5.93% B. 6.52% C. 7.94% D. 8.12% E. 9.38% 31. You currently hold a 7-year fixed rate bond paying 5% annually. You would like to hedge against changes in the level and slope of the yield curve by using 1-year and 7-year zero coupon bonds. How many 1-year and 7-year zero coupon bonds should be sold short? Make use of the table below. maturity 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 A. B. C. D. E. Z(t, T ) 1 2 1.1150 -0.2540 0.9800 0.9940 -0.3010 0.9600 0.9640 -0.1470 0.9300 0.9330 0.0080 0.8900 0.9300 0.1620 0.8500 0.9260 0.3160 0.8100 0.9270 0.4230 0.7700 0.9270 0.5300 0.7300 0.4651 and 1.1231 0.5112 and 1.1845 0.6038 and 1.2249 0.7422 and 1.3172 0.7716 and 1.3961 For questions 32 to 35, use the interest rates data in the Excel file \"Factor Analysis - Data for Questions 32-35.\" Use this data and do factor analysis with respect to the three factors Level, Slope, and Curvature. 32. What is the coefficient of the 3-year rate with respect to the level factor? A. 0.9763 B. 0.9812 C. 0.9900 D. 1.0063 E. 1.0291 33. What is the coefficient of the 20-year rate with respect to the slope factor? A. -0.3903 B. -0.4724 C. 0.7335 D. 0.9138 E. None of the above 34. What is the coefficient of the 5-year rate with respect to the curvature factor? A. 0.1836 B. 0.2112 C. 0.3727 D. -0.2764 E. -0.2936 F. None of the above 35. Which of these interest rates has the smallest coefficient with respect to the level factor? A. 1-year rate B. 3-year rate C. 5-year rate D. 10-year rate E. 20-year rate