Homework 1

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University of Rhode Island *

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424

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Finance

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Jan 9, 2024

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Homework 1 (FIN 424-Fall2023) [Submit in Brightspace, by Wednesday, October 4, 2023 for Questions and by November 15, 2023 for Bloomberg BMC] Chapter 4 4. Answer the below questions for bonds A and B. Bond A Bond B Coupon 8% 9% Yield to maturity 8% 8% Maturity (years) 2 5 Par $100.0 0 $100.00 Price $100.0 0 $104.055 Modified Duration 1.815 3.994 Convexity 4.277 19.764 (a) Calculate the actual price of the bonds for a 100-basis-point increase in interest rates. (b) Using duration, estimate the price of the bonds for a 100-basis-point increase in interest rates. (c) Using both duration and convexity measures, estimate the price of the bonds for a 100-basis-point increase in interest rates. (d) Comment on the accuracy of your results in parts b and c, and state why one approximation is closer to the actual price than the other. (e) Without working through calculations, indicate whether the duration of the two bonds would be higher or lower if the yield to maturity is 10% rather than 8%. 6. State why you would agree or disagree with the following statement: When interest rates are low, there will be little difference between the Macaulay duration and modified duration measures. 14. Answer the below questions. (a) Suppose that the spread duration for a fixed-rate bond is 2.5. What is the approximate change in the bond’s price if the spread changes by 50 basis points? (b) What is the spread duration of a Treasury security? 17. Consider the following portfolio: Bond Market Value Duration (years) W $13 million 2 X $27 million 7 Y $60 million 8 Z $40 million 14 (a) What is the portfolio’s duration? (b) If interest rates for all maturities change by 50 basis points, what is the approximate percentage change in the value of the portfolio? (c) What is the contribution to portfolio duration for each bond? Page 1 of 2
Chapter 6 1. Following are U.S. Treasury benchmarks available on December 31, 2007: US/T 3.125 11/30/2009 3.133 US/T 3.375 11/30/2012 3.507 US/T 4.25 11/15/2017 4.096 US/T 4.75 02/15/2037 4.518 On the same day, the following trades were executed: Issuer Issue Yield (%) Time Warner Cable Inc. TWC 6.55 05/01/2037 6.373 McCormick & Co. Inc. MKC 5.75 12/15/2017 5.685 Goldman Sachs Group Inc. GS 5.45 11/01/2012 4.773 Based on the above, complete the following table: Issue Yield (%) Treasury Benchmark Benchmark Spread (bps) Relative Yield Spread TWC 6.55 05/01/2037 6.373 MKC 5.75 12/15/2017 5.685 GS 5.45 11/01/2012 4.773 13. You observe the yields of the following Treasury securities (all yields are shown on a boLnd-equivalent basis): Year (Period)Yield to Maturity (%)Spot Rate (%)Year (Period)Yield to Maturity (%)Spot Rate (%) 0.5 (1) 5.25 5.25 5.5 (11) 7.75 7.97 1.0 (2) 5.50 5.50 6.0 (12) 8.00 8.27 1.5 (3) 5.75 5.76 6.5 (13) 8.25 8.59 2.0 (4) 6.00 7.0 (14) 8.50 8.92 2.5 (5) 6.25 7.5 (15) 8.75 9.25 3.0 (6) 6.50 8.0 (16) 9.00 9.61 3.5 (7) 6.75 8.5 (17) 9.25 9.97 4.0 (8) 7.00 9.0 (18) 9.50 10.36 4.5 (9) 7.25 9.5 (19) 9.75 10.77 5.0 (10) 7.50 10.00 (20) 10.00 11.20 All the securities maturing from 1.5 years on are selling at par. The 0.5 and 1.0-year securities are zero- coupon instruments. Answer the below questions. (a) Calculate the missing spot rates. (b) What should the price of a 6% six-year Treasury security be? (c) What is the six-month forward rate starting in the sixth year? Bloomberg If you have already taken the Bloomberg BMC, just submit your certificate or proof by November 15, 2023. If you haven’t done it, take the Bloomberg BMC, then submit the certificate by November 15, 2023. The class code is 2X5L78BJH9 . Instructions to use the Bloomberg terminal can be found in the file “BMC FIN424 HW1 Fall2023” posted on Brightspace. Page 2 of 2
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