b) Draw the graph of spot rates and yield to maturity (y axis) over the life of the Treasury note ( x axis) and comment briefly. c) Explain why the value of the Treasury note should be based on discounting each cash flow using the corresponding Treasury spot rates. Problem 5. A 4-year 5.8% coupon bond is selling to yield 7%. The bond pays interest annually. a) What is the price of the 4 -year 5.8% coupon bond selling to yield 7% ? b) What is the price of this bond one year later assuming the yield is unchanged at 7% ? c) What is the price of this bond one year later if the yield decreases to 6.2% ? d) What is the price of this bond one year later if the yield increases to 7.8% ? e) Compute the price change and comment briefly: - Price change attributable to moving to maturity (no change in discount rate) - Price change attributable to a decrease in the discount rate from 7% to 6.2% - Price change attributable to an increase in the discount rate from 7\% to 7.8% Problem 6. Suppose that a bond is purchased between coupon periods. The number of days between the settlement date and the next coupon period is 115 . There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semi-annual coupon payments remaining. a) What is the dirty (full) price for this bond if a 5.6% discount rate is used? b) What is the accrued interest for this bond? c) What is the clean (flat) price? d) Redo the same calculations if the number of days between the settlement date and the next coupon period is 60,90,180. e) Give a brief comment of your result and explain why bonds are quoted at their clean price? Problem 7. Suppose that a corporation has semi-annual coupon bond trading in the United States with a YTM of 6.25% and an annual coupon bond traded in Europe with a YTM of 6.3%. Which has the greater yield? Problem 8. Consider a 3-year, 9% annual coupon corporate bond trading at 89.464. The YTM is 13.5% and the YTM of a 3-yaear Treasury is 12%. Compute the nominal spread (GSpread) and the zero-volatility spread (Z-spread) of the corporate bond. The 1-, 2-, and 3year spot rates on Treasuries are 4%,8.167% and 12.377% respectively. Problem 9. The current 1-year rate (f0,1) is 4%, the 1-year forward rate for lending from time =1 to time 2(f1,1) is 5%, and 1-year forward rate for lending from time =2 to time =3 (f2,1) is 6%. b) Draw the graph of spot rates and yield to maturity (y axis) over the life of the Treasury note ( x axis) and comment briefly. c) Explain why the value of the Treasury note should be based on discounting each cash flow using the corresponding Treasury spot rates. Problem 5. A 4-year 5.8% coupon bond is selling to yield 7%. The bond pays interest annually. a) What is the price of the 4 -year 5.8% coupon bond selling to yield 7% ? b) What is the price of this bond one year later assuming the yield is unchanged at 7% ? c) What is the price of this bond one year later if the yield decreases to 6.2% ? d) What is the price of this bond one year later if the yield increases to 7.8% ? e) Compute the price change and comment briefly: - Price change attributable to moving to maturity (no change in discount rate) - Price change attributable to a decrease in the discount rate from 7% to 6.2% - Price change attributable to an increase in the discount rate from 7\% to 7.8% Problem 6. Suppose that a bond is purchased between coupon periods. The number of days between the settlement date and the next coupon period is 115 . There are 183 days in the coupon period. Suppose that the bond purchased has a coupon rate of 7.4% and there are 10 semi-annual coupon payments remaining. a) What is the dirty (full) price for this bond if a 5.6% discount rate is used? b) What is the accrued interest for this bond? c) What is the clean (flat) price? d) Redo the same calculations if the number of days between the settlement date and the next coupon period is 60,90,180. e) Give a brief comment of your result and explain why bonds are quoted at their clean price? Problem 7. Suppose that a corporation has semi-annual coupon bond trading in the United States with a YTM of 6.25% and an annual coupon bond traded in Europe with a YTM of 6.3%. Which has the greater yield? Problem 8. Consider a 3-year, 9% annual coupon corporate bond trading at 89.464. The YTM is 13.5% and the YTM of a 3-yaear Treasury is 12%. Compute the nominal spread (GSpread) and the zero-volatility spread (Z-spread) of the corporate bond. The 1-, 2-, and 3year spot rates on Treasuries are 4%,8.167% and 12.377% respectively. Problem 9. The current 1-year rate (f0,1) is 4%, the 1-year forward rate for lending from time =1 to time 2(f1,1) is 5%, and 1-year forward rate for lending from time =2 to time =3 (f2,1) is 6%
