a)
Price of zero coupon bond at 8.25% YTM:
Bond price can be calculated by using the following excel
formula:
=PV(rate,nper,pmt,fv)
=PV(8.25%,9,0,-1000)
= $489.95
Price of zero coupon bond at 9.25% YTM:
Bond price can be calculated by using the following excel
formula:
=PV(rate,nper,pmt,fv)
=PV(9.25%,9,0,-1000)
= $451.03
Price of 6.5% coupon bond at at 8.25% YTM:
Bond price can be calculated by using the following excel
formula:
=PV(ate,nper,pmt,fv)
=PV(8.25%,30,-65,-1000)
= $807.55
Price of 6.5% coupon bond at at 9.25% YTM:
=PV(9.25%,30,-65,-1000)
= $723.62
Actual loss = (Bond price at 9.25% YTM - Bond price at 8.25% YTM)/Bond price at 8.25% YTM
Actual loss (zero coupon bond) = (451.03 - 489.95) /489.95 =7.94%
Actual loss (6.5% coupon bond) = (723.62 - 807.55)/807.55 = 10.39%
Predicted Loss/Gain (Duration-with-Convexity Rule) = [(-Modified Duration)*(Change in Yield)] + [.5*Convexity*(Change in Yield)^2]
Predicted loss (zero coupon bond) = (-8.06 * (1%)) + (0.5 * 156.3 * (1%)^2) = 7.28%
Predicted loss (6.5% coupon bond) = (-8.04 * (1%)) + (0.5 * 248.2 * (1%)^2) = 6.80%
b)
Price of zero coupon bond at 7.25% YTM:
Bond price =PV(7.25%,9,0,-1000)
= $532.63
Price of 6.5% coupon bond at 7.25% YTM:
Bond price =PV(7.25%,30,-65,-100)
= $909.22
Actual gain (Zero coupon bond) = (532.63 - 489.95)/489.95 = 8.71%
Actual gain (6.5% coupon bond) = (909.22 - 807.55)/807.55 = 12.59%
Predicted gain (zero coupon bond) = (-8.06 * (-1%)) + (0.5 * 156.3 * (-1%)^2) = 8.84%
Predicted gain (6.5% coupon bond) = (-8.04 * (-1%)) + (0.5 * 248.2 * (-1%)^2) = 9.28%
A 9-year maturity zero-coupon bond selling at a yield to maturity of 8.25% (effective annual yield)...
A 12.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 139.2 and modified duration of 11.34 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration--12.30 years--but considerably higher convexity of 272.9. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? il...
A 13.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 161.9 and modified duration of 12.27 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration-12.30 years-but considerabl higher convexity of 272.9 a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What...
A 13.05-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 1572 and modified duration of 12.08 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration--12.30 years—but considerably higher convexity of 272.9. a. Suppose the yield to maturity on both bonds increases to 9%. 1. What will be the actual percentage capital loss on each bond?...
Question 1 A 12.58-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 146.5 and modified duration of 11.65 years. A 30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration—-11.79 years—-but considerably higher convexity of 231.2. a. Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each...
Return to question A 12.25-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 1392 and modified duration of 11.34 years. A 40-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical modified duration -12.30 years--but considerably higher convexity of 272.9. 1.25 points a. Suppose the yield to maturity on both bonds increases to 9% IWhat will be the actual percentage...
A 30-year maturity 6% coupon bond making annual coupon payments selling at a yield to maturity of 8% has a duration of 11.79 years and a convexity of 231.2. a. Suppose the yield to maturity increases to 9%. What will be the actual percentage capital loss on the bond? What percentage capital loss would be predicted by the duration rule and the duration-with-convexity rule? b. Repeat part (a), but this time assume the yield to maturity decreases to 7%. c....
A 12.75-year maturity zero-coupon bond selling at a yield to maturity of 8% (effective annual yield) has convexity of 150.3 and modified duration of 11.81 years. A30-year maturity 6% coupon bond making annual coupon payments also selling at a yield to maturity of 8% has nearly identical duration—11.79 years—but considerablyhigher convexity of 231.2.Suppose the yield to maturity on both bonds increases to 9%. What will be the actual percentage capital loss on each bond? What percentage capital loss would bepredicted...
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5% has duration of 9.96 years and convexity of 144.6. The bond currently sells at a yield to maturity of 10%. a. Find the price of the bond if its yield to maturity falls to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of the bond $ b. What price would be predicted by the duration rule? (Do not round intermediate...
A 30-year maturity bond making annual coupon payments with a coupon rate of 14.3% has duration of 11.34 years and convexity of 185.7. The bond currently sells at a yield to maturity of 8%. a. Find the price of the bond if its yield to maturity falls to 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to...
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5% has duration of 9.96 years and convexity of 144.6. The bond currently sells at a yield to maturity of 10%. a. Find the price of the bond if its yield to maturity falls to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to...