Question

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 What percentage capital loss would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero-Coupon Bond Coupon Bond Actual loss Predicted loss b. Suppose the yield to maturity on both bonds decreases to 7%. What will be the actual percentage capital gain on each bond? What percentage capital gain would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero-Coupon Bond Coupon Bond Actual gain Predicted gain

Answer 1

a. Using a financial calculator, we find that the price of the zero-coupon bond (with $1000 face value) is For yield to maturity of 8%: $374 84 For yield to maturity of 99% $333.28 The price of the 6% coupon bond is: For yield to maturity of 8%: $774.84 For yield to maturity of 9% $691 79 Zero coupon bond Actual % loss = $335.28 $374.84 – 0.1109 an $374.84 The percentage loss predicted by the duration-with-convexity rule is: Predicted % loss = [( 11.81)x0.011-10,5 x 150,3 (0.0191 --0.1106, an 11,06% loss Coupon bond $691.79 - $774.84 Actual % loss = = 0.1072. a 10.72% loss m $774.84 The percentage loss predicted by the duration-with-convexity rule is: Predicted % loss = [(-11.79) 0.01] – [0.5 231.2 (0.01)* = -0.1063, a 10 63% loss b. Now assume yield to maturity falls to 7%. The price of the zero increases to $422.04. and the price of the coupon bond increases to $875.91. Zero coupon bond $422.04-$374.84 Actual % vain = sa $4 = 0.1259 a 12.59% gain $374.84 The percentage gain predicted by the duration-with-convexity rule is: Predicted % gain - [i-11.81)*(-0.01)] + [0.5 x 150.3 % (-0.01)') -0.1256, a 12.56% gain Coupon bond 0,1304, a 13.04% gain $774.84 The percentage gain predicted by the duration-with-convexity rule is. Actual % gain $875.91 - $774.84 Predicted % gain = [(-11.79) (0,01)1+0,5 231,2 x (001)*1 = 0.1295, a 12.95% gain

a. Using a financial calculator, we find that the price of the zero-coupon bond (with $1000 face value) is For yicld to maturity of 8%: $374.84 For yicld to maturity of 9%: $333.28 The price of the 6% coupon bond is For yield to maturity of 8%: $774.84 For yield to maturitv of 9%: $691 79 Zero coupon bond $333.28 $374.84 = 0.1109. an 11.09% loss Actual loss= $374.84 The percentage loss predicted by the duration-with-convexity rule is Predicted % loss = [(11.81) x 0.01]- [0.5 x 150.3 x (0.01 --0.1106, an 11,06% loss Coupon bond $691.79 $774.84 Actual loss= 0.1072, a 10.72% loss $774,84 The percentage loss predicted by the duration-with-convexity rule is Predicted % loss L(-11.79) x 0.01L0.5 x 231.2 x (0.01) =0,1063, a 10 63% loss b. Now assume yield to maturity falls to 7%. The price of the zero increases to S422.04, and the price of the coupon bond increases to $875.91. Zero coupon bond $422,04-$374.84 0.1259, a 12.59% gain Actual % ain = $374.84 The percentage gain predicted by the duration-with-convexity rule is Predicted % gain -11.81) x (-0.01)+[0.5 x 150.3 x (-0.01) -0,1256, a 12.56% gain Coupon bond $875,91-S774,84 Actual % gain 0.1304, a 13.04% gain $774,84 The percentage gain predicted by the duration-with-convexity rule is Predicted % gain = [(-11,79) (-0,01)1+ f0,5 x 231,2 x (-0 01) 0.1295, a 12.95% gain