Question

A 8-year maturity zero-coupon bond selling at a yield to maturity of 9% (effective annual yield) has convexity of 155.1 and modified duration of 7.06 years. A 30-year maturity 5% coupon bond making annual coupon payments also selling at a yield to maturity of 9% has nearly identical duration—7.04 years—but considerably higher convexity of 244.8.a.Suppose the yield to maturity on both bonds increases to 10%. What will be the actual percentage capital loss/gain on each bond? What percentage capital loss/gain would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.)b.Suppose the yield to maturity on both bonds decreases to 8%. What will be the actual percentage capital loss/gain on each bond? What percentage capital loss/gain would be predicted by the duration-with-convexity rule? (Input all amounts as positive values. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Answer 1

Step-by-step explanation:

Zero Coupon

N 8 30

PMT 0 5

YTM 9% 9%

PV (at 9%) $50.19 $58.91

PV (at 10%) $46.65 $52.87

Actual Loss -7.05% -10.25%

PV (at 8%) $54.03 $66.23

Actual Gain 7.65% 12.43%

Duration 7.06 7.04

Convexity 155.1 244.8

Predicted Loss -6.28% -5.82%

Predicted Gain 7.84% 8.26%

As the yield increases, the bond prices fall and vice versa. Hence, there will be a loss when yields rise and a gain when yields fall.

In order to calculate the actual gains and losses, we need to find the bond prices at yields 8%, 9% and 10% using PV formula. PV(rate, nper, pmt, fv, 0)

Predicted loss and gain can be calculated using following equation

% Change in bond price = - Duration x (change in yield) + 1/2 x Convexity x (change in yield)^2

When YTM = 10%, change in yield = +1% and when YTM = 8%, change in yield = -1%