Question

Question 4. A 12.75-year maturity zero-coupon bond has convexity of 150.3 and modified duration of 11.81 years. A 30-year maturity 6% coupon bond with annual coupon payments has nearly identical modified duration of 11.79 years, but considerably higher convexity of 231.2.

Suppose the yield to maturity on both bonds increases by 1%. What percentage change in price of the bonds as predicated by the duration plus convexity model? (6)

Repeat part (a), but this time assume that the yield to maturity decreases by 1%. (6)

Answer 1

(a) Zero Coupon Bond:

Convexity = 150.3 and Modified Duration = 11.81

Change in YTM = 1 % or 100 bps

Duration Effect = - 11.81 x (0.01) = - 0.1181 or - 11.81 %

Convexity Effect = 1/2 x 150.3 x (0.01)^(2) = 0.007515

% Impact on Bond Price = (-0.1181 + 0.007515) = - 11.0585 or - 11.0585 %

Coupon Bond:

Convexity = 231.2 and Modified Duration = 11.79

Duration Effect = 0.01 x - 11.79 = -0.1179

Convexity Effect = 1/2 x 231.2 x (0.01)^(2) = 0.01156

% Change in Bond Price = (-0.1179 + 0.01156) = - 0.10634 or - 10.634 %

(b) Zero Coupon Bond:

Convexity = 150.3 and Modified Duration = 11.81

Change in YTM = -1 % or 100 bps

Duration Effect = - 11.81 x (-0.01) = 0.1181 or 11.81 %

Convexity Effect = 1/2 x 150.3 x (-0.01)^(2) = 0.007515

% Impact on Bond Price = (0.1181 + 0.007515) = 0.125615 or 12.5615 %

Coupon Bond:

Convexity = 231.2 and Modified Duration = 11.79

Duration Effect = - 0.01 x - 11.79 = 0.1179

Convexity Effect = 1/2 x 231.2 x (-0.01)^(2) = 0.01156

% Change in Bond Price = (0.1179 + 0.01156) = 0.12946 or 12.946 %