Question

The six-year 6.1% ANNUAL coupon bond above had a yield to maturity of 9% and an annual Macaulay Duration of 5.10. Convexity is 17.25. Assuming that the yield to maturity of 9% increases by 80 basis points to 9.8%. 18. How much is the bond price change (%) if we use duration only? 19. How much is the bond price change (%) if we use duration and convexity?

Answer 1

Modified Duration = Macaulay Duration/(1 + YTM/n)

Modified Duration = 5.10/(1.09) = 4.68 years

a.

Change in Bond Price = -Modified Duration(Change in YTM)

Change in Bond Price = -4.68(0.0080)

Change in Bond Price = -3.74%

So bond prices decrease by 3.74%

b.

Change in Bond Price = -Modified Duration(Change in YTM) + 0.50Convexity(Change in YTM)²

Change in Bond Price = -4.68(0.0080) + 0.50(17.25)(0.0080)²

Change in Bond Price = -3.69%

So bond prices decrease by 3.69%