Question

You own an annual coupon bond with a duration of 11.11 years and a convexity of 128.62. The bond is currently priced at $805.76 and the yield to maturity is currently 6%. However, you expect the yield to maturity to increase to 8%. What will be the new price of the bond?

Answer 1

Modified duration = Macaulay duration / (1 + r)

Modified duration = 11.11 / (1 + 0.08)

Modified duration = 10.28704

Change in yield = 8% - 6% = 2%

Change in percentage price = -(Modified duration * change in yield) + [(0.5 * convexity * (change in yield)^2]

Change in percentage price = -(10.28704 * 0.02) + [(0.5 * 128.62 * (0.02)^2]

Change in percentage price = -0.205741 + 0.025724

Change in percentage price = -0.180017 or -18.0017%

New price = 805.76 (1 - 0.180017)

New price = $660.71