Assignment:
Consider a bond that has a 30- year maturity, an 8% coupon rate, and sells at an initial yield to maturity of 8%. Because the coupon rate equals the yield to maturity, the bond sells at par value: P = $1,000.00. Also, you are told that the modified duration (D*) of the bond, at its initial yield, is 11.26 years, and that the bond's convexity is 212.4. Suppose that the bond's yield increases from 8% to 10%.
(a) Predict how much the bond price would decline by applying the duration rule.
(b) You can compute (exactly) that the bond price will actually fall to $811.46, corresponding to a decline of 18.85%. Can you explain differences with the result in item (a)?
(c) Now consider that you are interested in predicting how much the bond price would change by applying the duration-with-convexity rule. How do you analyze the result in this case?
(d) Now consider that there is a much smaller change in bond's yield of 0.1%, so that the price of the bond would actually fall to $988.85, which corresponds to a decline of 1.115%. Predict how much the bond price would change by applying both the duration and the duration-with convexity rules, and then analyze how the results differ from those in (a) and (c).