Consider a non-callable bond with 5 years to maturity and an annual coupon of 4%. The bond yields 3% and you may assume that the yield will remain constant throughout the holding period.
a. What price should you be willing to pay for this bond?
b. What is the (Macaulay) duration of the bond? What is the modified duration of the bond?
c. Use modified duration to estimate the new market value of the bond, should bond market yields increase by 0.50% (i.e. 50 basis points).
d. Assume the convexity of the bond is 25.568. Now, using the duration plus convexity estimate, what is your estimate of the market value of the bond upon a 0.50% yield increase?
e. Suppose your institution issued this bond, but, using available current assets, wants to temporarily immunize against interest rate risk by acquiring zero-coupon bonds as assets. You can assume that these zero-coupon bonds have similar yields. What portfolio weights would you require to construct an immunizing portfolio comprised of 1-year and 7-year zero coupon bonds?
f. Why is convexity the bondholder’s friend?