Question

A 9-year maturity, AAA rated corporate bond has a 6% coupon rate. The bond's promised yield is currently 5.75%. The bond pays interest semiannually.

1. What is the bond's duration?
2. What is the bond's convexity?
3. If promised yields decrease to 4.85% what is the bond's predicted new price, excluding convexity? What is the bond's predicted new price including convexity?
4. If promised yields increase to 6.5% what is the bond's predicted new price, excluding convexity? What is the bond's predicted new price including convexity?
5. Based on your result in part c and d), would you prefer to have a bond with more or less convexity? Explain.

Answer 1

Macaulay duration is calculated as:

where CF = cash flow at time period t; i = periodic yield and Vb = current bond price

Modified duration is calculated as: Macaulay duration/(1 + yield/frequency) where frequency = number of coupon payments made in a year

Convexity is calculated as:

a). Macaulay duration = 7.10 years

Modified duration = 6.90 years

b). Convexity = 58.49

c). If yield changes to 4.85% then the new predicted price (with modified duration) = 1,080.59

new predicted price (including convexity) = 1,083.00

d). If yield changes to 6.50% then the new predicted price (with modified duration) = 964.70

new predicted price (including convexity) = 966.37

e). Bonds with higher convexity are preferable as they show greater increase in prices when yields fall. The fall in bond prices when yields increase are lower, comparatively.

Calculations:

Formulas: