A normal (non-callable) 4-year UK government bond pays coupons semi-annually. The face value is 10,000, the annual coupon rate is 10% and the current yield to maturity is 10% per year.

(a) The modified duration for these types of bonds increases as both coupon rates and yields fall. Compare the duration for the bond above with a zero coupon bond with the same life (4 years) and face value (10,000) but a yield to maturity of only 2% per year. Explain what these duration values mean to a bond investor.

(b) Explain and illustrate what is meant by convexity with regard to the price-yield relationship for normal bonds and how it can help to improve estimates of prices changes, beyond what we can infer from using modified duration.

(c) What are callable bonds and how do these embedded options influence the price-yield relationship of these bonds?