Convexity and Price-yield Relationship

QUESTION 4

1. Explain what is meant by convexity with regard to the price-yield relationship, and how it varies between callable and non-callable bonds. Also, what is meant by the yield to call?
2. A non-callable 5 years UK government bond pays semi-annually coupons. The face value is £10,000, the annual coupon rate is 8% and the yield to maturity is 10% per year.

Calculate the annualised values for both Macaulay’s duration and the modified duration, and show how the latter may be used to estimate the pricing impact of a change in the yield from 8% to 4%.