Question

For a change in yield to maturity, explain in your own words why the approximate bond price calculated using duration is always less than the fully recalculated bond price using the new yield to maturity. Use a diagram with yield to maturity on the horizontal axis and bond price on the vertical axis to help explain your point.

Answer 1

The diagram shows the relationship between Bond price and yield-to-maturity and compares the actual price and the price as predicted by the duration.

Duration is the weighted average of the time to maturity of each coupon and principal payment. Due to this, duration measures a linear relationship between Yield to maturity and the bond price, in reality, the relationship is convex in nature. As observed in the diagram, the convex shows the actual relationship between the bond price and yield to maturity while the duration predicts a linear relationship.

Due to this when the yield are low, duration underestimates the price increase ie. predicts lower than actual .bond price. When the yields rise, duration over-estimates the price decrease, thus predicting lower than actual bond price. This is the reason we need to consider the convexity of the bond to predict the bond price more accurately.