The price value of a basis point will be the same regardless if the yield is increased or decreased by 1 basis point. However, the price value of 100 basis points (i.e

Question

, the change in price for a 100-basis-point change in interest rates) will not be the same if the yield is increased or decreased by 100 basis points. Why?

Answer 1

The convex relationship explains why the price value of a basis point (i.e., the change in price for a 1-basis-point change in interest rates) will be roughly the same regardless if the yield is increased or decreased by 1 basis point, while the price value of 100 basis points will not be the same if the yield is increased or decreased by 100 basis points. More details are below.

When the price-yield relationship for any option-free bond is graphed, it displays a convex shape. When the price of the option-free bond declines, we can observe that the required yield rises. However, this relationship is not linear. The convex shape of the price-yield relationship generates four properties concerning the price volatility of an option-free bond. First, although the prices of all option-free bonds move in the opposite direction from the change in yield required, the percentage price change is not the same for all bonds. Second, for very small changes in the yield required (like 1 basis point), the percentage price change for a given bond is roughly the same, whether the yield required increases or decreases. Third, for large changes in the required yield (like 100 basis points), the percentage price change is not the same for an increase in the required yield as it is for a decrease in the required yield. Fourth, for a given large change in basis points, the percentage price increase is greater than the percentage price decrease.