Which of the following statements are true in respect of a fixed income portfolio:
1. A hedge based on portfolio duration is valid only for small changes in interest rates and needs periodic readjusting
II. A duration based portfolio hedge can be improved by making a convexity adjustment
III. A long position in bonds benefits from the resulting negative convexity
IV. A duration based hedge makes the implicit assumption that only parallel shifts in the yield curve are possible
A hedge based on portfolio duration alone makes the assumption that the price/yield relationship is linear, and ignores the convexity or non-linearity of the price/yield relationship. As prices change beyond small changes, the non-linear effect kicks in, which can be offset by making a convexity adjustment to the hedge. Therefore statements I and II are correct.
Statement III is incorrect - negative convexity has an adverse effect on bond prices regardless of whether prices rise or fall.
Statement IV is correct, a bond hedge based on duration alone may be mismatched along the yield curve (eg, hedging a 10 year maturity bond with a 3 year futures contract, even though of identical total durations), which is based upon the implicit assumption that all rates will move together (ie parallel shifts).