Bond Convexity

Convexity : "a measure of the curvedness of the price-yield relationship". 

   In finance, convexity is a measure of the sensitivity of the duration                   

   of a bond to changes in interest rates. In general, the higher the

   convexity, the more sensitive the bond price is to decreasing

   interest rates and the less sensitive the bond price is to increasing

   rates.

   

   Duration is a linear measure or 1st derivative of how the price of a

   bond changes in response to interest rate changes. As interest rates

   change, the price is not likely to change linearly, but instead it

   would change over some curved function of interest rates. The

   more curved the price function of the bond is, the more inaccurate

   duration is as a measure of the interest rate sensitivity.

        Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest rate, i.e. how the duration of a bond changes as the interest rate changes.

        Duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question. Then the convexity would be the second derivative of the price function with respect to the interest rate.

        The higher the rating or credibility of the issuer the less the convexity and the less the gain from risk-return game or strategies; less convexity means less price-volatility or risk; less risk means less return.

Mathematical definition:

If the flat floating interest rate is r and the bond price is B, then the convexity C is defined as

        If the combined convexity and duration of a trading book is high, so is the risk. However, if the combined convexity and duration are low, the book is hedged, and little money will be lost even if fairly substantial interest movements occur.

        Convexity is also useful for comparing bonds. If two bonds offer the same duration and yield but one exhibits greater convexity, changes in interest rates will affect each bond differently. A bond with greater convexity is less affected by interest rates than a bond with less convexity. Also, bonds with greater convexity will have a higher price than bonds with a lower convexity, regardless of whether interest rates rise or fall. This relationship is illustrated in the following diagram: 

 

Using convexity, Given a choice, portfolio managers should seek higher convexity while meeting the other constraints in their bond portfolios

­They minimize the adverse effects of interest rate volatility for a given portfolio duration

 

Presented By:

MAULIK B PATEL