What is a ‘bulge’
Convexity is a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the Duration of a bond changes as interest rates change. Convexity is used as a risk management tool that helps to measure and control the amount of market risk bond portfolio.
Breaking down the ‘bulge’
As interest rates rise, bond yields increase, and consequently lower prices for bonds. Conversely, as interest rates fall, the fall of bond yield and bond prices are rising. In the example figure shown above, Bond has greater convexity than Bond B, which indicates that everyone is equal, and the relationship will always have a higher price than bond b as interest rates rise or fall.
Convexity and risk
The bulge is the best measure of interest rate risk in relation to duration because the concept of action suggests that interest rates and bond prices have linear dependence. Duration can be a good indicator of how bond prices may be affected due to small and sharp fluctuations in interest rates. However, the relationship between bond prices and yields are usually more inclined or convex. Thus, convexity is a more accurate indicator to assess the impact on bond prices when there are large fluctuations in interest rates.
With increasing convexity, systemic risk to the portfolio increases. As convexity decreases, the exposure to market interest rates declining and bond portfolio can be considered hedged. In General, the higher the coupon rate, the smaller the convexity (or market risk) bonds. This is because market rates will rise sharply to exceed the bond’s coupon, then there is less risk for the investor.
Positive and negative convexity
If the Duration of a bond increases as to increase the yield, the bond, as they say, negative convexity. In other words, forms of communication, are called concave. Therefore, if the bond has negative convexity, the price will increase in value as interest rates rise, and Vice versa. Some examples of relationships that demonstrate negative convexity bonds with the traditional provision of call preference bonds and most mortgage-backed securities (MBS).
If the Duration of the bond increases and the yield falls, bond say positive convexity. If the bond has a positive convexity, as a rule, experience more price increases if yields fall, reducing prices while increasing yield. Typical types of bonds with positive convexity bond to do all the provisions, call and offer goo. Under normal market conditions, the higher the coupon rate, the lower the bond’s degree of convexity. Consequently, zero-coupon bonds have the greatest degree of convexity, because they do not offer any coupon payments.