Question

1.Discuss the concept of bond convexity and explain why bond investors should consider convexity when making investment decisions (4).

2. Explain the impact of a call feature on the attractiveness of a bond for investors. In your answer, make sure that you refer to at least the following:

2.1. why so many bonds are callable (2)

2.2. disadvantages of a callable bond to the investor (2)

Answer 1

Bond Convexity - Convexity is a measure of the curvature, or the degree of the curve, in the relationship between bond prices and bond yields. Convexity demonstrates how the duration of a bond changes as the interest rate changes. Portfolio managers will use convexity as a risk-management tool, to measure and manage the portfolio's exposure to interest rate risk.

1.Convexity is a risk-management tool, used to measure and manage a portfolio's exposure to market risk.

2. Convexity is a measure of the curvature in the relationship between bond prices and bond yields.

3. Convexity demonstrates how the duration of a bond changes as the interest rate changes.

4. If a bond's duration increases as yields increase, the bond is said to have negative convexity.

5. If a bond's duration rises and yields fall, the bond is said to have positive convexity.

Bond investors should consider convexity when making investment decisions because :

The price sensitivity to parallel changes in the term structure of interest rates is highest with a zero-coupon bond and lowest with an amortizing bond (where the payments are front-loaded). Although the amortizing bond and the zero-coupon bond have different sensitivities at the same maturity, if their final maturities differ so that they have identical bond durations then they will have identical sensitivities. That is, their prices will be affected equally by small, first-order, (and parallel) yield curve shifts. They will, however, start to change by different amounts with each further incremental parallel rate shift due to their differing payment dates and amounts.

For two bonds with the same par value, coupon, and maturity, convexity may differ depending on what point on the price yield curve they are located.

Suppose both of them have at present the same price yield (p-y) combination; also you have to take into consideration the profile, rating, etc. of the issuers: let us suppose they are issued by different entities. Though both bonds have the same p-y combination, bond A may be located on a more elastic segment of the p-y curve compared to bond B. This means if yield increases further, the price of bond A may fall drastically while the price of bond B won’t change; i.e. bond B holders are expecting a price rise any moment and are therefore reluctant to sell it off, while bond A holders are expecting further price-fall and are ready to dispose of it.

This means bond B has a better rating than bond A.

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