Module 36.6 LOS 36.k and 36.i: One-sided durations and convexity of option bonds

When bonds come with embedded options, one-sided durations are better at capturing interest rate sensitivity. One-sided duration only captures sensitivity to rates rising or falling, not both. For a callable bond at or near-the-money, one-sided down duration will be lower than one-sided up duration. This is because the call caps the price of a bond, and the bond will not above that value no matter how far interest rates fall.  Conversely, a near-the-money putable bond will have larger one-sided down-duration than one-sided up-duration.

Straight bonds are said to have positive effective convexity. This means that the bond increases in value when rates fall than it decreases in value when rates rise. Putable bonds also exhibit positive convexity. For callable bonds however, when rates are very high and there is little chance of the bond being called, convexity is positive, but when the callable bond is near or at the money, convexity turns negative.

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