Question

1. Use duration to explain the “negative convexity” exhibited by callable bonds. Why is negative convexity a “negative” attribute from the investor’s viewpoint?

2. What happens to the “average life” of a pool of mortgages when prepayment speed increases? Why does prepayment speed increase when interest rates decrease? Discuss the negative convexity exhibited by mortgage-backed “passthrough” certificates in the context of duration and pre-payment speed.

3. Suppose a financial institution currently has a positive duration gap. How would its net worth be expected to vary with changes in interest rates? Explain. Explain how a financial institution could “immunize” its net worth from changes in interest rates.

4. In the context of duration gap management (or asset/liability management), explain the difference one would expect to see in the duration of the assets of a life insurance company as opposed to a commercial bank, assuming both institutions want to immunize their exposure to interest rate risk.

Answer 1

As per policy first question in answered below.

1. Negative convexity means that when yield increases there is more decline in price of bond than the increase in price of bond on account of yield when dropped. This happens in case of callable bonds which faces negative convexity, when yield starts to drop these bonds do not increase in value much as they are running at risk of being called and reedemed at Call price by company. This call price effectively caps the upside potential in the bond price.

From investor's point of view this negative convexity is negative as investor is participation fully in losses on account of rise on yield but when yields drop he is not allowed to fully participate in gains and these gains are capped by Call price.

From duration point of view, callable bonds duration increases when there is rise in yield happens, thereby making bond lose in value more in increasing yield, while duration drops in the time of yield decrease thereby reducing the gains on account of drop in yield.

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