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The following problem was found in "Heard on the Street":

You construct a yield curve for (coupon-bearing) treasuries. A particular five-year corporate zero-coupon bond has a default risk premium of 1% over the level of your treasuries yield curve at the five-year mark. You believe that the yield curve is going to flatten in such a way that the default risk premium of the five-ear corporate zero remains constant. What strategy should you pursue using the five-year zero-coupon bond and treasuries to position yourself to profit from your beliefs?

It is clear to me that just using treasuries you can go long the long-rate and short the short-rate while constraining your portfolio to have zero-duration. However, the solution offered in the book is to short the corporate bond and go long a Treasury with greater maturity than the corporate bond, again calibrating your purchases to maintain a zero-duration portfolio.

The explanation is not very clear to me. What I understand is that the coupon-bearing Treasury must be more convex than the corporate bond, and therefore it makes sense that level-shift rate-volatility will help the short-Corporate long-Treasury portfolio. But what is the crisp understanding for why this strategy will be highly profitable in a steepening scenario?

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