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In an american callable bond there is an expectation for the issuer to prepay its debt prior to maturity. I understand that this reduces it's value and therefore, higher yield.

But another way to think about it is that investing in a callable bond should yield the same as a non-callable bond with lower duration (due to the lower expected duration in a callable) bond. This second approach will have a lower yield in a positive slope curve envirement. What is wrong with this approach?

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    $\begingroup$ Nobody can say for sure that the callable bond will have a shorter maturity/duration; it could have the full maturity/duration promised at issue. That is why the first approach, which treats the call feature like an option that will be exercised rationally by the company is preferable. $\endgroup$ – noob2 Feb 22 at 19:41
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  1. Clarity suggestion: "Yield" on a callable bond is ambiguous. You should specify yield to call, yield to maturity, or yield to worst (often YTW=YTC).

  2. A callable bond has a price that consists of the noncallable bond less the premium (n.b. option premium, not bond premium!) paid by the borrower for the option to call in the bonds. Options have a nonzero value, so the NC bond price less the option premium gives a bond price for the callable bond that is cheaper, thus the higher yield (YTM here). The option price is a product of the forward curve and prevailing swaption volatilities and, following no arbitrage, the price of the option would accurately reflect the current market conditions and probability such an option would be exercised.

  3. Because of #2, the callable bond buyer is long risk free and credit, and short option vol. His increased return comes from the convexity he sells off. Duration is less important here than understanding the effect the option has on convexity of the position.

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