Chapter 16 - Embedded options

A quick question, in chapter 16, section 1.5 Effective Duration, the core reading says, "In most cases the term of the equivalent non-callable bond will be less than that of the callable bond".

I fail to understand this as I thought the term of non callable bond will be greater than callable (since it can be called in early at the borrower's discretion).


Because the bond can be called in early, it can not have a "longer" duration than a non-callable I would say. One way to think about it is that if interest rates fall significantly, the issuer will call the bond and re-issue at lower rates. This means that the bond's price will not rise above par, but can go lower than par. This restricts the price movement of the callable bond, where a non-callable would not be restricted. Since volatility (and hence duration) is (dP/di * -1/P ), then the callable bond will have a lower number.



Also the statement following this statement on why 'principal only' bonds have a very high effective duration , I think 'interest only' bonds too are very sensitive to change in interest rates and hence they too should have a very high duration?


With principal only bonds, when the issuer pre-pays the bond, you get your money back early. But getting your money back early for a zero coupon bond is ALWAYS a good thing. If an issuer repays your coupon bearing bond early, when you were receiving 16% coupons! then that's a bad thing. But with zero coupons its always good. Hence the price of a zero coupon can rise significantly when pre-payments kick off. Again, duration and volatility are the rate of change in price with rates, and this can therefore be higher than expected.



Am i missing something?
Also, what exactly is an Option adjusted spread, the flash cards says, "It can be thought of as the yield margin on the bond at its current price, AFTER allowance for the fact that an option is also embedded in the bond."

I am confused, as I was under the impression, OAS strips out the risk for the investor because of the option and only deals with Liquidity and credit risk of the bond and hence we could compare the parallel shift in the yield curve (OAS) to the extra return being offered on the non callable bond with same risk profile.


Yes - thats exactly what OAS is. It can be compared with a credit spread on a non-callable bond. Hence the reference to "after allowance for the fact that the option is also embedded". So in other words, we have stripped out the impact and the effect of the call option, and all we are left with is the credit margin.



And since we use the PV of cash flows at various future interest rate paths we ideally are removing the risk of payment being IR dependent and hence stripping the impact of the option from the bond.

Please help!![/QUOTE]