Few questions I have with respect to MD and ED: 1. Why is MD=ED for bonds that do not have an embedded option.
If a bond’s ED 3. If a bond’s ED>MD, why is it most likely a putable bond?
For callable bonds whose call option is not in the money, we would expect MD~ED for them. Why?
The only difference between effective duration and modified duration is that effective duration allows that the cash flows may change when interest rates change, whereas modified duration assumes that the cash flows do not change when interest rates change.
It is not necessarily true that Dmod = Deff for bonds without embedded options; a floating-rate bond would likely have a different modified duration and effective duration. If the coupon rate is constant (so that the only reason the cash flows would change is that an option is exercised), then Dmod = Deff for an option-free bond.
It isn’t.
The price change for a callable bond when the option is in the money (i.e., when interest rates are low) is less than the price change for an option-free bond, so Deff will be less than Dmod. (When the option is out of the money, Deff and Dmod should be equal (or darned close).) However, the price change for a putable bond when the option is in the money (i.e., when interest rates are high) is also less than the price change for an option-free bond, so Deff will be less than Dmod. (Again, when the option is out of the money, Deff and Dmod should be equal (or darned close).)
Whoever wrote this one is wrong. (I wish I knew where they get this stuff; it’s rotten to tell junk like this to candidates.)
It isn’t; see above. (Again, I hate seeing this kind of junk.)
The only kind of bond of which I can think immediately that would have Deff greater than Dmod is an inverse floater: when interest rates drop you have a higher coupon discounted at a lower YTM, so the price rises a lot; when interest rates rise you have a lower coupon discounted at a higher YTM, so the price drops a lot. Thus, the effective duration is very large (in fact, it is generally longer than the time to maturity).
Remember, the only difference between Deff and Dmod is that the former allows for cash flow changes, while the latter does not.
If the option is out of the money, then it is unlikely to be exercised, so the cash flows won’t change. When the cash flow don’t change, Deff = Dmod.
The same is true for an out-of-the-money put option.
Awesome. Simply awesome. Thanks a zillion.
You’re welcome a zillion-and-one.
Very detailed. Thanks
Five years ago I apparently knew something.