Wiley states that the difference between Modified and Effective duration gets smaller as
The yield curve is flatter
2.The time to maturity is shorter
3 the bond is priced closer to par which means that the difference between coupon rate and YTM is smaller
can anyone please explain these 3 points to me.I am not getting them.The only difference I know is that Effective duration considers a change in benchmark rates whereas modified considers a change in the YTM which includes the benchmark rate as a component. I am not able to relate this to these 3’points. Thanks in advance for helping
The difference between modified duration and effective duration is that modified duration assumes that the cash flows won’t change, while effective duration allows that the cash flows might change. The cash flows could change because:
The bond has embedded options (call option, put option, conversion option, prepayment option)
The bond has a floating interest rate
If the yield curve is flat, it’s less likely that an embedded option would be exercised, and any change in a floating rate will be small.
If the time to maturity is short, the effect of changing cash flows will be small.
If the bond is priced close to par, it’s less likely that an embedded option would be exercised.
Can you please elaborate the last point on why its less likely for a an embedded option to be exercised if it trades at par?callable bonds trade at high yields which translates to a bond issued at discount.So if the price were to increase to par this would mean the YTM would decrease so wouldnt that increase the chances of the bond getting called to refinance at lower rates?
Suppose that you issued 6% callable bonds and they’re trading at par: YTM is 6%. To call them you’ll likely have to pay a premium, and then you can issue new bonds at . . . 6%. Maybe a little lower than 6%, but likely not low enough that you’ll recoup the premium you paid.
For example, suppose that you were to call the bonds with 5 years remaining to maturity, at a price of 102. If you issued new, non-callable, 6% coupon, 5-year bonds they’d have to be trading at a YTM of 5.5366% for you to break even (i.e., you would issue them at 102); that’s an unusually large discount from the yield on the callable bonds.