Yield to maturity, Coupons, Time to maturity, and their relationship with Duration

CFA Level I Fixed Income
#1

Hey guys,
Here are some golden relationships i always keep in mind:

  • The lower the coupon, the higher the price sensitivity to a change in YTM
  • The longer the maturity, the higher the price sensivity to a change in YTM

First thing, given the two statements provided above, is it safe to say :

  • The lower the coupon, the higher the duration
  • The longer the maturity, the higher the duration

I mean, duration is a measure of price sensitivity to changes in YTM, so i guess i’m correct in the two last statements above?

Last thing, i would like to confirm what is the relationship between YTM and duration, for me they are inversely related, meaning, the lower the yield to maturity, the higher the duration, exactly as for coupons. But there’s the example of putable bonds, where we have a low YTM compared to an option free bond, but also a lower duration! Which makes me doubt my statement that says “YTM and duration are inversely related”. So, how are YTM and duration related?

Thanks guys.

#2

The higher the Macaulay or modified duration. Not necessarily the effective duration.

Modified duration is, and effective duration is, but Macaulay duration isn’t (necessarily).

Once again, this is true for Macaulay duration and for modified duration, but not necessarily for effective duration.

Now you’re talking about effective duration, not Macaulay duration or modified duration.

Perhaps the question to ask is this: do you understand the differences amongst Macaulay duration, modified duration, and effective duration?

1 Like
#3

Hi professor S2000Magician, thanks a lot for your insightful response, you always amaze me with your magic tricks.

I know that effective duration is used for bonds with embedded options because their YTM is difficult to determine, i also know that, given what i previously stated, effective duration measures changes of the bond price relative to the yield curve. I don’t know what that exactly means and i never understood the concept of yield curve and why would it be used for bonds with embedded options (i mean i know it’s because it’s difficult to determine their YTM, but i know this by heart, i don’t necessarly know what it really, concretely, implies).

Also, i never really understood the differences between Macaulay and Modified duration, i know it’s different formulas and just know where to use each depending on the questions i have…

You brought to the surface some huge learning gaps i have in Fixed Income and i thank you for that.

I’ll go do my research and get back to you if needed :slight_smile: .

#4

Effective Dur. is not the yield curve measure. It is the benchmark curve measure

1 Like
#5

Thanks sir, just misused the words since i’m talking about stuff i just know by heart… Going to put time and work into this.

#6

The difference between modified duration and effective duration is that modified duration assumes that the bond’s cash flows will not change when its yield changes, whereas effective duration allows that the cash flows might change when the yield changes.

Therefore, if you have a bond whose cash flows are likely to change when its yield changes, you should use effective duration to measure its interest rate sensitivity, as the assumption for modified duration is inaccurate. Examples of bonds whose cash flows can change with a change in yield are:

  • Callable bonds
  • Putable bonds
  • Floating rate bonds
  • Inverse floating rate bonds
  • Prepayable bonds (e.g., MBSs)

Note that for bonds whose cash flows don’t change with a change in yield (fixed-rate, option-free bonds), effective duration and modified duration will be the same.

1 Like