Duration vs Spread Duration vs Partial Duration

[blackscholesvol]

I am looking to clarify my understanding of the following terms : duration, spread duration, partial duration.
If I am evaluating a coporate bond with both Treasury risk and credit spread risk, then duration is just the % change of the price of the bond with respect to 100bp in the Yield to Maturity. In this case, duration measures how a change in yield impacts the overall price. It doesn’t matter if the yield change was a result of Treasury or credit spread.
For spread duration, it is the % change in the price of the bond with respect to 100bp change in the spread. This basically reflects the risk of the credit spread component assuming Treasuries are held constant.
Is this all correct? Is there a measure of duration that measures specifically Treasury risk. Can’t we subtract spread duration from overall duration.
Secondly, is partial duration then the sensitivity of the price of the bond with respect to changes in specific parts of the yield curve? Is this the Treasury curve? If I have a bond with 30 year maturity and the partial duration at the 5 year point is X, does this mean the bond’s sensivitiy if shocks are applied at the 5 year point on the Treasury curve?

 

[S2000magician]

blackscholesvol wrote:I am looking to clarify my understanding of the following terms: duration, spread duration, partial duration.

First, you need to clarify what you mean by, simply, “duration”. There are three basic types of duration (and several other specialized versions):

• Macaulay duration: the weighted-average time to receipt of cash flows, using the present value of each cash flow as the weight on the time until it’s received.
• Modified duration: (roughly) the (negative of the) percentage change in a bond’s price for a 1% change in its yield to maturity, assuming that its cash flows don’t change.
• Effective duration: (roughly) the (negative of the) percentage change in a bond’s price for a 1% change in its yield to maturity, allowing that its cash flows might change.

All of these measures can be applied to bonds of any sort (though if the bond’s cash flows can change when its YTM changes, Macaulay duration and modified duration aren’t appropriate).
These three are the only ones that appear in the Level I curriculum. I wrote an article on them that may be of some use: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-....
Next we have spread duration and key-rate (what you’re calling “partial”) duration; these don’t appear until the Level II curriculum:

• Spread duration: (roughly) the (negative of the) percentage change in a bond’s price for a 1% change in its spread over a Treasury of the same maturity; although nobody ever says so, you can have modified spread duration (assuming that its cash flows don’t change) and effective spread duration (allowing that its cash flows might change).
• Key-rate duration: (roughly) the (negative of the) percentage change in a bond’s price for a 1% change in the YTM of a Treasury of a given maturity; again, you can have modified key-rate duration (assuming that its cash flows don’t change) and effective key-rate duration (allowing that its cash flows might change).

Spread duration is of interest only for risky bonds, and key-rate duration is of interest only for portfolios of bonds (because a single bond’s key-rate duration is zero if the key-rate is not at that bond’s maturity, and is the modified or effective duration if the key rate is at that bond’s maturity).

 

[oktavian]

Are you studying level 1? I finished fixed income material but never saw “partial duration”

blackscholesvol wrote:
I am looking to clarify my understanding of the following terms : duration, spread duration, partial duration.
If I am evaluating a coporate bond with both Treasury risk and credit spread risk, then duration is just the % change of the price of the bond with respect to 100bp in the Yield to Maturity. In this case, duration measures how a change in yield impacts the overall price. It doesn’t matter if the yield change was a result of Treasury or credit spread.

This is modified duration.
What is treasury risk?
CFA level 1 syllabus has five to learn:
- Macauley Duration
- Modified Duration
- Effective Duration
- Money Duration
- Price Value of a Basis Point
Spread Duration is level 3 (?) and Key-Rate is level 2

 

[blackscholesvol]

Yes, I think you’re right. I was reading about spread duration and partial duration when using another reference for studying.
I am confused S2000magician :
“Key-rate duration: (roughly) the (negative of the) percentage change in a bond’s price for a 1% change in the YTM of a Treasury of a given maturity”
It is the sensitivity of a bond with respect to change in Treasury yield of a given maturity? Or do you mean of the yield of a specific maturity of the risky bond/portfolio.
I always thought duration was the sensitivity to changes in yield to maturity of the risky bond/portfolio itself and that sensitivity was driven by changes in Treasury yields and credit spreads. If we use your statement, then you’re saying that if the Treasury yield at the 10yr maturity changes, then somehow this drives the change on my risky portfolio?