# Duration vs Spread Duration vs Partial Duration

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?

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-effective-duration/.

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 generally of interest only for portfolios of bonds.

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

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

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?

Yes.

Modified (and effective) duration measures the change in a bond’s price relative to a change in its YTM. Key-rate duration measures the change in a bond’s price relative to a change in the YTM of a Treasure of a given maturity.

Imagine you have a portfolio of corporate bonds of varying maturities, each priced by a spread over a Treasury of the same maturity. If the 5-year Treasury rate changes, the yields (and, therefore, prices) of some of your bonds will change, while those of other bonds will remain unchanged; the 5-year key-rate duration of your portfolio will give you the price sensitivity of your portfolio to changes in that key (Treasury) rate.

Thanks for that clarification.

If I have a portfolio of corporate bonds with 1, 5, 10, 30 year maturities. And lets say the 5yr corporate bond yield rise by 100 basis points due to spread widening and not due to Treasury yield changes, wouldn’t the 5-year key rate duration also be effective? So shouldn’t it NOT matter if its Treasury or spread contribution. Or am I totally misunderstanding this?

You calculate key rate duration the same way you do effective duration: %ΔP / ΔYTM, but in this case the YTM is for the Treasury, not for your bond.

Suppose that you have a 5-year corporate bond with a spread duration of 4.2 years and a 5-year key-rate duration of 4.2 years. If spreads widen by 100bp, then the price will drop by (about) 4.2%:

%ΔP ≈ -key-rate duration × key rate change – spread duration × spread change

=-4.2(0) – 4.2(1%)

= -4.2%

Thanks, I visited that website on FinancialExam article that you wrote about. It frequently mentions parallel shift of the par (yield curve). Does this make intuitive sense? Shouldn’t it be spot curve because we can get the zero coupon rates and discount at each specifc time period.

Because (modified or effective) duration measures the sensitivity of a bond’s price to a change in its yield to maturity, and the (modified or effective) duration of a portfolio is the weighted average of the durations of its constituent bonds, you can calculate the (approximate) price change of a portfolio using its duration, but only if all of the bonds’ YTMs change by the same amount. The par curve gives the YTMs for coupon-paying bonds, so if all the bonds’ YTMs change by the same amount, that’s a parallel shift in the par curve.

A parallel shift in the spot curve will lead to a nonparallel shift in the par curve (unless the spot curve’s flat), so the duration formula for a portfolio would fall apart.

I’m confused with the definition of a par curve.

http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/

It’s mentioned in that website that the par curve is the Treasury curve. Since the Treasury curve consists of a bond with no credit risk, liquidity risk, we then apply a specific change to YTM for a maturity to observe the price change. But this is only for Treasuries. What about non-Treasuries (corporate bond)? Is the par curve the par curve for the corporate bond? How can you generate a par curve if I just have one corporate bond with one observed YTM.

The problem with trying to create any sort of yield curve – par curve, spot curve, or forward curve – for risky bonds is that the values will depend on the risks associated with those bonds. It’s an impossible exercise.

Thus, we create yield curves for risk-free bonds (or as close to risk-free as is possible in the real world), then incorporate the individual risks in each risky bond by adding a spread to the risk-free yield: (potentially) a different spread for each different risky bond.

You cannot, any more than you can create a line with only one point. You need the YTM for bonds of various maturities, and you create a curve that connects all of those points.

Hi, could you please elaborate more on "cash flows don’t change (modified duration) and cash flows migh change (effective duration)?

Does it mean, fixed coupon can use modified duration and floating rate coupon shall use effective duration? Thanks

Yes.

Also use effective duration on any bond with embedded options (e.g., callable bonds, putable bonds, convertible bonds, asset-backed securities (ABSs), and so on) because their cash flows can change when their YTM changes (e.g., callable bonds may be called when yields are low).

You’re welcome.

I think “thanks” above is autoreply.

Let me thank you by myself! Thank you so much!! I’ve read a lot of your explanation at other posts. They’re always very clear and precise. Stay safe for this hard time!