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# Portfolio Duration with defaulted bonds

#### Regi725

##### New Member
Hi all - would love to get some insight and feedback on this. What would be an accurate representation of a portfolio duration that holds defaulted bonds? Let's 20% of total market value is in default securities. Would you weight those bonds using a duration of 0 or exclude their market values for the total portfolio duration?

#### Sixcarbs

##### Active Member
Subscriber
Hi all - would love to get some insight and feedback on this. What would be an accurate representation of a portfolio duration that holds defaulted bonds? Let's 20% of total market value is in default securities. Would you weight those bonds using a duration of 0 or exclude their market values for the total portfolio duration?
My gut tells me exclude them, but I am just a Part I student here. They are no longer functioning like bonds, they are in default. How can you (Why would you) model them like bonds?

#### Matthew Graves

##### Member
Subscriber
I would set the duration to zero but keep them included in the calculation. Remember, (modified) duration is the sensitivity to Yield but defaulted or distressed securities tend to start trading based on Price (estimate of recoverable value) rather than Yield so rates become essentially irrelevant, hence duration is irrelevant for those securities.

Although the defaulted securities are no longer rates sensitive they likely have some residual value. Excluding them would give an artificially high duration for the portfolio as you are ignoring a proportion of the portfolio market value.

#### Sixcarbs

##### Active Member
Subscriber
I would set the duration to zero but keep them included in the calculation. Remember, (modified) duration is the sensitivity to Yield but defaulted or distressed securities tend to start trading based on Price (estimate of recoverable value) rather than Yield so rates become essentially irrelevant, hence duration is irrelevant for those securities.

Although the defaulted securities are no longer rates sensitive they likely have some residual value. Excluding them would give an artificially high duration for the portfolio as you are ignoring a proportion of the portfolio market value.
But keeping them in the portfolio, and setting their durations to 0, actually lowers the duration of the part of the portfolio that is actually composed of bonds and performs like bonds.

Are defaulted bonds a function of yields? No, they are a function of recoverable assets.

They need to be parked somewhere, but by including them with the bonds at 0 you are not giving yourself the best possible model for the change in your bond portfolio with yield. Say you want to know the effects of an increase in yield. Change in Bonds=(-D)*(Change in Yield)*(Current Bond Price). That equation will not be a good predictor of the future value of the portfolio if it includes defaulted bonds marked at a duration of 0.

#### Matthew Graves

##### Member
Subscriber
But keeping them in the portfolio, and setting their durations to 0, actually lowers the duration of the part of the portfolio that is actually composed of bonds and performs like bonds.
This is not correct. It will lower the overall weighted average duration of the portfolio but this is correct as the defaulted bonds are no longer rates sensitive but still have market value.

Are defaulted bonds a function if yields? No, they are a function of recoverable assets.
This is exactly what I've said.

They need to be parked somewhere, but by including them with the bonds at 0 you are not giving yourself the best possible model for the change in your bond portfolio with yield. Say you want to know the effects of an increase in yield. Change in Bonds=(-D)*(Change in yield)*(Current Bond Price). That equation will not be a good predictor of the future value of the portfolio if it includes defaulted bonds marked at a duration of 0.
This is not correct. Including them with zero actually gives the best estimate of the overall portfolio value change with a change in rates as the defaulted bonds are no longer rates sensitive.

Consider an example portfolio:
$10,000,000 in Bond A (Dur=1)$90,000,000 in Cash (Dur=0)
Total: $100,000,000 If rates decrease by 1%, values are: Bond A:$10,100,000
Cash: $90,000,000 Total=$100,100,000

Portfolio Duration From market value weights: 10%*1 + 90%*0 = 0.1
Portfolio Duration from valuations: (100,100,000 / 100,000,000 -1)*100 = 0.1

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#### Regi725

##### New Member
Thank you both for your replies!

Very helpful indeed. My concern was artificially lowering the duration of the portfolio but the example above illustrates the point differently. Appreciated!

#### Sixcarbs

##### Active Member
Subscriber
This is not correct. It will lower the overall weighted average duration of the portfolio but this is correct as the defaulted bonds are no longer rates sensitive but still have market value.

This is exactly what I've said.

This is not correct. Including them with zero actually gives the best estimate of the overall portfolio value change with a change in rates as the defaulted bonds are no longer rates sensitive.

Consider an example portfolio:
$10,000,000 in Bond A (Dur=1)$90,000,000 in Cash (Dur=0)
Total: $100,000,000 If rates decrease by 1%, values are: Bond A:$10,100,000
Cash: $90,000,000 Total=$100,100,000

Portfolio Duration From market value weights: 10%*1 + 90%*0 = 0.1
Portfolio Duration from valuations: (100,100,000 / 100,000,000 -1)*100 = 0.1
You are correct. Thanks for the lesson and Review.