Calculation of Spread Duration

[sam226]

Hi guys,
How is the spread duration of the portfolio being calculated?
Provided that the poirtfolio consists of (i) Treasuries, (ii) Corporates and (iii) MBS and their durations are given, shall we deduct the duration of (ii) and (iii) from (i) and times the respective portfolio weight of (ii) and (iii) for the spread duration of the portfolio? Thanks.

 

[cfa_student29]

just ignore treasuries, and calculate weighted duration of all others, that would give u the spread duration

 

[SWhip]

cfa_student29 wrote:
just ignore treasuries, and calculate weighted duration of all others, that would give u the spread duration

Correct. Treasuries have 0 spread duration.
Just remember that when calculating the weighted average, make sure its for the whole portfolio (not ex treasury bonds). IE if corporate bonds is 50% of portfolio and treasuries is 50% then the portfolio spread dur is 50% of the corporate spread dur, not 100% of corporate spread dur.

 

[sam226]

Then the difference between the portfolio duration and spread duration is only the exclusion of treasury duration contributed to the portfolio?

 

[cfa_student29]

yes

 

[S2000magician]

The spread duration of a Treasury is zero.
The spread duration of a non-treasury is its modified (or effective) duration.
The spread duration of a portfolio is the (market-value) weighted average of the spread durations of its constituent bonds: all of them, incouding Treasuries.
For example, you have a portfolio with:

• $1,000,000 market value of 9-year Treasury Notes, with a modified duration of 7 years
• $2,000,000 market value of a 7-year corporate bond with a modified duration of 5 years
• $3,000,000 market value of a 2-year corporate with a modified duration of 1.8 years

The spread duration of the portfolio is:
($1,000,000/$6,000,000) × 0 years + ($2,000,000/$6,000,000) × 5 years + ($3,000,000/$6,000,000) × 1.8 years
= 2.57 years.
For comparison, the modified duration of the portfolio is:
($1,000,000/$6,000,000) × 7 years + ($2,000,000/$6,000,000) × 5 years + ($3,000,000/$6,000,000) × 1.8 years
= 3.73 years.