spread duration=portfolio duration

Dear all,

I am attempting to do Finquiz questions

It says ‘For a portfolio of non-treasury securities, spread durationn equals portfolio duration’.

My understanding is duration includes risk free rate + spread for that bond

Whereas spread duration just includes the spread for that bond and not therisk free rate.

Can anyone please explain where I am missing.

Thank you

The portfolio’s (modified or effective) duration is the percentage change in the portfolio’s price when yields change by 1%.

The spread duration is the percentage change in the portfolio’s price when spreads change by 1%.

If there are no Treasury securities, then the portfolio cannot tell whether the YTM on each of its bonds changed by 1% because Treasury yields increased by 1%, or because spreads widened by 1% while Treasury yields remained unchanged; either way, the YTM increases by 1%. Thus, portfolio (modified or effective) duration equals spread duration.

(Note that this may not be true for some bonds with embedded options. Spreads widening by 100bp won’t affect prepayments on MBSs, but Treasury yields increasing by 100bp very well might.)


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Thank you


You’re quite welcome.