Spread duration = duration?

Guys,

Why is it that spread duration equals duration for a portfolio without Treasuries?

That makes no sense. Credit spread can’t equal duration.

UNLESS they mean spread duration I’d total duration minus the duration of treasuries. That’d be right.

I never said nothing about credit spread.

What other spread duration type is there lol?

Credit spread as far as I understand can change for a lot of reasons - e.g. liquidity, risk-aversion toward that particular security, credit risk, etc.

Liquidity risk isn’t credit risk but I kno what you mean in that illiquidity can impact the spread. Now we are getting away from your question I feel like. Anyways

Find below the direct quote from CFAI text book:

“For a portfolio of non-Treasury securities, spread duration equals portfolio duration. However, because the spread duration of Treasury securities is zero, a portfolio that includes both Treasury and non-Treasury securities will have a spread duration that is different from the portfolio duration.”

Can anyone clarify that?

The first sentence is confusing. The second sentence is exactly what I was trying to tell you.

The first sentence makes no sense because portfolio duration is the sum of the weighted averages of position durations. The spread duration is duration above that of treasuries. So if spread duration is only part of the bonds entire duration they can’t be equal.

Helpful example from the legend S2000magician himself:

https://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91331539

https://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91331810

"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."

"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."

You guys ascribe far too much intelligence and sentience to bonds.

In a word, bonds are stupid. They do only what they’re told to do.

Here’s your conversation with a bond that has an effective duration of 4.5 years:

“Yo, bond!”

“'Sup?”

“Your YTM just increased by 1%. Whatcha gonna do 'bout that?”

“I’ma drop my price by about 4.5%, yo.”

Notice what the bond didn’t do. It didn’t ask, “Did the Treasury par curve move up 1% while my spread remained unchanged?”

It didn’t ask, “Did the Treasury par curve remain unchanged while by spread widened by 1%?”

It didn’t even ask, “Did the Treasury par curve move up by ½% and my spread widen by ½%?”

All it did was what it was told to do: its YTM went up 1% (for whatever reason), so it dropped its price by about 4.5%.

1 Like

Nice. Works for me lol

To quote Tommy Boy, “that … was … AWESOME!”

Wait, so S2000 magician, is it possible to segregate what portion of duration is attributable to spread or treasure curve?

Yes, usually risk systems will tell label it as spread risk vs interest rate risk. But for the purpose of CFAI we only need to understand the concept.

Okay so its too complicated to do without computers? Works for me. Thanks buddy.

I just realized that I may have left y’all with the wrong impression, so I want to clear up any potential misunderstanding.

Although I called bonds stupid, then showed a bond talking like a brotha’ from the 'hood, I in no way meant to imply that everyone who adopts the speech pattern of bondz is stupid.

Yo.

Hahaha you’re safe

yeah yo safe !!!

(in your own tongue)