Z Spread

Discussion in 'David's Notebook' started by Abhishek Verma, Dec 16, 2016.

  1. Abhishek Verma

    Abhishek Verma New Member

    Hi David,

    Does Z spread for a same bond, when calculated at different time periods changes ?

    For example lets say we are valuing a bond on January 2000 that will mature in January 2010 bond. Lets say z spread for the bond is 100 bps at Jan 2000. Will Z spread be the same when we will value the same bond on January 2005?

    Provided interest rate doesn't changes.
    Last edited: Dec 16, 2016
  2. ShaktiRathore

    ShaktiRathore Well-Known Member

    The Z-spread reflects the credit risk associated with the Bond ,as maturity changes the credit risk profile of the Bond changes therefore the Z-spread should also change.As the Bond becomes more risky the investors sells it therefore the price drops down and the spread goes up and when the Bond becomes less risky the investors buys it therefore the price goes up and the spread goes down.
    Last edited: Dec 17, 2016
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  3. Abhishek Verma

    Abhishek Verma New Member

    @ShaktiRathore - Thanks :)

    I've another doubt.

    In case of interest changes we consider OAS that removes the sensitivity of interest rate volatility, considering a bond trading at par and everything about the bond remains constant i.e all the risks remain constatnt (Credit, liquidity, default etc), so in these ideal conditions OAS must remain constant throughout maturity?

    Please clarify me on this.

  4. David Harper CFA FRM

    David Harper CFA FRM David Harper CFA FRM (test) Staff Member

    Hi @Abhishek Verma I like your first question because it requires us to understand the definition of the z-spread. The z-spread is a function of the traded price, so the question "does the Z-spread change as the bond approaches maturity?" is interesting but requires any assumption about the bond's price behavior as maturity approaches. I populated this spreadsheet quickly to illustrate. My assumption is that both the risk-free term structure (aka, theoretical spot rate for Treasury securities) and the yield to maturity (aka, yield) is constant. My risk-free term structure = {0.20% @ 0.5 years, 0.30% @ 1.0 years, ..., 1.0% @ 3.0 years} and I assume a semi-annual bond paying 2.0% per annum. We can see the following:
    • When maturity = 3 years, and given an observed (traded price) of $95.00, the z-spread = 2.79%. Notice that we require a price input assumption, in my example $95.00; compared to the $102.98 which is implied by discounting the 3-year bond at the risk free rates.
    • When we shift "forward in time" to 2 years, the issue is choosing the price assumption. I selected constant yield (in this case 3.78% implied by the $95 price for the 3-year bond); in this case, a constant yield of 3.78% implies a price (for the shorter 2-year bond) of $96.60. Notice that, appropriately, the bond price has "pulled to par" from $95.00 to $96.60. The updated z-spread equals 3.18%, so it has increased noticeably. I hope that's interesting!

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