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I wanted to understand how I can use Z-spreads in the context of gov bond RV.

I understand how to compute Z-spreads although I am having some trouble interpreting the meaning. I am solving for the amount I need to shift the ZC swap curve in order to reprice the particular bond in question correctly (as given by the market price).

Say I have one bond (A) with a z-spread of +50bps and another similar maturity bond (B) with a spread of +20bps. Does this imply the swap market is actually saying: on the raw swap curve (i.e. unbumped) the pv of A is very high, relative to the market price therefore to reduce it to the market price the discount rates must be increased? In this sense, this bond is actually richer than B which only has a spread of +20bps?

thanks.

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  • $\begingroup$ Other way around. You have to move the curve up 50bp to reprice bond A , versus only 20bp for bond B. So A must be relatively cheap. $\endgroup$
    – dm63
    Aug 4, 2023 at 19:37
  • $\begingroup$ Thank you, makes sense. Maybe as a follow up - is it typically more common to compare bonds with similar duration or maturity on a z-sprd basis? $\endgroup$
    – user67825
    Aug 4, 2023 at 20:43
  • $\begingroup$ Definitely duration $\endgroup$
    – dm63
    Aug 5, 2023 at 3:24
  • $\begingroup$ is the mkt convention to add the z-spread onto ZC rates or subtract? I see Tuckmans book has it as subtract. My example above was based on todays US curve, i.e. bonds are cheaper (yield more) then swaps -> therefore, I need to shift up the ZC swap curve by say +50bps to get the bond PV, therefore I would say the z-sprd is +50bps. Whereas following Tuckmans formulae (arguable he's talking about TED spreads) it would be -50bps. $\endgroup$
    – user67825
    Aug 5, 2023 at 8:59
  • $\begingroup$ As you said, in current market z spread of Treasuries versus swaps is positive. Prior to 2008 was negative. Reason = massive issuance of Treasuries. $\endgroup$
    – dm63
    Aug 5, 2023 at 11:40

1 Answer 1

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If a bond's Z-spread increases, and nothing else changes, then the bond's yield also increases, and the price decreases. Conversely, if a bond's Z-spread decreases, this the yield also decreases, and the price increases.

If A's Z-spread is greater than B's, and you want to bet that the difference between their Z-spreads will decrease, then you would deem A cheap, and buy it, and deem B rich, and sell it.

But the markets are usually efficient, so before trading based on the Z-spread being different just one day, you should ponder whether the Z-spread difference has been like that for some time, and what might be an explanation for that. E.g. if both bonds had Z-spread 20 bps for the last few months, and suddenly today A is 50, but B is still 20, then their convergence seems more plausible, than if they had been 50 and 20 during the same period.

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  • $\begingroup$ sure. I'd assume liquidity premia and financing effects of different bonds are usually something that can explain spreads between bonds? is there a resource which you can recommend which has a clear (and relevant) explanation of bond RV. Thank you. $\endgroup$
    – user67825
    Aug 5, 2023 at 8:40
  • $\begingroup$ in your initial response - you're assuming that bond yield is approx = zc swap rate + z spread, right? that holds by approximation not equality, correct? $\endgroup$
    – user67825
    Aug 5, 2023 at 9:06
  • $\begingroup$ I liked amazon.com/Fixed-Income-Relative-Analysis-Website/dp/1118477197 for example. Yes, yield approximately = swap rate + Z-spread. $\endgroup$ Aug 5, 2023 at 11:32

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