OAS/Z-spread

CFA Level II Fixed Income
#1

I cannot for the life of me fully conceptualize the OAS and its relationship to the z spread. I’ve watched Mark’s videos and I’m still not confident that i can grasp this idea- its really the only thing in the curriculum that is giving me so much trouble. If anyone has a way of explaining it in the simplest way possible (particularly the formula Z=OAS-V(call) itd be much appreciated.

#2

I wrote an article comparing the nominal spread, z-spread, and OAS: http://www.financialexamhelp123.com/yield-spreads/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

In a nutshell:

  • The nominal spread is added to one point on the (risk-free) par curve
    • It’s the difference between the YTM of a given (presumably risky) bond and the YTM of a risk-free bond of the same maturity
    • It ignores the shape of the yield curve
  • The z-spread is added to every rate on the (risk-free) spot curve
    • It’s the additional yield earned (at each payment date) on the risky bond over that earned on a risk-free bond of the same maturity
    • It takes into account the shape of the yield curve
  • The OAS is added to every forward rate in a binomial interest rate tree
    • It removes the value of options embedded in a bond; thus, it is a spread for the underlying option-free bond
    • It’s the additional yield earned (at each payment date) on the risky (but option-free) bond over that earned on a risk-free bond of the same maturity
    • It takes into account the shape of the yield curve
    • It takes into account the assumed volatility of future interest rates

Because the z-spread does not remove the value of any embedded options, whereas the OAS does remove that value, the difference is a measure of the value of the embedded options, _ measured in basis points of additional yield _. However, the formula:

z-spread = OAS – option value

(Equivalently: option value = OAS – z-spread)

is somewhat misleading because the OAS and the z-spread are not directly comparable: they’re added to rates on different curves (the forward curve and the spot curve, respectively). The formula provides a good visualization, but not an accurate yield measure.

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