Explain the I-spread and curves built from swap rates
The idea
The swap rate curve is the term structure of fixed rates on interest rate swaps, and it serves as a benchmark in markets where the government curve is distorted by scarcity, regulation or central bank purchases. It is continuous across maturities in a way government issuance is not, and it reflects the funding conditions of bank counterparties rather than a sovereign's credit. The I-spread is a bond's yield less the swap rate at its maturity, interpolated where necessary; it is simple and widely quoted, but it compares a single yield with a single rate and ignores the shape of the curve between them.
A practice question
What is the I-spread?
- The spread between a bond's yield and the swap rate at its maturity — correct
- The spread between a bond's bid and ask pricesWhy not: That is the bid-offer spread, a transaction cost rather than a valuation measure.
- The spread between two government bondsWhy not: A yield curve spread. The I-spread measures a bond against the swap curve.
It is a simple difference between the bond's yield and the interpolated swap rate for the same term, which is why it is quoted so widely.
A harder one
Central bank purchases push a government bond's yield well below comparable rates. What does that do to spreads measured against it?
- It widens them artificially — correct
- It narrows them artificiallyWhy not: Backwards. A lower benchmark yield makes the gap to any corporate bond larger, not smaller.
- It leaves them unaffectedWhy not: A spread is a difference from the benchmark, so distorting the benchmark distorts every spread measured from it.
That is a reason to use the swap curve instead. A distorted benchmark contaminates every spread measured from it, and the distortion is not the bond's.
The hardest tier
What is the principal limitation of the I-spread as a measure of value?
- It cannot be computed for bonds with embedded optionsWhy not: It can be computed for any bond with a yield. What an option requires is an option-adjusted measure, which is a further step beyond the Z-spread.
- It requires a full term structure modelWhy not: The opposite — its appeal is that it needs only two numbers. It is the more sophisticated measures that require a model.
- It ignores the curve over the bond's life — correct
It compares one yield with one rate. Two bonds of the same maturity and the same I-spread can have quite different cash flow timing, and the Z-spread addresses this by applying the spread at every point on the curve.
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