Sovereign Bond Spread Measures and Asset Swap Analysis
This is the second half of Chapter 5, where the authors get into the weeds of how to actually measure value in bonds. If the first half was about understanding the yield curve, this half is about the tools you use to identify which bonds are cheap and which are rich.
The short version: there are a lot of spread measures, nobody agrees on which one is “right,” and each one tells you something slightly different.
Breaking Down Bond Yields
A bond’s yield can be decomposed into layers. At the foundation is the government benchmark yield for a matching maturity. On top of that sits a swap spread (reflecting interbank credit risk). Then there is a market risk premium (reflecting liquidity concerns). And finally there is company-specific default risk.
The traditional “credit spread” lumps a lot of this together. That is why the market developed more refined measures. Let’s go through them.
G-Spread
The simplest measure. Take the bond’s yield to maturity and subtract an interpolated government bond yield of the same maturity. “Interpolated” matters because there is unlikely to be a government bond that matures on the exact same date as your bond.
The G-spread is easy to calculate and easy to understand. Its weakness is that it relies on a single government yield as the reference point, which might not be representative if government bond yields are distorted by supply-demand issues.
I-Spread
Same idea, different benchmark. The I-spread is the difference between a bond’s yield and the interest rate swap rate of the same maturity. Since swaps are thought of as representing interbank credit risk (somewhere between AA and A rated), the I-spread tells you how much extra yield you are earning above that level.
The I-spread’s weakness: it only looks at one point on the swap curve. It ignores the shape of the entire curve.
TED Spread
Originally, this was the difference between a Treasury bill future price and a Eurodollar futures price. It measured the credit spread between the interbank market and the risk-free rate. Over time, the concept was extended. You can create a synthetic zero-coupon LIBOR bond using a strip of Eurodollar futures, then compare that yield to a Treasury note. When applied to corporate bonds, the TED spread measures the credit risk between LIBOR and the specific issuer.
Z-Spread
This is where things get more rigorous. The Z-spread (zero-volatility spread) fixes the I-spread’s biggest flaw by using the entire zero-coupon curve instead of a single maturity point.
Here is how it works. Take each cash flow on the bond and discount it using the zero-coupon rate for that maturity, plus a fixed spread. The Z-spread is the value of that fixed spread that makes the present value of all cash flows equal to the bond’s observed market price.
The authors walk through an example with a 4-year 5.5% corporate bond. Without any spread, discounting at the zero-coupon LIBOR rates gives a present value of 99.16. But the market price is 98.88. By adding 8 basis points to every zero-coupon rate, the model price matches the market price. Those 8 basis points are the Z-spread.
The Z-spread is more accurate than the I-spread because it accounts for the term structure of rates. A steeply sloped curve will produce different results for the two measures.
Option-Adjusted Spread (OAS)
The OAS is related to the Z-spread but adds one more layer: it adjusts for embedded options in the bond. Many bonds (especially high-yield issues) have call features that let the issuer redeem the bond early.
The Z-spread ignores these features. It assumes the bond will run to its stated maturity. The OAS uses a model to account for the probability that the issuer exercises the call. For a callable bond, the investor is short an option and needs to be compensated. So the OAS will typically be larger than the Z-spread.
There are edge cases where the OAS could be smaller, like with shorter-dated callable bonds where the option’s time value is decaying rapidly. But the general rule holds: for callable bonds, OAS and Z-spread give different answers. For non-callable bonds, they should be the same (assuming the same underlying curve is used).
Asset Swap Spread
This is the one the authors really want you to understand, and they note that both of them have found it poorly understood by practitioners despite being central to fixed income analysis.
The asset swap spread (ASW) is the incremental return over LIBOR that an investor earns by buying a fixed-coupon bond and simultaneously entering into an interest rate swap. The result is a synthetic floating-rate note. The spread reflects the market’s perception of the issuer’s credit risk.
There are three types of asset swaps:
Yield/Yield Spread
The simplest version. You buy the bond and pay fixed on a swap. The spread is just the numerical difference between the bond yield and the swap rate. This is basically the I-spread by another name. No adjustment for cash flow timing or whether the bond trades at a premium or discount.
Par/Par Asset Swap
More sophisticated. The bond is purchased at par regardless of its market price. The fixed rate on the swap equals the bond’s coupon. The investor receives LIBOR plus or minus a spread, set so that the whole package has zero net present value.
The authors give a detailed example. A 10-year government bond with a 5% coupon in a 3% yield environment trades at a dirty price of 117.06. But the investor pays par. That creates a cash flow advantage of 17.06. To make the package fair, the LIBOR spread is set at negative 55 basis points, clawing back the advantage over time.
Notice: the spread is negative because the government is a better credit than the banks. If the bond becomes more expensive in the market, the spread becomes even more negative, which is described as “widening.” Yes, the terminology is confusing. A more negative number is a wider spread for sovereign asset swaps.
Market Value Asset Swap
Same principle, but the bond is bought at its actual dirty price instead of par. The swap notional on the fixed leg equals the bond’s par value (so the coupons net out). But the floating leg notional equals the dirty price (so the return is based on what you actually invested). At maturity there is a net exchange to settle the difference.
There is a formula linking par/par and market value asset swap spreads, so if you know one you can derive the other.
Identifying Value Using Asset Swaps
The practical application is straightforward. Plot the asset swap spreads for an entire population of bonds against maturity. Fit a curve through the data. Bonds sitting above the curve are cheap (higher spread than expected). Bonds below are rich.
But the authors warn you not to stop there. Several factors can explain why a bond sits off the curve:
- Short-dated bonds may be expensive because they are used as Central Bank collateral.
- Certain bonds may be deliverable into futures contracts, increasing demand and making them rich.
- A bond might be on special in the repo market.
- Illiquid bonds may trade cheap simply because nobody wants to hold them.
The Z-score helps here. It measures how many standard deviations a bond’s spread is from its recent average (typically a 3-month lookback). A positive Z-score means the bond has been getting cheaper. A negative Z-score means it has been getting richer. This helps you avoid buying something that looks cheap but is actually in the middle of a cheapening trend.
Comparing Sovereign Credit Using Asset Swaps
One powerful use of asset swaps is comparing sovereign issuers. The authors show how AAA-rated euro sovereigns (Germany, Netherlands, Spain at the time) traded at very similar asset swap spreads from 2003 to 2008. Investors essentially ignored differences between them. Then the financial crisis hit and spreads diverged by 150 basis points. The “AAA means AAA” assumption died.
Germany consistently traded at the tightest spreads, with Austria, France, and the Netherlands sitting wider. The market was pricing in different degrees of sovereign credit risk even among identically rated issuers.
Forward Asset Swap Spreads
The chapter closes with an advanced topic: forward asset swap spreads. The idea is that comparing spot ASW spreads can be misleading if the bonds have different repo rates.
If bond A trades special in repo (cheap financing) and bond B does not, both might show the same spot ASW spread. But bond A is actually cheaper because you are earning extra carry from the favorable repo rate. The forward ASW accounts for this. It tells you what spread you will earn on an asset swap starting at some future date.
The practical rule: the bond with the largest forward ASW spread is the best investment. When two bonds have the same forward ASW, the market has priced in the repo difference and there is no edge left.
My Take
The spreads section can feel like a vocabulary lesson at first. G-spread, I-spread, Z-spread, ASW, OAS, TED. But each one answers a slightly different question, and knowing which to use in which situation is a real skill.
The Z-spread is probably the most broadly useful. It uses the full curve, it is well-defined, and it applies to any bond. The asset swap spread is the most practically important because it is how a large chunk of the professional market actually thinks about relative value.
The forward ASW concept was the biggest “aha” for me. You can stare at two bonds with identical spot ASW spreads and think they are equivalent. But if their repo rates differ, one is genuinely cheaper than the other. The forward ASW reveals this. It is a small detail that matters a lot for real money investors who need to finance their positions.
The broader lesson of Chapter 5 is that “cheap” and “rich” are relative terms that depend heavily on your choice of benchmark, your measure of spread, and the time horizon you are looking at. There is no single number that tells you the full story. You need several angles to see the picture clearly.