Credit Spread Measures for Fixed-Income Portfolios

Probably not. Only under a specific circumstance.

Make sure you keep all of those credit spread measures in mind as you get deeper into credit strategies. There are quite a few.

That's right. Now you're calculating a __G-spread__, which is the same idea with some interpolation. Using the durations, you find the weight on Government Bond A to be 25%. $$\displaystyle w_A(5.0) + (1 - w_A)(7.0) = 6.5 $$, so $$ w_A = \frac{6.5 - 7.0}{5.0 - 7.0} = 0.25 $$ Then you can use those weights to interpolate the yield. $$\displaystyle 0.25(0.02) + 0.75(0.03) = 0.0275 = 2.75 \% $$ The G-spread is the difference between this interpolated government yield and the yield on the risky bond, which is 2.25%. The G-spread is useful for figuring out how to hedge portfolios or to estimate the credit spread for illiquid bonds.

No. That would take you furthest from the true value, actually.

Not quite. That would be close, but it wouldn't match perfectly.

If you're calculating any of these so far, what would be a real threat to accurately measuring a bond's credit risk with these measures?

The __I-spread__ is similar: interpolate the rate you need from durations, and find the difference. But for the I-spread, you use swap rates instead of government yields. The swap curve is usually smoother than the government yield curve, so it's sometimes preferred. It really just depends on what you're using to hedge; the instrument should match the measure.

That's right. If the government debt isn't really risk-free, then a difference won't give you the spread you're looking for. If the banking sector of a country also is in a risky place, then swap rates might not work right in giving you an accurate I-spread.

No. Other risky securities don't matter here. Just consider the two yields being compared.

And that's common. You might have a 6.5-duration bond, you want to measure its credit spread, and you have both five-year and seven-year duration government securities. | | Duration | Yield | |---|---|---| | Risky Bond | 6.5 | 5.0% | | Government A | 5.0 | 2.0% | | Government B | 7.0 | 3.0% | What do you think would give you the best measure?

The __Z-spread__ and the __option-adjusted spread (OAS)__ are both implicit calculations. Instead of a simple spread difference, the Z-spread is the spread added to each point on the spot curve that will cause the bond's implied price to match market value. It's a good measure for option-free bonds. Also, the "credit default swap (CDS) basis" refers to the difference between the Z-spread on some bond and the CDS spread of the same maturity for that issuer. The option-adjusted spread is similar, but it uses the interest rate tree instead, so it works for any bond you want. Which one sounds like it has some added assumptions built into it?

Yes!

No, it's the OAS.

The interest rate tree itself introduces these assumptions. It's built with assumptions of binary movements and predetermined up or down movements. Interest rates don't really do that; it's just a model. Another issue is that it provides an estimated spread for bonds that just won't happen. It's estimated in expected value, but the option will either be exercised or it won't be. But it's still widely used, and what's really nice is that any bond can be compared using the OAS since the tree can be used to model any bond. For portfolios, OAS is the best as well. Just weight each bond OAS by market value, and you're there.

Asset swaps turn a bond's coupon into some market reference rate plus a spread, so this spread is pretty close to the bond's credit risk. The __asset swap spread (ASW)__ is the difference between a bond's coupon and the fixed rate used on an interest rate swap, when that fixed rate is being swapped for the market reference rate. How would the ASW differ from the I-spread?

Not really. Any risky bond will have default risk. This is about measuring that risk. Consider what might be a threat to the measurement.

If the maturities didn't match perfectly and the risky bond matured a little faster than the government issue, how do you think that would affect the benchmark spread?

Start simple: the __benchmark spread__, or yield spread. You take the 5.6% yield of a risky bond with duration of 10, and subtract the 2.4% yield from an on-the-run (that's the most recently issued) government bond with the same duration, for a benchmark spread of 3.2%.

Absolutely. If the curve is perfectly flat, no problem. Maybe it's 2.4% everywhere. But if there's a slope, then it will be off.

Not quite. Only under a specific circumstance.

Actually, the ASW can easily be larger than the I-spread, especially if the bond is trading at a premium.

Actually, the I-spread estimates the spread over a reference rate using the bond's yield to maturity, but not the ASW.

Right. A bond may pay a 3.2% coupon, but have a 3.1% yield to maturity. If the appropriate fixed rate of a swap is 3.0%, then the asset swap spread is 20 basis points while the I-spread is just 10 basis points. Yes, there are quite a few spreads to keep track of in the world of fixed income!

To summarize: [[summary]]

The bond has default risk

The government itself has credit risk

There are other securities with even more credit risk

A weighted average

Using the five-year bond

Using the seven-year bond

OAS

Z-spread

It would be too low

It would be too high

It would depend on the yield curve

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The ASW would always be lower

The ASW uses the bond's current yield to maturity

The ASW uses the bond's current coupon payment

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