Yield Spreads Over the Benchmark Yield Curve

If you wanted to capture the level of default risk on a bond, you could take the easy path by relying on Moody's or Standard and Poor's and their ratings on debt securities. You could also use the G-spread or the I-spread, but these yield spread measures assume constant discount rates over the term structure and life of the bond. A more realistic way to isolate credit risk in which discount rates reflect expectations of future economic activity is to use the __Z-spread__, sometimes referred to in its full name, the __zero-volatility spread__. The Z-spread reflects a constant risk premium in basis points added to the spot curve that results in the estimated price being equal to the market price of the bond. The best part of the Z-spread is that not only does it capture credit risk but also liquidity and option risk.

The Z-spread is the spread over the entire government bond benchmark yield curve, which means that it explicitly considers every spot rate along the term structure. It is most useful when comparing bonds. Suppose you own two bonds, with similar durations and coupons, issued by industry leaders in the food service sector. The first bond is callable, and the second bond is not. What could you reasonably conclude regarding these bonds?

Incorrect. Two bonds can only sell for the same price if they have identical cash flows and risk-adjusted discount rates. Identical Z-spreads will likely result in bond prices that are close, but callable bonds will have different spreads than non-callable bonds, especially if the two issuers are similar.

Correct. Z-spreads show the compensation bondholders demand for credit, liquidity, and option risk. Since bond prices for callable bonds will be less than the prices for straight bonds, it makes perfect sense the Z-spread will be higher for a callable bond.

Incorrect. The callable bond contains credit, liquidity, and option risk, so it will have a larger Z-spread.

Z-spreads can be difficult to calculate and typically require the use of minimization techniques found in spreadsheet software. That does not preclude them from being easy to understand, nor does it preclude the process to calculate them from being equally easy to understand. First, find the benchmark spot rates over the entire term structure and then form the spot curve. Second, add a constant premium to each spot rate such that the present value of the bond's cash flows will equal the current market price. These two steps will produce the Z-spread for a bond.

Since the Z-spread considers the option risk of a bond, another yield measure is necessary to be able to compare straight bonds with those bonds having embedded options. This measure is the __option-adjusted spread (OAS)__. The OAS is defined as the difference between the Z-spread and the basis point option value. It essentially removes the option from spread analysis, so credit risk and liquidity risk can be compared without having the complications of early exercise of the embedded option. The Z-spread on a 15-year callable bond is 220 basis points, and the value of the embedded option is 20 basis points. What will the OAS be on this bond?

Incorrect. The OAS is the Z-spread minus the value of the embedded option, which means the OAS will be less than the Z-spread.

Not quite. The difference between the Z-spread and the OAS is the value of the embedded option. Therefore, for a callable bond, the Z-spread and the OAS will never be identical.

Good. This should make perfect sense. If the OAS removes the effects of the embedded option, then it will be less than the Z-spread.

Both the Z-spread and the OAS are quite useful when comparing bonds. The Z-spread provides an indication of the credit, liquidity, and option risk contained in any bond, while the OAS removes the option from the analysis so only credit and liquidity risk remain. Both are considered to be yield spreads over the benchmark yield curve.

In summary: [[summary]]

The bonds have identical Z-spreads

The callable bond has the higher Z-spread

The callable bond has the lower Z-spread

At least 220 basis points

Exactly 220 basis points

Less than 220 basis points

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