Bond spreads

Return from a holding of fixed-income securities may be measured in more than one way. The most common approach is to consider the asset-swap spread. More sophisticated investors also consider the basis spread between the cash bond and the same-name credit default swap price, which is known as the basis. In this chapter we consider the most accessible way to measure bond return. 

The spread that is selected is an indication of the relative value of the bond and a measure of its credit risk. The greater the perceived risk, the greater the spread should be. This is best illustrated by the credit structure of interest rates, which will (generally) show AAA- and AA-rated bonds trading at the lowest spreads and BBB-, BB- and lower-bonds trading at the highest spreads. Bond spreads are the most commonly used indication of the risk-return profile of a bond. 

In this section we consider the Treasury spread, asset swap spread, Z-spread, and basis. 

A bond s swap spread is a measure of the credit risk of that bond, relative to the interest-rate swaps market. Because the swaps market is traded by 

The spread over swaps is sometimes called the I-spread. It has a simple relationship to swaps and Treasury yields, shown here in the equation for corporate bond yield. 

---

As orbitals spread into bands, orbitals oriented for a or a bonds spread into the widest bands. 7t orbitals form narrower bands and 5 bonding orbitals form the narrowest bands. 

Two of the four electrons of the beryllium atom are valence electrons. The bonding in the metallic solid must be accomplished by a combination of 2s and 2p orbitals if not, the s band would be completely filled and Be would be an insulator, or perhaps not a room-temperature solid at all. In the orbital description, the two valence electrons of each Be atom participate in two 2s2p hybrid electron pair bonds, spread over the 12 nearest neighbors of the hep structure. 

In many molecules or ions one electron pair in a double bond spreads... 

Both sulfrir-to-oxygen bonds are double bonds wliich occupy more space than single bonds and die repulsion beti een the double bonds spread out the angle close to 120°. 

In this concept, the skeleton of a bonds is invariant. These bonds, (like each of the others that have been discussed above) are said to be localised, which means that they are hmited to the region between two atoms. Unlike the a bonds, the tt bonds spread out between aU of the contributing atoms, to give delocalised orbitals, and are not restricted to lie between pairs of atoms. To indicate that the bonding... 

Other Intra-Euro Bond Spread Drivers... 

The calibrated tree can now be used to calculate corporate bond spreads as well as bond options. The outlined procedure is close to that advanced by Black, Derman, and Toy in that the process fits observed market rates and short rate volatility. There is, however, a danger that interest rates could go negative in this procedure. 

Pi j = one-month probability of transitioning from rating / to / D = bond spread dnration... 

In many molecules or ions one electron pair in a double bond spreads over an adjacent single bond, thereby delocalizing its charge, which stabilizes the system. In such cases, more than one Lewis structure, each called a resonance form, can be drawn, and the species actually exists as a resonance hybrid, a mixture of the resonance forms. 

Thin panels are more economical and due to their low weight, allow costs to be saved with the frame overall. In the case of screwed or riveted fastening, forces are only absorbed by the face of the holes. Thin panels therefore need more fastening points. Elastic bonding spreads stress evenly (see Fig. 14) and acts in the same way as an infinite number of fastening points. 

An approximate treatment of tt electron systems was introduced in 1931 by Erich Huckel (Figure 15.17) and is called the Huckel approximation of tt orbitals. The first step in a Huckel approximation is to treat the sigma bonds separately from the pi bonds. Therefore, in a Huckel approximation of a molecule, only the tt bonds are considered. The usual assumption is that the <7 bonds are understood in terms of regular molecular orbital theory. The <7 bonds form the overall structure of the molecule, and the tt bonds spread out over, or span, the available carbon atoms. Such 77 bonds are formed from the side-on overlap of the carbon 2p orbitals. If we are assuming that the tt bonds are independent of the cr bonds, then we can assume that the 77 molecular orbitals are linear combinations of only the 2p orbitals of the various carbon atoms. [This is a natural consequence of our earlier linear combination of atomic orbitals—molecular orbitals (LCAO-MO) discussion.] Consider the molecule 1,3-butadiene (Figure 15.18). The tt orbitals are assumed to be combinations of the 2p atomic orbitals of the four carbon atoms involved in the conjugated double bonds ... 

Of course, the basic relative value measure is the Treasury spread or government bond spread. This is simply the spread of the bond yield over the yield of the appropriate government bond. Again, an interpolated yield may need to be used to obtain the right Treasury rate to use. The bond spread is given by ... 

Dealers, often brokerage firms with large retail investor customer bases, purchase bonds in the wholesale or institutional marketplace in bulk. Once acquired, the large bond position must be subdivided and sold to numerous investors. If not all of the bonds can be sold immediately, the broker will hold the bonds in inventory until the position is completely liquidated. The dealer can inventory the bonds anywhere from a day to a few months, and this is the reason that retail bond spreads tend to be large. There is always the risk that the broker may have to hold the bonds in inventory for an extended period of time— hence, a large spread is typically "built" into the price. 

You are most likely already familiar with bond spreads. The spread is the markup, or the difference between what the dealer bought for the bond and what that firm is offering to the customer. This spread or markup is how the dealer makes money, as the differential is embedded in the price. The more seasoned bond investor understands spreads and is familiar with the markup process. 

---