Maturity yield spread

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

Figure 8.2 shows the Bloomberg YAS page for Tesco bond SVi% 2019, as at October 9, 2014. The bond has a price of 109.345 and yield to maturity of 3.46%. On the date, the yield spread over a government bond benchmark UK 41 % Treasury 2019 is 200 basis points. The G-spread over an interpolated government bond is 181.5 basis points. Conventionally, the difference between these two spreads is narrow. We see also that the asset-swap spread is 173.6 basis points and Z-spread is 166.3 basis points. 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

Like Black and Cox s work, the authors find spreads similar to the market spreads. Moreover, they find a correlation between credit spread and interest rate. In fact, they illustrate that firms with similar default risk can have a different credit spread according to the industry. The evidence is that a different correlation between industry and economic environment affects the yield spread on corporate bonds. Then, the duration of a corporate bond changes following its credit risk. For high-yield bonds, the interest-rate sensitivity increases as the time to maturity decreases. 

Traditional yield spread analysis for a nongovernment bond involves calculating the difference between the risky bond s yield and the yield on a comparable maturity benchmark government security. As an illustration, let s use a 5.25% coupon BMW Finance bond described in Exhibit 3.10 that matures on 1 September 2006. Bloomberg s Yield Spread Analysis screen is presented in Exhibit 3.14. The yield spreads against various benchmarks appear in a box at the bottom left-hand corner of the screen. Using a settlement date of 9 July 2003, the yield spread is 31 basis points versus the interpolated 3.1-year rate on the Euro Benchmark Curve. This yield spread measure is referred to as the nominal spread. 

There is, therefore, a rationale behind the yield spread differential witnessed between two like issues occupying the same maturity band, and the above points must be factored in when assessing the fair value of a particular Pfandbrief. As of early 2003, it is generally felt that the market has found its echelon in regard to curve spread and that current relative valuations should remain to a large extent intact in the near term. In this context, any short-term deviations from fair value could represent profitable trading opportunities for investors. 

The market quotes bonds with embedded options in terms of yield spreads. A cheap bond trades at a high spread, a dear one at a low spread. The usual convention is to quote the spread between the redemption yield of the bond being analyzed and that of a government bond having an equivalent maturity. This is not an accurate measure of the actual difference in value between the two bonds, however. The reason is that, as explained in chapter 1, the redemption yield computation unrealistically discounts all a bond s cash flows at a single rate. 

The OAS-derived yield spread is based on the present values of expected cash flows discounted using government bond—derived forward rates. The spread berween the cash flow yield and the government bond yield is based on yields to maturity. The OAS spread is added to the entire yield curve, whereas a yield spread is over a single point on the government bond yield curve. For these reasons, the two spreads are not strictly comparable. 

A more easily defined situation can be seen in production of Macintosh apples. These apples, which make up a very significant portion of the northeastern U.S. apple crop, are notorious for dropping off the tree as soon as they have reached maturity. Prior to the development of stop-drop chemicals, it was expected that at least 20-25% of the crop would go on the ground before harvest. The stop-drop programs of today can virtually eliminate this problem, spread the harvest over a longer period of time, and improve the quality of the fruit as it is sold fresh or as it comes out of long-term storages. The value of the stop-drop effect alone could be calculated to be at least 500 on a 300-box-per-acre yield. 

Making comparison between bonds could be difficult and several aspects must be considered. One of these is the bond s maturity. For instance, we know that the yield for a bond that matures in 10 years is not the same compared to the one that matures in 30 years. Therefore, it is important to have a reference yield curve and smooth that for comparison purposes. However, there are other features that affect the bond s comparison such as coupon size and structure, liquidity, embedded options and others. These other features increase the curve fitting and the bond s comparison analysis. In this case, the swap curve represents an objective tool to understand the richness and cheapness in bond market. According to O Kane and Sen (2005), the asset-swap spread is calculated as the difference between the bond s value on the par swap curve and the bond s market value, divided by the sensitivity of 1 bp over the par swap. 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

Generally, the theoretical default spread is almost exactly proportional to the default probability, assuming a constant default probability. Generally, however, the default probability is not constant over time, nor do we expect it to be. In Figure 8.3, we show the theoretical default spread for triple-B-rated bonds of various maturities, where the default probability rises from 0.2% to 1 % over time. The longer dated bonds, therefore, have a higher aimual default risk and so their theoretical default spread is higher. Note that after around 20 years the expected default probability is constant at 1%, so the required yield premium is also fairly constant. 

The research compares the model spread to the one observed in the market. In order to determine the term structure of credit spread. Eons uses historical probabilities by Moody s database, adopting a recovery rate of 48.38%. The empirical evidence is that bonds with high investment grade have an upward credit spread curve. Therefore, the spread between defaultable and default-free bonds increases as maturity increases. Conversely, speculative-grade bonds have a negative or flat credit yield curve (Figure 8.7). 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

The zero-volatility spread, also referred to as the Z-spread or static spread, is a measure of the spread that the investor would realize over the entire benchmark spot rate curve if the bond were held to maturity. Unlike the nominal spread, it is not a spread at one point on the yield curve. The Z-spread is the spread that will make the present value of the cash flows from the nongovernment bond, when discounted at the benchmark rate plus the spread, equal to the nongovernment bond s market price plus accrued interest. A trial-and-error procedure is used to compute the Z-spread. 

The nominal spread is the traditional spread measnre. The nominal spread is simply the difference between the yield on a nongovernment issue and the yield on a comparable maturity government. When the spread is taken to be the nominal spread, spread duration indicates the approximate percentage change in price for a 100 basis point change in the nominal spread holding the government yield constant. 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

Issues are initially priced and sold at a fixed spread over the reference rate. The price of an FRN can fluctuate considerably during the life of the issue, mainly depending on trends in the issuer s credit quality. The frequent resets in the reference rate means that changes in market interest levels have a minimal impact on an FRN s price. For investors, movements in an FRN s price are reflected in changes in the discount rate. The discount rate is effectively the yield needed to discount the future cash flows on the security to its current price. It thus functions in the same way as the yield to maturity for a fixed-rate instrument. And like a fixed-rate bond, the market convention is to use a constant spread... 

The fixed rate is some spread above the benchmark yield curve with the same term to maturity as the swap. In our illustration, suppose that the 10-year benchmark yield is 8.35%. Then the offer price that the dealer would quote to the fixed-rate payer is the 10-year benchmark rate plus 50 basis points versus receiving EURIBOR flat. For the floating-rate payer, the bid price quoted would be EURIBOR flat versus the 10-year benchmark rate plus 40 basis points. The dealer would quote such a swap as 40-50, meaning that the dealer is willing to enter into a swap to receive EURIBOR and pay a fixed rate equal to the 10-year benchmark rate plus 40 basis points and it would be willing to enter into a swap to pay EURIBOR and receive a fixed rate equal to the 10-year benchmark rate plus 50 basis points. 

As we have seen, interest rate swaps are valued using no-arbitrage relationships relative to instruments (funding or investment vehicles) that produce the same cash flows under the same circumstances. Earlier we provided two interpretations of a swap (1) a package of futures/forward contracts and (2) a package of cash market instruments. The swap spread is defined as the difference between the swap s fixed rate and the rate on the Euro Benchmark Yield curve whose maturity matches the swap s tenor. 

Each corporate bond will only be exposed to one of these factors, with an exposure that will typically increase with the bond s maturity. A rule of thumb is that it will be comparable to the bond s exposure to the shift factor. The spread risk of almost all AAA, AA, and A rated bonds will be less than their interest rate risk, and it is only for BBB rated bonds and in some very specific market sectors such as Energy and Telecoms that spread risk starts exceeding benchmark risk. Spread risk is by far the dominant source of systematic risk for high-yield instruments. 

With the introduction of the credit element, a new dimension is added to the concept of the yield curve. It becomes imperative to look at the credit spread curve, that is, the spreads offered by instruments in various credit quality buckets over the maturity continuum on the horizontal axis with the associated spread associated with those ratings on the vertical axis, as shown in Exhibit 26.14. 

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