Fixed rate spread

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. 

EXHIBIT 8,8 Euro Corporate Fixed-Rate Spread... 

Source Lehman Brothers— US credit market fixed-rate spread. 

A feasibility study estimated a capital of 100 million , from which 10% working-capital and 90% fixed-capital spread over three years as follows 30, 50, and 10 million . The plant lifetime is 15 years. Table 15.2 gives the forecast of revenue and operating costs (excluding depreciation) in millions . The revenue in the last year includes the salvage of capital. Consider a tax rate of 35%. Analyse the profitability of this project. 

In Chapter 8, we described several models to measure the term structure of credit spread and we introduced the model proposed by Longstaff and Schwartz (1995) for pricing fixed-rate debt. The authors propose also a model to valuing floating-rate notes. The equation derived for pricing floating-rate bonds is given by (10.2) ... 

Chapter 8 shows several spread measures that can be used to compare fixed-rate bonds. Conventionally for floating-rate notes, traders use the discounted margin. To analyse a floating-rate note with a fixed-rate note, one method is to compare the discounted margin of a floater with the asset swap spread of fixed-rate bonds. 

The problem is, what spread is assumed to change There are three measures that are commonly used for fixed-rate bonds nominal spread, zero-volatility spread, and option-adjusted spread. Each of these spread measures were defined earlier in this book. 

A sensible question arises How do you know whether a spread duration for a fixed-rate bond is a spread based on the nominal spread, zero-volatility spread, or the OAS The simple answer is you do not know You must ask the broker/dealer or vendor of the analytical system. To add further to the confusion surrounding spread duration, consider the term OAS duration that is referred to by some market participants. What does it mean On the one hand, it could mean simply the spread duration that we just described. On the other hand, many market participants use the term OAS duration interchangeably with the term effective duration. Once again, the only way to know what OAS is measuring is to ask the broker/dealer or vendor. 

That said, there are two reasons why the performance of German swap spreads are related to Euro peripheral spreads. The first one is that, flows apart, the bond-swap spread reflects the yield difference between a government rate and the composition of a string of EURI-BOR rates (i.e., a swap fixed rate). As the average credit quality of the banks in the EURIBOR panel is A-AA, any increase in the investors preference for credit quality will make both swap and peripheral spreads widen versus the core Euro government rate, thus increasing the correlation between both differentials. Yet this increase in the correlation will be mainly due to the outperformance of the benchmark asset... 

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 European CMBS market presents investors with a wide variety of investment opportunities ranging from short-dated floating-rate notes to long-dated, fixed-rate issues across a rating spectrum from AAA to BB, and so it should appeal to a wide section of the investor community. It is, however, a relatively complex asset class. There are many underlying asset types, which can be spread across more than one country, and there are a number of possible transaction structures. As a result, it is not always easy to compare one transaction against another. 

Strictly speaking, the FIAT 1 transaction does not generate excess spread. This explains the high level of credit enhancement from the unrated class M notes (usually, unrated tranches are either privately sold or kept as an equity tranche by the originator). On the closing date, an amount of notes was issued which was equal to the net present value of all future cash payments due from the collateral (as opposed to the principal balance of the collateral). The discount rate used was the fixed rate payable to the swap counterparty (swap rate plus coupon on the class A notes and all fees associated with the transaction). Structured this way, the receivables always yield the discount rate, leaving no excess spread in the transaction. However, losses on the FIAT 1 portfolio can be covered to a certain degree from interest collections because the structure provides for delinquent principal and defaults to be covered before interest is paid on the class M notes. 

The offer price that the dealer would quote the fixed-rate payer would be to pay 8.85% and receive EURIBOR flat. (The word flat means with no spread.) The bid price that the dealer would quote the floating-rate payer would be to pay EURIBOR flat and receive 8.75%. The bid-offer spread is 10 basis points. 

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. 

An example would be that a protection buyer holding a fixed-rate risky bond and wishes to hedge the credit risk of this position via a credit default swap. However, by means of an asset swap the protection seller (e.g., a bank) will agree to pay the protection buyer LIBOR +/-spread in return for the cash flows of the risky bond. In this way the protection buyer (investor) may be able to explicitly finance the credit default swap premium from the asset swap spread income if there is a negative basis between them. If the asset swap was terminated, it is common for the buyer of the asset swap package to take the unwind cost of the interest rate swap. 

In this example, the bank is quoting an offer rate of 5-25 percent, which is what the fixed-rate payer will pay, and a bid rate of 5-19 percent, which is what the floating-rate payer will receive. The bid-offer spread is therefore 6 basis points. The fixed rate is always set at a spread over the government bond yield curve and is often quoted that way. Say the 5-year Treasury is trading at a yield of 4.88 percent. The 5-year swap bid and offer rates in the example are 31 basis points and 37 basis points, respectively, above this yield, and the bank s swap trader could quote the swap rates as a swap spread 37-31. This means that the bank would be willing to enter into a swap in which it paid 31 basis points above the benchmark yield and received LIBOR or one in which it received 37 basis points above the yield curve and paid LIBOR. 

Asset-swap pricing is commonly applied to credit-default swaps, especially by risk management departments seeking to price the transactions held on credit traders book. A par asset swap typically combines an interest rate swap with the sale of an asset, such as a fixed-rate corporate bond, at par and with no interest accrued. The coupon on the bond is paid in return for LIBOR plus, if necessary, a spread, known as the asset-swap spread. This spread is the price of the asset swap. It is a function of the credit risk of the underlying asset. That makes it suitable as the basis for the price payable on a credit default swap written on that asset. 

Equation (1.27) may be stated in terms of discount factors instead of the reference rate. The. yield to maturity spread method of evaluating FRNs is designed to allow direct comparison between FRNs and fixed-rate bonds. The yield to maturity on the FRN rmf) is calculated using (1.27) with both re + DM) and (re + DM) replaced with rmf. The yield to mamrity on a reference bond rmb) was shown earlier in this chapter. The yield to maturity spread is defined as ... 

The asset swap spread is equal to the underlying asset s redemption yield spread over the government benchmark, minus the spread on the associated interest rate swap. The latter, which reflects the cost of converting the fixed-rate coupons of benchmark bonds to a floating rate during the life of the asset, or the default swap, is based on the swap rate for the relevant term. 

An asset swap is a package that combines an interest-rate swap with a cash bond, the effect of the combined package being able to transform the interest-rate basis of the bond. Typically, a fixed-rate bond will be combined with an interest-rate swap in which the bond holder pays fixed coupon and received floating coupon. The floating coupon will be a spread over LIBOR (see Choudhry et al. 2001). This spread is the asset-swap spread and is a function of the credit risk of the bond over and above interbank credit risk. Asset swaps may be transacted at par or at the bond s market price, usually par. This means that the asset swap value is made up of the difference between the bond s market price and par, as well as the difference between the bond coupon and the swap flxed rate. 

Plume Containment. WeUs can be placed at a contaminated site to prevent the contamination from spreading further or migrating offsite. In the past, containment efforts often reHed on physical methods such as bentonite slurry trenches, grout curtains, sheet pilings, weU points, and fixative injections. Containment by judiciously placed weUs generally costs less, takes less time to install, and is more flexible because pumping rates and locations can be varied. 

In any gas burner some mechanism or device (flame holder or pilot) must be provided to stabilize the flame against the flow of the unbumed mixture. This device should fix the position of the flame at the burner port. Although gas burners vary greatly in form and complexity, the distribution mechanisms in most cases are fundamentally the same. By keeping the linear velocity of a small fraction of the mixture flow equal to or less than the burning velocity, a steady flame is formed. From this pilot flame, the main flame spreads to consume the main gas flow at a much higher velocity. The area of the steady flame is related to the volumetric flow rate of the mixture by equation 18 (81,82)... 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

Various experimental methods to evaluate the kinetics of flow processes existed even in the last centuty. They developed gradually with the expansion of the petrochemical industry. In the 1940s, conversion versus residence time measurement in tubular reactors was the basic tool for rate evaluations. In the 1950s, differential reactor experiments became popular. Only in the 1960s did the use of Continuous-flow Stirred Tank Reactors (CSTRs) start to spread for kinetic studies. A large variety of CSTRs was used to study heterogeneous (contact) catalytic reactions. These included spinning basket CSTRs as well as many kinds of fixed bed reactors with external or internal recycle pumps (Jankowski 1978, Berty 1984.)... 

The objectives of fire suppression systems are to provide cooling, control the fire (i.e., prevent it from spreading) and provide extinguishment of the fire incident. A variety of fire suppression methods are available to protect a facility. Both portable and fixed systems can be used. The effectiveness of all fire extinguishing measures can be determined by the rate of flow of the extinguishing agent and the method or arrangements of delivery. 

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