Nominal spread

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. 

The nominal spread measure has several drawbacks. For now, the most important is that the nominal spread fails to account for the term strnctnre of spot rates for both bonds. We will pose an alternative spread measnre that incorporates the spot rate curve. 

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 for the nongovernment bond is 148.09 basis points. Let s use the information presented in Exhibit 3.15. The second column in Exhibit 3.15 shows the cash flows for the 7%, 5-year nongovernment issue. The third column is a hypothetical benchmark spot rate curve that we will employ in this example. The goal is to determine the spread that, when added to all the Treasury spot rates, will produce a present value for the non-government bond equal to its market price of 101.9141. 

Suppose we select a spread of 100 basis points. To each benchmark spot rate shown in column 3 of Exhibit 3.15, 100 basis points are added. So, for example, the 1-year spot rate 5.33% (4.33% plus 1%). This spot rate is used to calculate the present values shown in the fourth column. Because the present value is not equal to the nongovernment issue s price of 101.9141, the Z-spread is not 100 basis points. If a spread of 120 basis points is tried, it can be seen from the next-to-last column of Exhibit 3.15 that the present value is 103.1835 again, because this is not equal to the nongovernment issue s price, 120 basis points is not the Z-spread. The last column shows the present value of the cash flows is equal to the nongovernment issue s price. Accordingly, 150 basis points is the Z-spread, compared to the nominal spread of 148.09 basis points. 

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. 

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. 

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. 

In most experiments, light sourees have a "spread" of frequeneies assoeiated with them that is, they provide photons of various frequeneies. To eharaeterize sueh sourees, it is eommon to introduee the speetral souree funetion g(co) dco whieh gives the probability that the photons from this souree have frequeney somewhere between co and co+dco. For narrow-band lasers, g(co) is a sharply peaked funetion about some "nominal" frequeney cOq broader band light sourees have mueh broader g(co) funetions. 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

When spontaneous spreading occurs, the bulk of the advancing liquid is preceded by a precursor film, usually a few millimeters in width and a few hundred nanometers or less in thickness [58], as pictured in Fig. 12. The observed dynamic contact angle is that which is made by the bulk liquid against the precursor film, and it itself depends on the rate of the advance of the nominal interline. The relationship between the rate of spontaneous spreading, i.e. the rate of movement of the nominal interline normal to itself, (/, and the dynamic contact... 

Fig. 12. The morphology of spreading. Liquid advances over the solid by means of a precursor foot (usually a few to a few hundred nanometers in thickness) moving out typically several millmeters ahead of the nominal bulk liquid interline.

A process is in control when the average spread of variation coincides with the nominal specification for a parameter. The range of variation may extend outside the upper and lower limits but the proportion of parts within the limits can be predicted. This situation will remain as long as the process remains in statistical control. A process is in statistical... 

Figure 4.29. Back-calculated results for files VALIDX.dat. The data are presented sequentially from left to right. The ordinate is in % of the nominal concentration. Numbers X = 1,2, and 3 indicate the data file. Each bracket indicates a day s worth of results (sorted by concentration). The log/log format tends to produce positive deviations at low concentrations, while the lin/lin format does the opposite, to the point of suggesting negative concentrations The reason is that the low concentration values are tightly clustered at the left end of the lin/lin depiction whereas the values are evenly spread in the log/log depiction, with commensurate effects on the position of Xmean, the sum Sxx< and the influence each coordinate has on the slope. The calibration design was optimized for the log/log format.

Note that Table 4-1 applies at OV DC. In general, vendors state the nominal capacitance in a datasheet as measured at an applied voltage of IVrms, at 1kHz and 25°C. But in an actual circuit we could see the following typical spreads (after 100k hours, and also considering the possibility of both AC and DC voltages) ... 

The granular treatment was applied on May 2nd, 1974 by spreading Treflan 5G commercial formulation from a conventional gravity fed spreader at a nominal rate of 0.7 kg/h of active ingredient. On May 8th, the emulsion-plot received 0.66 kg/h trifluralin as a spray of Treflan 4EC emulsifiable concentrate diluted with water according to commercial practice. (Note Mention of a proprietary product is for purposes of identification only and does not constitute endorsement by the U.S. Department of Agriculture over products of a similar nature not mentioned). 

The mean value of the distribution is 1000 and the standard deviation, a, is 12.5. A 1 kQ, 5% resistor will have values from 950 Q to 1050 Q. Deviations of 4o achieve this spread. This distribution shows us that almost all of the resistors are within plus or minus three standard deviations from the nominal value, 3[Pg.505]

An innovative aspect of this course, which was nominally chemical and biological in emphasis, included medical geography and epidemiology to analyze the spread of avian flu. This activity reinforced the idea, very early in a student s career, that health-related issues are inherently complex and multidisciplinary in nature, extending beyond the STEM disciplines to the social sciences. In the spirit of John Snow, the father of... 

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