Yield spread measures

A bond s yield is a measure of its potential return. Market participants commonly assess a security s relative value by calculating a yield or some yield spread. There are a number of yield measures that are quoted in the market. These measures are based on certain assumptions necessary to carry out the calculation. However, they also limit effectiveness of a yield measure in gauging relative value. In this section, we will explain the various yield and yield spread measures as well as document their limitations. 

YIELD SPREAD MEASURES RELATIVE TO A SPOT RATE CURVE... 

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 are several yield spread measures or margins that are routinely used to evaluate floaters. The four margins commonly used are spread for life, adjusted simple margin, adjusted total margin, and discount margin. To illustrate these measures, we will assume a floater that has a coupon formula equal to 3-month LIBOR plus 45 basis points and delivers cash flows quarterly. 

In order to have a uniform exposure to electrons over the entire wafer, a standard transmission microscope (RCA EMV-3) was used. The apertures were opened and the 40 kv beam spread out over a circle larger than the wafer itself. The coated wafer was introduced into the microscope via the film cassette drawer (below the fluorescent screen). Charge density was measured with a Faraday Cup. Each polymer was irradiated at doses of 2, 5, 10, and 20 yC/cm. The radiation chemical yield was measured from plots of 1/Mjj versus the incident dose. A sample plot is shown in Figure 1, in this case for itaconic acid-MMA copolymers. The slope of such a plot is given by ... 

The area under any portion of the Gaussian distribution, for example, between a value Xi and a value X2, corresponds to the fraction of the measurements which will yield a measured value of x between and including these two values. The spread of the Gaussian distribution, that is, the width of the bell-shaped curve, is expressed in terms of the population standard deviation cr. The standard deviation cr coincides with... 

Z-spread is an alternative spread measure to the ASW spread. This type of spread uses the zero-coupon yield curve to calculate the spread, in which in this case is assimilated to the interest-rate swap curve. Z-spread represents the spread needful in order to obtain the equivalence between the present value of the bond s cash flows and its current market price. However, conversely to the ASW spread, the Z-spread is a constant measme. 

Traditionally, information on inflation expectations has been obtained by survey methods or theoretical methods. These have not proved reliable however, and were followed only because of the absence of an inflation-indexed futures market. Certain methods for assessing market inflation expectations are not analytically valid for example, the suggestion that the spread between short- and long-term bond yields cannot be taken to be a measure of inflation expectation, because there are other factors that drive this yield spread, and not just inflation risk premium. 

There are several ways to measure the yield spread of a corporate bond ... 

The price of a corporate bond is a yield spread for conventional bonds or on an OAS basis for callable or other option-embedded bonds. If an OAS calculation is undertaken in a consistent framework, price changes that result in credit events will result in changes in the OAS. Therefore, we can speak in terms of a sensitivity measure for the change in value of a bond or portfolio in terms of changes to a... 

We will discuss two approaches for assessing the interest rate risk exposure of a bond or a portfolio. The first approach is the full valuation approach that involves selecting possible interest rate scenarios for how interest rates and yield spreads may change and revaluing the bond position. The second approach entails the computation of measures that approximate how a bond s price or the portfolio s value will change when interest rates change. The most commonly used measures are duration and convexity. We will discuss duration/convexity measures for bonds and bond portfolios. Finally, we discuss measures of yield curve risk. 

The ESE ratio is defined as excess spread divided by portfolio yield it measures the ability of the servicer to turn yield into excess spread. The greater the ratio, the smaller the predicted impact of a slowing economy on the performance of the collateral. As Exhibit 13.21 shows, the prime issuer (issuer 1) has a much higher ESE ratio than the subprime issuer. The September 2002 ratios for European and US credit card portfolios are 44% and 39%, respectively. 

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 area under any portion of the Gaussian distribution, for example, between a value and a value X2, corresponds to the fraction of the measurements which will yield a measured value of x between and including these two values. The spread of the Gaussian distribution, that is, the width of the bell-shaped curve, is expressed in terms of the population standard deviation o. The standard deviation a coincides with the point of inflection of the curve as can be seen in Figure 1.5. The curve is symmetrical, so we have two inflection points, one on each side of the maximum. The x-axis relates the area under the curve to the standard deviation. For 0 on either side of the maximum, 68.3% of the area under the curve lies in this range of x. This means that 68.3% of all measurements of X will fall within the range x = p o. About 95.5% of the area under the curve lies between X = p 2o and 99.7% of the area lies between x = p 3o. 

The CCE spreads the investment over the lifetime of the measure into equal annual payments with the familiar capital recovery factor. The annual payment is then divided by the annual energy savings to yield a cost of saving a unit of energy. It is calculated using the following formula ... 

During the method validation phase, the calibration, using the CS solutions, is repeated each day over at least one week to establish both the within-day and the day-to-day components of the variability. To this end, at least 6 CS, evenly spread over the concentration range, must be repeatedly run (m = 8-10 is usual), to yield n 50 measurements per day. If there are no problems with linearity and heteroscedacity, and if the precision is high (say, CV < 2-5%, depending on the context), the number of repeats m per concentration may be reduced from the second day onwards (m = 2 - 3 is reasonable). The reasoning behind... 

Capacitance-voltage (C-V) measurements on Schottky diodes orp-n junctions can provide information similar to that yielded by spreading resistance, namely the net charge density of fixed centers that are ionized in the... 

Fig. 12 shows the spread factors simulated on meshes with different resolutions along with the measurement value of Wachters and Westerling (1966). The spread factor is defined as the radius of the droplet on the solid surface divided by the initial radius of the droplet. Although the convergence is not perfect, the agreement between the experiment and the simulations is relatively good for all resolutions. Consistent with the results of Fig. 11, the effect of the mesh resolution on spread factor becomes notable after 8 ms since the moment of impact, and the coarser resolution tends to yield a slower rebounding process. 

The control of ammonia loss by injection has been measured directly and indirectly through crop yields. Hoff et al (21) measured the proportion of applied NH4+-N lost as NH3-N from pig manure over a 3.5 day sampling period. Losses were 14.0, 12.2 and 11.2% from 90, 135 and 180m3/ surface spread respectively. Only 2.5% was lost from 90 and 180 m3/ha injected. 

Lindon and eo-workers" employed Maximum Entropy deeonvolution in order to measure eouplings in eomplex multiplets. Here, doublets ete. were incorporated into the Point Spread Funetion (PSF), whieh would normally only encode line shape. The maximum entropy proeedure yielded the most likely couplings. Clearly, this is a proeedure well suited to high eonvolution and high noise situations, but it is less elear how amenable it would be to automation. 

---