Expected Loss

Lx = the loss on the notes under scenario x px = the probability of the scenario x occurring 

Note holders expected losses are determined by considering the impact on their cash flows of the credit losses—flosses from loan defaults— occurring in various scenarios, taking into account how such losses are allocated to the issue s tranches. The cash flows to the note holders depend on whether a default has occurred and the size of the resulting loss. The severity of the loss equals the par value of the note less the recovery rate. The probability of default may be inferred from the rating of the underlying credit exposures. Expected losses are calculated using Monte Carlo techniques, which simulate thousands of scenarios and cash flows and so require sophisticated computational models. 

The period 2005 to first half2007 was a period of very high growth for the issuance of CDOs. During this period the growth in the CDO product was investor-driven and high volumes of arbitrage CDO transactions were issued. However, a big impact of the credit crunch from 2007 has been a sharp decline in new issuance of CDO product. 

The growth in the CDO market had been driven by large volumes of ABS CDO (collateralized debt obligations referencing ABS) and CLO (collateralized loan obligations)  

The investor-related weakness with the ABS CDO product was its significant concentration to newly issued U.S. subprime RMBS, which subse-quendy performed poorly from 2006 onward, mainly due to poor or nation standards and rising USD interest rates. 

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A common risk evaluation and presentation method is simply to multiply the frequency of each event by consequence of each event and then sum these products for all situations considered in the analysis. In insurance terms, this is the expected loss per year. The results of an uncertainty analysis, if performed, can be presented as a range defined by upper and lower confidence bounds that contain the best estimates. If the total risk represented by the best estimate or by the range estimate is... 

It is also important to realize that Taguchi loss functions not only bring into consideration both issues of location and dispersion of z but also provide a consistent format for combining them. By taking expectations on both sides of Eq. (19), and after a few algebraic rearrangements, we can show that the expected loss, [L(z)] is... 

For a zone X in the decision space to lead to a small conditional expected loss, E[L(z)lX], it must achieve both precise (reduced cr ) and accurate (fi =z ) performance with respect to z. Finding such robust zones and operating on them results in inoculating the process against the transmission of variation from disturbances and the decision space to the performance space (Taylor, 1991). 

Traditionally, insurance is the main mechanisms available to individuals and business to manage the financial consequences of risky events, such as natural hazards like windstorms and floods. Insurance companies used to work making each individual or business pay a premium to protect themselves against an uncertain loss. The premium is calculated by pooling risks across a large and diverse population considering the pool s expected losses. 

Without having the thermochemistry data at hand, it is not trivial to decide which pair of products will be preferred over the other. In general, the formation of the higher substituted and/or larger carbenium ion is preferred, because it can more easily stabilize a charge. However, the tendency is the same for the radicals and one may expect loss of ethyl to be favored over loss of methyl, for example. Thus, the formation of both the ionic and the radical fragments are of decisive influence on the final distribution of products. 

Increasing the sample size would reduce both alpha and beta, but samples and especially their analyses cost money. Intuitively the minimal actual loss should occur when the expected losses are equal. So the relative alpha and beta should be found from equating expected loss from type I error with the expected loss from type II error. 

The above studies concerning rhodium deposition provide evidences of the crucial importance of surface chemistry on the final quality of the deposit. Purity can be controlled by addition of reactive components that assist the expected loss of ligands, which otherwise would leave contaminants such as halides, carbides or oxides on the deposits. 

Prevention of the expected loss of lumbar spine bone density and plasma lipid changes consistent with a reduction in the risk for atherosclerosis have also been reported in tamoxifen-treated patients following spontaneous or surgical menopause. However, this agonist activity also affects the uterus and may increase the risk of endometrial cancer. 

The nitrovinylbenzindole 286 adds DMAD in a Diels-Alder manner to give the carbazole 287.182 This synthesis involves an oxidative step instead of the expected loss of nitrous acid. 

A reversible vinylidene insertion was proposed to explain die formation of (55) on flash vacuum pyrolysis of the anthracene derivative (56) at 1100 °C.65 The expected loss of HC1 followed by 1,2-H shift and 1,5-CH insertion of the resulting vinylidene species would give rise to the strained paracyclophane (57). This is proposed to ring open to the alternative alkylidene (58) before proceeding to the observed product (55). 

Still, in most liquid—liquid distribution systems one of the liquid phases is more aqueous while the other is mainly non-aqueous. Therefore, a major consideration of the choice of the solvent for solvent extraction is its immiscibility with water and the expected losses of the solvent to the aqueous phase. In many solvent extraction applications the solvent is used as a diluent for an active extractant, which may be either a solid or a liquid when neat. In these cases, where a separate active extractant is used, the chemical processes taking place in the selective extraction of the desired solute or solutes and their recovery in the stripping stage are of prime importance, but a discussion of which is outside the... 

Two sulfido-bridged complexes, (XCV) and (XCVI), have been examined by Preston and Reed (167), and the expected loss of carbonyl and alkyl (or aryl) groups is observed. 

The solutions are found by averaging out and folding back (Raiffa and Schlaifer, 1961), so that we compute the expected loss at the chance nodes (open circles), given everything to the left of the node. We determine the best actions by minimizing the expected loss at the decision nodes. The first decision is the choice of the inference method a and the optimal decision a (or Bayes action) is found by minimizing the expected loss E L(n, 6, y, a, c), where the expectation is with respect to the conditional distribution of 0 given n and y. The expected loss evaluated in the Bayes action a is called the Bayes risk and we denote it by... 

Other, less stable cyclopropanones, such as the 2,2-dimethyl compound, can be made by carbene addition (Chapter 40) to ketenes. This compound did the Favorskii reaction with methoxide in methanol the only product came from the expected loss of the less unstable carbanion. This will, of course, be general-acid-catalysed by methanol as no free carbanion can be released into an alcoholic solvent. 

Cucurbitacin B (99) biosynthesis has been studied in Cucurbita pepo. When [2- " C,3/ ,4/ - H]mevalonate was used, four tritium atoms were incorporated, of which one was at C-10. Using [2- C,2- H2]mevalonate, ten tritium atoms were incorporated. Thus only the expected losses from C-3, C-20, and C-22 occurred. The presence of tritium at C-8 excludes lanosterol as an intermediate. Either cycloartenol (which is present in this plant) or parkeol may be intermediates. 

Pyrolysis of the intrachaimel polyacrylonitrile led to the expected loss of nitrogen, similar to observations in bulk and thin film experiments. As in the case of polyaniline in MCM-41 (see above), nitrogen sorption isotherms showed reduced pore volumes for the inclusion compounds, demonstrating the formation of PAN and carbonized material in the chaimels of the host. 

From the data in Table 20, four important points should be kept in mind. First, free radical reduction of 139 and 137 with all reducing agents, as well as the tin hydride reduction of 138 and 140, occurred with the expected loss of stereochemistry. Second, the ratio of exo-/endo-norbomane-2-D obtained from these reductions was independent of the stereochemistry of starting material. Third, almost identical ratios of exo-/ ndo-norbornane-2-D were obtained from the four starting materials. Finally, the ratio of exo-(endo-norbornane-2-D was independent of the nature of the metal. 

XRD experiments indicated that the expected loss of the zeolite crystallinity during the reaction cannot he responsible for the activity decay. Application of the stabilized Y-zeolites and. nickel... 

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