Constructing a GDP-based Index for Use as Benchmark

The gross domestic product [GDP] is a fundamental economic indicator that is frequently used as a benchmark for local equity indices. The widespread appeal of this association is understandable because an equity index, especially if broad, could, like the GDP, also manifest the state of the economy. At the same time, however, the validity of a direct relation between the two is debatable since the GDP is known to be characteristically different from the typical equity index, however broad. In this work, we review some of the key elements that separate the GDP from a typical broad equity index in order to explain why the two cannot be compared directly with each other. We then incorporate a readily available mapping technique to create a GDP-based index that circumvents their inherent disparities and, thus, enable us to benchmark one against the other.GDP; equity index; benchmark; relative valuation; duration;

Incorporating default risk into Hamada's Equation for application to capital structure

Implemented widely in the area of corporate finance, Hamada’s Equation enables one to separate the financial risk of a levered firm from its business risk. The relationship, which results from combining the Modigliani-Miller capital structuring theorems with the Capital Asset Pricing Model, is used extensively in practice, as well as in academia, to help determine the levered beta and, through it, the optimal capital structure of corporate firms. Despite its regular use in the industry, it is acknowledged that the equation does not incorporate the impact of default risk and, thus, credit spread - an inherent component within every levered institution. Several attempts have been made so far to correct this, but, for one reason or another, they all seem to have their faults. This, of course, presents a major setback, as there is a strong need, especially by practitioners, to have in place a solid methodology to enable them to assess a firm’s capital structure in a consistent manner. This work addresses the issue and provides a robust modification to Hamada’s Equation, which achieves this consistency.corporate finance; capital structure; optimal leverage; debt; equity; Modigliani-Miller; Hamada's Equation; beta

Soliton Stability in a Generalized Sine-Gordon Potential

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations can be cast in terms of a Schrodinger-like operators for fluctuations and their spectra are calculated

Thermodynamic scheme of inhomogeneous perfect fluid mixtures

We analyze the compatibility between the geometrodynamics and thermodynamics of a binary mixture of perfect fluids which describe inhomogeneous cosmological models. We generalize the thermodynamic scheme of general relativity to include the chemical potential of the fluid mixture with non-vanishing entropy production. This formalism is then applied to the case of Szekeres and Stephani families of cosmological models. The compatibility conditions turn out to impose symmetry conditions on the cosmological models in such a way that only the limiting case of the Friedmann-Robertson-Walker model remains compatible. This result is an additional indication of the incompatibility between thermodynamics and relativity

Quantum lattice gauge fields and groupoid C*-algebras

We present an operator-algebraic approach to the quantization and reduction of lattice field theories. Our approach uses groupoid C*-algebras to describe the observables and exploits Rieffel induction to implement the quantum gauge symmetries. We introduce direct systems of Hilbert spaces and direct systems of (observable) C*-algebras, and, dually, corresponding inverse systems of configuration spaces and (pair) groupoids. The continuum and thermodynamic limit of the theory can then be described by taking the corresponding limits, thereby keeping the duality between the Hilbert space and observable C*-algebra on the one hand, and the configuration space and the pair groupoid on the other. Since all constructions are equivariant with respect to the gauge group, the reduction procedure applies in the limit as well.Comment: 23 pages, 6 figure

On marginal deformation of WZNW model and PP-wave limit of deformed AdS3×S3AdS_{3}\times S^{3} string geometry

We discuss the Penrose limit of the classical string geometry obtained from a truly marginal deformation of $SL(2)\otimes SU(2)$ WZNW model.Comment: 10 pages, late