Credit Enhancement through Financial Engineering: Freeport-McMoRan's Gold-Denominated Depository Shares

In 1993 and early 1994, Freeport McMoRan Copper and Gold (FCX), a mining company, issued two series of gold-denominated depositary shares to raise 430 million dollars expanding their mining capacity in Indonesia. We price the depositary shares using a term structure model for the forward rates implied by gold futures and we show that FCX successfully enhanced the credit quality of the issue. This credit enhancement is achieved because the effect of linking the payoff of the depositary shares to gold reduces default risk and is similar to conventional risk management. However, the bundling of financing and risk management allows the firm to target hedging benefits only to the newly issued securities. The design of the security also overcomes the asset substitution problem. The depositary shares issued by FCX illustrate how firms can enhance credit quality through financial engineering without changing the existing priority ordering of their capital structure.Risk management, Gold-linked, Hybrid Securities

The Structure of AdS Black Holes and Chern Simons Theory in 2+1 Dimensions

We study anti-de Sitter black holes in 2+1 dimensions in terms of Chern Simons gauge theory of anti-de Sitter group coupled to a source. Taking the source to be an anti-de Sitter state specified by its Casimir invariants, we show how all the relevant features of the black hole are accounted for. The requirement that the source be a unitary representation leads to a discrete tower of states which provide a microscopic model for the black hole.Comment: 17 pages, LaTex. The presentation in Section 5 was improved; other minor improvements. Final form of the manuscrip

Local electronic nematicity in the one-band Hubbard model

Nematicity is a well known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen by many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high $T_c$ superconductors has shown even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional Hubbard model provides strong support of the recent experimental results on local rotational $C_4$ symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity

Surface Vacuum Energy in Cutoff Models: Pressure Anomaly and Distributional Gravitational Limit

Vacuum-energy calculations with ideal reflecting boundaries are plagued by boundary divergences, which presumably correspond to real (but finite) physical effects occurring near the boundary. Our working hypothesis is that the stress tensor for idealized boundary conditions with some finite cutoff should be a reasonable ad hoc model for the true situation. The theory will have a sensible renormalized limit when the cutoff is taken away; this requires making sense of the Einstein equation with a distributional source. Calculations with the standard ultraviolet cutoff reveal an inconsistency between energy and pressure similar to the one that arises in noncovariant regularizations of cosmological vacuum energy. The problem disappears, however, if the cutoff is a spatial point separation in a "neutral" direction parallel to the boundary. Here we demonstrate these claims in detail, first for a single flat reflecting wall intersected by a test boundary, then more rigorously for a region of finite cross section surrounded by four reflecting walls. We also show how the moment-expansion theorem can be applied to the distributional limits of the source and the solution of the Einstein equation, resulting in a mathematically consistent differential equation where cutoff-dependent coefficients have been identified as renormalizations of properties of the boundary. A number of issues surrounding the interpretation of these results are aired.Comment: 22 pages, 2 figures, 1 table; PACS 03.70.+k, 04.20.Cv, 11.10.G

Transition to complete synchronization in phase coupled oscillators with nearest neighbours coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.Comment: 6 pages, 4 figures, to appear in CHAO

Topologically massive magnetic monopoles

We show that in the Maxwell-Chern-Simons theory of topologically massive electrodynamics the Dirac string of a monopole becomes a cone in anti-de Sitter space with the opening angle of the cone determined by the topological mass which in turn is related to the square root of the cosmological constant. This proves to be an example of a physical system, {\it a priory} completely unrelated to gravity, which nevertheless requires curved spacetime for its very existence. We extend this result to topologically massive gravity coupled to topologically massive electrodynamics in the framework of the theory of Deser, Jackiw and Templeton. These are homogeneous spaces with conical deficit. Pure Einstein gravity coupled to Maxwell-Chern-Simons field does not admit such a monopole solution

Credit Enhancement Through Targeted Risk Managment: Freeport-McMoRan's Gold-Dominated Depository Shares

In 1993 and early 1994, Freeport McMoRan Copper and Gold (FCX), a mining company, issued two series of gold-denominated depositary shares to raise 430 million dollars for expansion of their mining capacity in Indonesia. We price the depositary shares using a term structure model for the forward rates implied by gold futures and we show that FCX successfully enhanced the credit quality of the issue. This credit enhancement is achieved because the effect of linking the payoff of the depositary shares to gold reduces default risk and is similar to conventional risk management. The building of financing and risk management, however, allows the firm to target hedging benefits only to the newly issued securities. The design of the security overcomes the asset substitution problem and credibly commits the firm to hedging. The depositary shares issued by FCX illustrate how firms can enhance credit quality through financial engineering without changing the existing priority ordering of their capital structure

Gravity-driven instability in a spherical Hele-Shaw cell

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.Comment: 13 pages, 4 ps figures, RevTex, to appear in Physical Review