Capital Asset Prices With and Without Negative Holding

Prize Lecture to the memory of Alfred Nobel, December 7, 1990.Finance;

Bank Capital Adequacy, Deposit Insurance and Security Values, Part I

This paper provides a formal setting for the analysis of the capital adequacy of an institution with deposits insured by a third party. An insured depositor has a claim against the institution and a contingent claim against the insurer. This paper analyzes the effect of the riskiness of the asset mix and the relative amount of deposits and capital on the potential liability of the insurer. It shows that an increase in asset risk, holding value constant, increases the value of equity and raises the potential liability of the insurer.

Physical Results from Unphysical Simulations

We calculate various properties of pseudoscalar mesons in partially quenched QCD using chiral perturbation theory through next-to-leading order. Our results can be used to extrapolate to QCD from partially quenched simulations, as long as the latter use three light dynamical quarks. In other words, one can use unphysical simulations to extract physical quantities - in this case the quark masses, meson decay constants, and the Gasser-Leutwyler parameters L_4-L_8. Our proposal for determining L_7 makes explicit use of an unphysical (yet measurable) effect of partially quenched theories, namely the double-pole that appears in certain two-point correlation functions. Most of our calculations are done for sea quarks having up to three different masses, except for our result for L_7, which is derived for degenerate sea quarks.Comment: 26 pages, 12 figures (discussion on discretization errors at end of sec. IV clarified; minor improvements in presentation; results unchanged

Perspective on Bank Capital Adequacy: Time-Series Analysis

The first part of this paper provides a historical perspective on bank risks. Five-year moving average measures of total risk, market risk, and nonmarket risk are computed for an index of New York banks from 1929-1975 and for an index of outside New York banks from 1950-1976.We use a carefully constructed series of bank balance sheet data to compute correlations among various components of New York banks' port-folios and observe trends over time. The time series relationship between book values and market values is investigated, and classical measures of capital adequacy are calculated using surrogates for market values rather than book values. Finally, data are presented on the movement of interest rates and the term structure over time. Serial correlations and cross-correlations are computed. The second part of the paper uses the technique proposed in Sharpe ("Bank Capital Adequacy, Deposit Insurance and Security Values," June 1978) to gain information about capital adequacy. He has shown that for a bank with deposit liabilities that do not extend beyond the review period a "value preserving spread" in asset risk is likely to increase the value of capital. Moreover, the less adequate the capital, the larger this effect should be. We outline the method used to develop an econometric model to test for this effect. The model is then applied to time series data from 1938 to 1975.

Unphysical Operators in Partially Quenched QCD

We point out that the chiral Lagrangian describing pseudo-Goldstone bosons in partially quenched QCD has one more four-derivative operator than that for unquenched QCD with three flavors. The new operator can be chosen to vanish in the unquenched sector of the partially quenched theory. Its contributions begin at next-to-leading order in the chiral expansion. At this order it contributes only to unphysical scattering processes, and we work out some examples. Its contributions to pseudo-Goldstone properties begin at next-to-next-to-leading order, and we determine their form. We also determine all the zero and two derivative operators in the $O(p^6)$ partially quenched chiral Lagrangian, finding three more than in unquenched QCD, and use these to give the general form of the analytic next-to-next-to-leading order contributions to the pseudo-Goldstone mass and decay constant. We discuss the general implications of such additional operators for the utility of partially quenched simulationsComment: 13 pages, 11 figures Version 2: Additional footnote and parenthesis in section

Applications of Partially Quenched Chiral Perturbation Theory

Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B_K and the K+ decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta are also considered. We find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in Phys. Rev.

Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e. those in which the valence and sea quark masses, $m_V$ and $m_S$, are different. I point out that for lattice fermions which retain some chiral symmetry on the lattice, e.g. staggered fermions, the leading order prediction of the chiral expansion is that the mass of the pion depends only on $m_V$, and is independent of $m_S$. This surprising result is shown to receive corrections from loop effects which are of relative size $m_S \ln m_V$, and which thus diverge when the valence quark mass vanishes. Using partially quenched chiral perturbation theory, I calculate the full one-loop correction to the mass and decay constant of pions composed of two non-degenerate quarks, and suggest various combinations for which the prediction is independent of the unknown coefficients of the analytic terms in the chiral Lagrangian. These results can also be tested with Wilson fermions if one uses a non-perturbative definition of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected (alpha_4 is replaced by alpha_4/2

Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit

The linear stability of freely propagating, adiabatic, planar premixed ames is investigated in the context of a simple chain-branching chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and contrasted with those from a previous purely thermal-di�usive constant density linear stability study. It is shown that when thermal expansion is properly accounted for, a region of stable ames predicted by the constant density model disappears, and instead the ame is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak e�ect on the critical fuel Lewis number required for instability. These e�ects of thermal expansion on the two-step chain-branching ame are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in the limit that the chain-branching crossover temperature tends to the adiabatic ame temperature, the two-step model can be described to leading order by the one-step model with a suitably de�ned e�ective activation energy

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe