Self-Consistent Asset Pricing Models

We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alpha's and beta's of the factor model are unobservable. Self-consistency leads to renormalized beta's with zero effective alpha's, which are observable with standard OLS regressions. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value $\alpha_i$ at the origin between an asset $i$'s return and the proxy's return. Self-consistency also introduces ``orthogonality'' and ``normality'' conditions linking the beta's, alpha's (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from Jan. 1990 to Feb. 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal components analysis (PCA), thus providing a direct link between model-driven and data-driven constructions of risk factors.Comment: 36 pages with 8 figures. large version with 6 appendices for the Proceedings of the 5th International Conference APFS (Applications of Physics in Financial Analysis), June 29-July 1, 2006, Torin

Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices

Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an eigenvalue spectrum predicted by random matrix theory (RMT) and a few very large eigenvalues in large empirical correlation matrices is shown to result from a bottom-up collective effect of the underlying time series rather than a top-down impact of factors. Our results, in excellent agreement with previous results obtained on large financial correlation matrices, show that there is relevant information also in the bulk of the eigenvalue spectrum and rationalize the presence of market factors previously introduced in an ad hoc manner.Comment: 4 pages with 3 figur

Quantum fluctuations for drag free geodesic motion

The drag free technique is used to force a proof mass to follow a geodesic motion. The mass is protected from perturbations by a cage, and the motion of the latter is actively controlled to follow the motion of the proof mass. We present a theoretical analysis of the effects of quantum fluctuations for this technique. We show that a perfect drag free operation is in principle possible at the quantum level, in spite of the back action exerted on the mass by the position sensor.Comment: 4 pages, 1 figure, RevTeX, minor change

Acquired A amyloidosis from injection drug use presenting with atraumatic splenic rupture in a hospitalized patient: a case report

<p>Abstract</p> <p>Introduction</p> <p>Little is known about splenic rupture in patients who develop systemic acquired A amyloidosis. This is the first report of a case of atraumatic splenic rupture in a patient with acquired A amyloidosis from chronic injection drug use.</p> <p>Case presentation</p> <p>A 58-year-old Caucasian man with a long history of injection drug use, hospitalized for infective endocarditis, experienced atraumatic splenic rupture and underwent splenectomy. Histopathological and microbiological analyses of the splenic tissue were consistent with systemic acquired A amyloidosis, most likely from injection drug use, that led to splenic rupture without any recognized trauma or evidence of bacterial embolization to the spleen.</p> <p>Conclusion</p> <p>In patients with chronic inflammatory conditions, including the use of injection drugs, who experience acute onset of left upper quadrant pain, the diagnosis of atraumatic splenic rupture must be considered.</p

New Upper Limit of Terrestrial Equivalence Principle Test for Rotating Extended Bodies

Improved terrestrial experiment to test the equivalence principle for rotating extended bodies is presented, and a new upper limit for the violation of the equivalence principle is obtained at the level of 1.6$10^{\text{-7}}$, which is limited by the friction of the rotating gyroscope. It means the spin-gravity interaction between the extended bodies has not been observed at this level.Comment: 4 page

Testing the Principle of Equivalence by Solar Neutrinos

We discuss the possibility of testing the principle of equivalence with solar neutrinos. If there exists a violation of the equivalence principle quarks and leptons with different flavors may not universally couple with gravity. The method we discuss employs a quantum mechanical phenomenon of neutrino oscillation to probe into the non-universality of the gravitational couplings of neutrinos. We develop an appropriate formalism to deal with neutrino propagation under the weak gravitational fields of the sun in the presence of the flavor mixing. We point out that solar neutrino observation by the next generation water Cherenkov detectors can improve the existing bound on violation of the equivalence principle by 3-4 orders of magnitude if the nonadiabatic Mikheyev-Smirnov-Wolfenstein mechanism is the solution to the solar neutrino problem.Comment: Latex, 17 pages + 6 uuencoded postscript figures, KEK-TH-396, TMUP-HEL-9402 (unnecessary one reference was removed

Dealing with the Inventory Risk. A solution to the market making problem

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll and formalized mathematically by Avellaneda and Stoikov. The market is modeled using a reference price $S_t$ following a Brownian motion with standard deviation $\sigma$, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price $S_t$ and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton-Jacobi-Bellman equations associated to the stochastic optimal control problem can be transformed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approximations based on a spectral characterization of the optimal quotes