Market ecology of active and passive investors

We study the role of active and passive investors in an investment market with uncertainties. Active investors concentrate on a single or a few stocks with a given probability of determining the quality of them. Passive investors spread their investment uniformly, resembling buying the market index. In this toy market stocks are introduced as good and bad. If a stock receives sufficient investment it will survive, otherwise die. Active players exert a selective pressure since they can determine to an extent the investment quality. We show that the active players provide the driving force whereas the passive ones act as free riders. While their gains do not differ too much, we show that the active players enjoy an edge. Their presence also provides better gains to the passive players and stocks themselves.Comment: 16 pages, 4 figure

Style migration in Europe

This paper complements the literature on style migration by examining value and size premiums throughout Europe. Information from more than 25 European markets indicates an average value premium of 9.58% per year. The primary determinants of the persistent value outperformance are: 1) value firms migrating to a neutral or growth portfolio, and 2) growth stocks migrating to neutral or value portfolios. The financial health metric F_SCORE helps uncover outperforming stocks ex ante, and provides preliminary evidence on the probability of migration, but only for small stocks

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

Quantum Finance

Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.Comment: Improved 32 page version that is to appear in Physica A. One appendix scrapped, typos corrected, section on conditions for efficient markets extended. References adde

Statistical properties of short term price trends in high frequency stock market data

We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives a qualitative agreement with real data.Comment: 10 pages, 9 figures, in ver. 2 one chapter adde

Scaling analysis of multivariate intermittent time series

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk forecasts: the probability of observing next day a large price movement is (super-universally) inversely proportional to the length of the ongoing low-variability period. Finally, a method is devised for a multi-factor scaling analysis. We apply the simplest, two-factor model to equity index and trading volume time series.Comment: 16 pages, 5 figures, accepted for publication in Physica

Toward a Theory of Marginally Efficient Markets

Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it favorable games}, in the sense that there is a small probabilistic edge that smart speculators can exploit. We propose to identify this probability using conditional entropy concept. A perfect random walk has this entropy maximized, and departure from the maximal value represents a price history's predictability. We propose that market participants should be divided into two categories: producers and speculators. The former provides the negative entropy into the price, upon which the latter feed. We show that the residual negative entropy can never be arbitraged away: infinite arbitrage capital is needed to make the price a perfect random walk.Comment: 9 pages, 3 ps figure

Usefulness of image guidance in the surgical treatment of petrous apex cholesterol granuloma

The petrous apex is a pyramid-shaped structure, located medial to the inner ear and the intrapetrous segment of the internal carotid artery. Lesions of the petrous apex can be surgically treated through different surgical routes. Because of the important neurovascular structures located inside the temporal bone, anatomical 3D knowledge is paramount. For this reason, image-guided surgery could represent a useful tool. We report the case of a young woman who came to our observation for a trigeminal neuralgia due to a petrous apex cholesterol granuloma. The lesion was treated through the placement of a drainage tube via an infracochlear approach, with the aid of neuronavigation and intraoperative MRI. Preoperative CT scan images and intraoperative MRI images were fused for surgical planning. The accuracy of the neuronavigation system has proved to be good, and the safety of the procedure was enhanced. Therefore, neuronavigation and intraoperative MRI, though not available in all neurootological centres, should be considered useful tools in these challenging procedures