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

The effect of non-ideal market conditions on option pricing

Option pricing is mainly based on ideal market conditions which are well represented by the Geometric Brownian Motion (GBM) as market model. We study the effect of non-ideal market conditions on the price of the option. We focus our attention on two crucial aspects appearing in real markets: The influence of heavy tails and the effect of colored noise. We will see that both effects have opposite consequences on option pricing.Comment: 26 pages and 8 colored figures. Invited Talk in "Horizons in complex systems", Messina, 5-8 December 2001. To appear in Physica-

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