Optimal Investment Horizons for Stocks and Markets

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices \cite{optihori,gainloss}. Such a distribution typically goes through a maximum at a time coined the {\em optimal investment horizon}, $\tau^*_\rho$, which defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we reported in \cite{gainloss} on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, the inverse statistics for 2/3 of the individual stocks presently in the DJIA is investigated. We show that this gain/loss asymmetry established for the DJIA surprisingly is {\em not} present in the time series of the individual stocks nor their average. This observation points towards some kind of collective movement of the stocks of the index (synchronization).Comment: Subm. to Physica A as Conference Proceedings of Econophysics Colloquium, ANU Canberra, 13-17 Nov. 2005. 6 pages including figure

Inverse Statistics for Stocks and Markets

In recent publications, the authors have considered inverse statistics of the Dow Jones Industrial Averaged (DJIA) [1-3]. Specifically, we argued that the natural candidate for such statistics is the investment horizons distribution. This is the distribution of waiting times needed to achieve a predefined level of return obtained from detrended historic asset prices. Such a distribution typically goes through a maximum at a time coined the {\em optimal investment horizon}, $\tau^*_\rho$, which defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we reported in [2,3] on a quantitative gain/loss asymmetry most pronounced for short horizons. In the present paper, this gain/loss asymmetry is re-visited for 2/3 of the individual stocks presently in the DJIA. We show that this gain/loss asymmetry established for the DJIA surprisingly is {\em not} present in the time series of the individual stocks. The most reasonable explanation for this fact is that the gain/loss asymmetry observed in the DJIA as well as in the SP500 and Nasdaq are due to movements in the market as a whole, {\it i.e.}, cooperative cascade processes (or ``synchronization'') which disappear in the inverse statistics of the individual stocks.Comment: Revtex 13 pages, including 15 figure

Inverse Statistics in the Foreign Exchange Market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) $\rho$ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained for the Japanese Yen against the$US. With high statistical significance, the presence of "resonance peaks" in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the markets participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new {\em stylized fact}, is observed for the waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale dependent features of the market activity.Comment: 8 pages. Accepted Physica

The Design of Random Surfaces with Specified Scattering Properties: Surfaces that Suppress Leakage

We present a method for generating a one-dimensional random metal surface of finite length L that suppresses leakage, i.e. the roughness-induced conversion of a surface plasmon polariton propagating on it into volume electromagnetic waves in the vacuum above the surface. Perturbative and numerical simulation calculations carried out for surfaces generated in this way show that they indeed suppress leakage.Comment: Revtex 6 pages (including 4 figures

Distinguishing fractional and white noise in one and two dimensions

We discuss the link between uncorrelated noise and Hurst exponent for one and two-dimensional interfaces. We show that long range correlations cannot be observed using one-dimensional cuts through two-dimensional self-affine surfaces whose height distributions are characterized by a Hurst exponent lower than -1/2. In this domain, fractional and white noise are not distinguishable. A method analysing the correlations in two dimensions is necessary. For Hurst exponents larger than -1/2, a crossover regime leads to a systematic over estimate of the Hurst exponent.Comment: 3 pages RevTeX, 4 Postscript figure

Substrate influence on the plasmonic response of clusters of spherical nanoparticles

The plasmonic response of nanoparticles is exploited in many subfields of science and engineering to enhance optical signals associated with probes of nanoscale and subnanoscale entities. We develop a numerical algorithm based on previous theoretical work that addresses the influence of a substrate on the plasmonic response of collections of nanoparticles of spherical shape. Our method is a real space approach within the quasi-static limit that can be applied to a wide range of structures. We illustrate the role of the substrate through numerical calculations that explore single nanospheres and nanosphere dimers fabricated from either a Drude model metal or from silver on dielectric substrates, and from dielectric spheres on silver substrates.Comment: 12 pages, 13 figure

Fear and its implications for stock markets

The value of stocks, indices and other assets, are examples of stochastic processes with unpredictable dynamics. In this paper, we discuss asymmetries in short term price movements that can not be associated with a long term positive trend. These empirical asymmetries predict that stock index drops are more common on a relatively short time scale than the corresponding raises. We present several empirical examples of such asymmetries. Furthermore, a simple model featuring occasional short periods of synchronized dropping prices for all stocks constituting the index is introduced with the aim of explaining these facts. The collective negative price movements are imagined triggered by external factors in our society, as well as internal to the economy, that create fear of the future among investors. This is parameterized by a ``fear factor'' defining the frequency of synchronized events. It is demonstrated that such a simple fear factor model can reproduce several empirical facts concerning index asymmetries. It is also pointed out that in its simplest form, the model has certain shortcomings.Comment: 5 pages, 5 figures. Submitted to the Proceedings of Applications of Physics in Financial Analysis 5, Turin 200

Synchronization Model for Stock Market Asymmetry

The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this, we introduce a market model consisting of randomly fluctuating stocks that occasionally synchronize their short term draw-downs. These synchronous events are parameterized by a ``fear factor'', that reflects the occurrence of dramatic external events which affect the financial market.Comment: 4 pages, 4 figure