From Rational Bubbles to Crashes

We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. First, bubbles are argued to be the equivalent of Goldstone modes of the fundamental rational pricing equation, associated with the symmetry-breaking introduced by non-vanishing dividends. Generalizing bubbles in terms of multiplicative stochastic maps, we summarize the result of Lux and Sornette that the no-arbitrage condition imposes that the tail of the return distribution is hyperbolic with an exponent mu<1. We then extend the RE bubble model to arbitrary dimensions d and, with the renewal theory for products of random matrices applied to stochastic recurrence equations, we extend the theorem of Lux and Sornette to demonstrate that the tails of the unconditional distributions follow power laws, with the same asymptotic tail exponent mu<1 for all assets. Two extensions (the crash hazard rate model and the non-stationary growth rate model) of the RE bubble model provide ways of reconciliation with the stylized facts of financial data. The later model allows for an understanding of the breakdown of the fundamental valuation formula as deeply associated with a spontaneous breaking of the price symmetry. Its implementation for multi-dimensional bubbles explains why the tail index mu seems to be the same for any group af assets as observed empirically. This work begs for the introduction of a generalized field theory which would be able to capture the spontaneous breaking of symmetry, recover the fundamental valuation formula in the normal economic case and extend it to the still unexplored regime where the economic growth rate is larger than the discount growth rate.Comment: Latex 27 pages with 3 eps figur

New procedures for testing whether stock price processes are martingales

We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov type strategies we find that martingale null hypotheses are rejected for many stock price processes

Fractal Profit Landscape of the Stock Market

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q. Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.Comment: 12 pages, 4 figure

The diminished effect of index rebalances

The author revisits the strategy of trading S&P 500 index re-compositions under the pre- and post-crisis financial environments, proving that the return structure has significantly changed. The results show for the first time, that there are currently no tradable abnormal returns between announcement and event dates in the post-crisis sample period, indicating smoother rebalancing mechanisms by bank’s client facing desks and better services for passive end-investors. The newly added firms inflate the S&P 500 index by less than 10 basis points per year. The results could be attributed to improved execution algorithms used by the banks, and potentially to the new regulatory reforms in the sector, which prevents financial institutions from taking large trading positions with their balance sheets

High frequency statistical arbitrage via the optimal thermal causal path

We consider the problem of identifying similarities and causality relationships in a given set of financial time series data streams. We develop further the “Optimal Thermal Causal Path” method, which is a non-parametric method proposed by Sornette et al. The method considers the mismatch between a given pair of time series in order to identify the expected minimum energy path lead-lag structure between the pair. Traders may find this a useful tool for directional trading, to spot arbitrage opportunities. We add a curvature energy term to the method and we propose an approximation technique to reduce the computational time. We apply the method and approximation technique on various market sectors of NYSE data and extract the highly correlated pairs of time series. We show how traders could exploit arbitrage opportunities by using the method

Investor heterogeneity and the cross-section of U.K. investment trust performance

We use the upper and lower bounds derived by Ferson and Lin (2010) to examine the impact of investor heterogeneity on the performance of U.K. investment trusts relative to alternative linear factor models. We find using the upper bounds that investor heterogeneity has an important impact for nearly all investment trusts. The upper bounds are large in economic terms and significantly different from zero. We find no evidence of any trusts where all investors agree on the sign of performance beyond what we expect by chance. Using the lower bound, we find that trusts with a larger disagreement about trust performance have a weaker relation between the trust premium and past Net Asset Value (NAV) performance

Enriched Population of PNS Neurons Derived from Human Embryonic Stem Cells as a Platform for Studying Peripheral Neuropathies

BACKGROUND: The absence of a suitable cellular model is a major obstacle for the study of peripheral neuropathies. Human embryonic stem cells hold the potential to be differentiated into peripheral neurons which makes them a suitable candidate for this purpose. However, so far the potential of hESC to differentiate into derivatives of the peripheral nervous system (PNS) was not investigated enough and in particular, the few trials conducted resulted in low yields of PNS neurons. Here we describe a novel hESC differentiation method to produce enriched populations of PNS mature neurons. By plating 8 weeks hESC derived neural progenitors (hESC-NPs) on laminin for two weeks in a defined medium, we demonstrate that over 70% of the resulting neurons express PNS markers and 30% of these cells are sensory neurons. METHODS/FINDINGS: Our method shows that the hNPs express neuronal crest lineage markers in a temporal manner, and by plating 8 weeks hESC-NPs into laminin coated dishes these hNPs were promoted to differentiate and give rise to homogeneous PNS neuronal populations, expressing several PNS lineage-specific markers. Importantly, these cultures produced functional neurons with electrophysiological activities typical of mature neurons. Moreover, supporting this physiological capacity implantation of 8 weeks old hESC-NPs into the neural tube of chick embryos also produced human neurons expressing specific PNS markers in vivo in just a few days. Having the enriched PNS differentiation system in hand, we show for the first time in human PNS neurons the expression of IKAP/hELP1 protein, where a splicing mutation on the gene encoding this protein causes the peripheral neuropathy Familial Dysautonomia. CONCLUSIONS/SIGNIFICANCE: We conclude that this differentiation system to produce high numbers of human PNS neurons will be useful for studying PNS related neuropathies and for developing future drug screening applications for these diseases