We investigate asset returns using the concept of beta herding, which measures cross-sectional variations in betas due to changes in investors’ confidence about their market outlook. Overconfidence causes beta herding (compression of betas towards the market beta), while under-confidence leads to adverse beta herding (dispersion of betas from the market beta). We show that the low-beta anomaly can be explained by return reversal following adverse beta herding, as high beta stocks underperform low beta stocks exclusively following periods of adverse beta herding. This result is robust to investors’ preferences for lottery-like assets, sentiment, and return reversals, and beta herding leads time variation in betas.

This paper presents novel regression and regularisation techniques based on Field Programmable Gate Array (FPGA) technology for large-scale datasets for machine learning and other applications. We introduce a customisable design which allows end-users to select their regression and regularisation techniques from a library supporting relevant methods such as Multiple Linear Regression, Ridge Regression, Adaptive/Lasso Regression and Elastic Net Regularisation. We introduce the first Adaptive Elastic Net architecture for FPGAs. Tests on dense and sparse datasets of varying sizes show 158 times speedup and (114)times enhancement in energy efficiency, when comparing an 8-FPGA system with the corresponding software C++ implementation on a 12-core CPU, for an Adaptive Elastic Net regularisation of a matrix with 11.56 * 10(9) coefficients.

We investigate asset returns using the concept of beta herding, which measures cross-sectional variations in betas induced by investors whose beliefs about the market are biased due to changes in confidence or sentiment. Overconfidence or optimistic sentiment causes beta herding (compression of individual assets’ betas towards the market beta), while under-confidence or pessimistic sentiment leads to adverse beta herding (dispersion of betas away from the market beta). We find that beta herding is related to the low-beta anomaly, as high beta stocks underperform low beta stocks on a risk-adjusted basis exclusively following periods of adverse beta herding. As an explanation of the low-beta anomaly, we propose the persistence of bias in betas (i.e., a large difference in betas) that lasts for more than one year as market uncertainty continues.

Genetic programming can be used to identify complex patterns in financial markets which may lead to more advanced trading strategies. However, the computationally intensive nature of genetic programming makes it difficult to apply to real world problems, particularly in real-time constrained scenarios. In this work we propose the use of Field Programmable Gate Array technology to accelerate the fitness evaluation step, one of the most computationally demanding operations in genetic programming. We propose to develop a fully-pipelined, mixed precision design using run-time reconfiguration to accelerate fitness evaluation. We show that run-time reconfiguration can reduce resource consumption by a factor of 2 compared to previous solutions on certain configurations. The proposed design is up to 22 times faster than an optimised, multithreaded software implementation while achieving comparable financial returns.

The classic Jacobi method, widely used for solving linear systems, is slow, especially when dealing with large matrices. This paper proposes a Custom Jacobi Solver (CJS) for large-scale linear systems. It is based on a column-wise Jacobi step operation which allows for increased dependence distance, enabling deep pipelining. Our solver allows customisation at run time between the classic Jacobi method and its more convergence efficient-counterpart, the weighted Jacobi method. It can be dynamically scaled to multiple FPGAs by appropriately partitioning the matrix data among the FPGAs. After evaluating our solver on a number of different datasets, CJS proves to be up to 71 times faster when comparing an 8-FPGA solution with a 12-core CPU C++ implementation.

A trading strategy is generally optimised for a given market regime. If it takes too long to switch from one trading strategy to another, then a sub-optimal trading strategy may be adopted. This paper proposes the first FPGA-based framework which supports multiple trend-following trading strategies to obtain accurate market characterisation for various financial market regimes. The framework contains a trading strategy kernel library covering a number of well-known trend-following strategies, such as “triple moving average”. Three types of design are targeted: a static reconfiguration trading strategy (SRTS), a full reconfiguration trading strategy (FRTS), and a partial reconfiguration trading strategy (PRTS). Our approach is evaluated using both synthetic and historical market data. Compared to a fully optimised CPU implementation, the SRTS design achieves 11 times speedup, the FRTS design achieves 2 times speedup, while the PRTS design achieves 7 times speedup. The FRTS and PRTS designs also reduce the amount of resources used on chip by 29% and 15% respectively, when compared to the SRTS design.

We propose a new non-parametric measure of herding, beta herding, by incorporating the interaction between sentiment and herding in standard linear factor models. Contrary to common belief that herding is significant when the market is under stress, we demonstrate that beta herding arises when investors are confident regarding the outlook for the market, whether it is rising or falling, rather than when the market is in crisis. In fact our study suggests that crises appear to lead investors to seek a the fundamenal risk-return relationship rather than herd. Our empirical results for the US equity market show that beta herding activity increases with market-wide sentiment. We also find that high beta stocks are priced following adverse herding when high (low) betas are biased higher (lower), although as in Fama and French (1992) beta does not unconditionally explain cross-sectional asset returns.

This chapter describes self-awareness in four financial applications. We apply some of the design patterns of Chapter 5 and techniques of Chapter 7. We describe three applications briefly, highlighting the links to self-awareness and self-expression. The applications are (i) a hybrid genetic programming and particle swarm optimisation approach for high-frequency trading, with fitness function evaluation accelerated by FPGA; (ii) an adaptive point process model for currency trading, accelerated by FPGA hardware; (iii) an adaptive line arbitrator synthesising high-reliability and low-latency feeds from redundant data feeds (A/B feeds) using FPGA hardware. Finally, we describe in more detail a generic optimisation approach for reconfigurable designs automating design optimisation, using reconfigurable hardware to speed up the optimisation process, applied to applications including a quadrature-based financial application. In each application, the hardware-accelerated self-aware approaches give significant benefits: up to 55x speedup for hardware-accelerated design optimisation compared to software hill climbing.

Over the past years, examining financial markets has become a crucial part of both the trading and regulatory processes. Recently, genetic programs have been used to identify patterns in financial markets which may lead to more advanced trading strategies. We investigate the use of Field Programmable Gate Arrays to accelerate the evaluation of the fitness function which is an important kernel in genetic programming. Our pipelined design makes use of the massive amounts of parallelism available on chip to evaluate the fitness of multiple genetic programs simultaneously. An evaluation of our designs on both synthetic and historical market data shows that our implementation evaluates fitness function up to 21.56 times faster than a multi-threaded C++11 implementation running on two six-core Intel Xeon E5-2640 processors using OpenMP.

Advances in high frequency trading in financial markets have exceeded the ability of regulators to monitor market stability, creating the need for tools that go beyond market microstructure theory and examine markets in real time, driven by algorithms, as employed in practice. This paper investigates the design, performance and stability of high frequency trading rules using a hybrid evolutionary algorithm based on genetic programming, with particle swarm optimisation layered on top to improve the genetic operators' performance. Our algorithm learns relevant trading signal information using Foreign Exchange market data. Execution time is significantly reduced by implementing computationally intensive tasks using Field Programmable Gate Array technology. This approach is shown to provide a reliable platform for examining the stability and nature of optimal trading strategies under different market conditions through robust statistical results on the optimal rules' performance and their economic value.

We investigate the effects of a behavioral bias in betas on cross-sectional asset returns. This bias, which we call beta herding, reflects the interaction between sentiment and herding in linear factor models. We demonstrate that beta herding is likely to arise when investors are more confident about the future direction of the market, regardless of whether the market is rising or falling, or when sentiment is high. Contrary to common belief that herding increases during market crises, our empirical evidence indicates that crises appear to lead investors to seek out the fundamental risk-return relationship rather than to herd. In terms of cross-sectional asset returns, we show evidence that beta matters conditionally on beta herding though it does not unconditionally. The conditional explanation of beta herding is distinct from other firm characteristics.

In this paper we examine the question of whether knowledge of the information contained in a limit order book helps to provide economic value in a simple trading scheme. Given the greater information content of the order book, over simple price information, it might naturally be expected that the order book would dominate. Using Dollar Sterling tick data, we find that despite the in-sample statistical significance of variables describing the structure of the limit order book in explaining tick-by-tick returns, they do not consistently add significant economic value out-of-sample. We show this using a simple linear model to determine trading activity, as well as a model-free genetic algorithm based on price, order flow, and order book information. We also find that the profitability of all trading rules based on genetic algorithms dropped substantially in 2008 compared to 2003 data.

In this paper we test whether investors are uncertainty averse during a real-life trading process in the foreign exchange market. We do this through an agent-based model in which fundamentalist and chartist beliefs of the exchange rate are allowed to be either uncertainty neutral or uncertainty averse. The uncertainty aversion is modelled via the maxmin expected utility approach. We find that traders are uncertainty averse in the FX market. The estimation results show that the inclusion of uncertainty averse agents improves the performance of the model and the uncertainty aversion parameter is significantly different from zero. Fundamentalists are found to be uncertainty neutral and chartists - mainly uncertainty averse.

We introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the dependency structure between the variables of interest. Hence, we extend Koenker and Bassett's (1978. Regression quantiles. Econometrica, 46, no. 1: 33–50.) original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X, and hence the specification of the quantile regression functions. The approach exploits the fact that the joint distribution function can be split into two parts: the marginals and the dependence function (or copula). We then deduce the form of the (invariably nonlinear) conditional quantile relationship implied by the copula. This can be achieved with arbitrary distributions assumed for the marginals. Some properties of the copula-based quantiles or c-quantiles are derived. Finally, we examine the conditional quantile dependency in the foreign exchange market and compare our quantile approach with standard tail area dependency measures.

The time-series relationship between investor sentiment and market returns, in particular the direction and size of the effects, remains ambiguous, being assessed under the restrictive assumption of linearity. This paper reveals the presence of four, intuitive, regimes in price and sentiment formation in the US stock market at the monthly level over the period 1965-2003, even after controlling for various economic and financial factors. An optimistic state of high returns (occurrence probability: 44%) alternates with a pessimistic state of low returns (35%), while two infrequent, highly volatile states capture temporal irregularities: episodes of extreme negative returns and strong pessimism (13%) and a reversal phase of intense optimism (8%). Five main findings arise: i) In the high return (low return) state, only individual (institutional) sentiment is influential, being a contrarian (momentum) signal for the subsequent return and responding positively (negatively) but weakly to its lagged value. In the former case, the impact of sentiment is consistent with correction of a previous mispricing, possibly induced by individuals, while in the latter, it indicates institutions' correct predictive ability. ii) The impact of institutional sentiment is substantial but constrained in the pessimistic state, while the effect of individual sentiment is moderate but augmented substantially at irregular times. iii) Individuals interpret institutional optimism as a positive signal, whereas institutions perceive individuals' optimism as a contrarian indicator. iv) Total arbitrage cost exerts a positive impact on both subsequent returns and institutional optimism. v) Interest rates' reductions amplify investors' optimism at irregular times, most evidently during the market reversal phase.

A general methodology for time series modelling is developed which works down from distributional properties to implied structural models including the standard regression relationship. This general to specific approach is important since it can avoid spurious assumptions such as linearity in the form of the dynamic relationship between variables. It is based on splitting the multivariate distribution of a time series into two parts: (i) the marginal unconditional distribution, (ii) the serial dependence encompassed in a general function, the copula. General properties of the class of copula functions that fulfill the necessary requirements for Markov chain construction are exposed. Special cases for the gaussian copula with AR(p) dependence structure and for archimedean copulae are presented. We also develop copula based dynamic dependency measures - auto-concordance in place of autocorrelation. Finally, we provide empirical applications using financial returns and transactions based forex data. Our model encompasses the AR(p) model and allows non-linearity. Moreover, we introduce non-linear time dependence functions that generalize the autocorrelation function.

This paper aims to provide an introductory review of copulae and their potential application finance, in particular in capturing the dependence between financial assets that follow non-gaussian distributions and hence for modelling credit risk, pricing options and portfolio design. We briefy review the failure of methods based on multivariate normality and where dependency is measured by correlation. Using a copula approach enables us to measure the different relationships that may exist between financial assets in different ranges of their behaviour- for instance do assets exhibit similar dependency patterns in the tails of their distributions as they do around their means? We review different measures of association and show that when these dependency measures can be expressed simply as functions of a copula they will be invariant to strictly monotone transformations of the random variables and hence the units in which we choose to express our data. The standard Pearson Correlation statistic is not in general invariant to scale changes in the data. We then discuss several statistical issues relating to the estimation of Copulae and their empirical application through both parametric and non parametric methods. An important issue lies in the statistical discrimination between copulae and we propose a encompassing framework based on simulation for discriminating between what are effectively separate statistical families. We then consider several applications, modelling default risk, tail dependence, quantile regression and portfolio design for non-gaussian assets.