In Search Of Anomalies
Universidad Carlos III de Madrid
October 12, 2015
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This paper develops a systematic method to search for asset pricing anomalies in the context of technical analysis. First, seeking strategies with positive and significant abnormal returns and low transaction costs, we document three trend-following anomalies whose returns cannot be explained by CAPM, Fama and French three- and four-factor models. This mechanism is able to search for anomalies with regard to any underlying asset pricing model and can be extended to include additional objective functions and other types of input information. Furthermore, we evaluate the overall performance of standard models to price technical trading rules. Surprisingly, we find CAPM as the best performing model while in general, the models exhibit poor performance.
In Search Of Anomalies – Introduction
Anomalies are cross-sectional or time-series empirical evidence inconsistent with a central asset pricing theory. Their detection insinuate realignment towards a new paradigm in asset pricing.1 However, there is no systematical method to search for them and their detection is mainly rooted along the researchers eagerness to explore among a huge amount of information.
This lack of searching methodology hinders the development of asset pricing theories. This paper provides a mechanism based on evolutionary algorithm to search for anomalies with regard to an underlying asset pricing model alongside technical trading rules. This technique can be easily extended to include additional objective functions such as drawdown and other types of input information such as accounting and macroeconomic data. In other words, we are able to find asset pricing anomalies anywhere and in any shape they are. As an experiment, we run our searching mechanism once, and document three trend-following (TF) anomalies. In an additional analysis, we compare the performance of CAPM, Fama and French three- and four-factor models to explain the cross-sectional profitability of technical trading rules. We find CAPM as the best performing model. However, in general, the models exhibit poor performance.
We develop our anomaly searching mechanism in the context of technical trading rules dubbed by Neftci (1991) as “informational prediction rules”. In most segments of investment industry, partial or exclusive application of technical analysis is prominent (see, e.g., Schwert, 2003; Covel, 2005; Lo and Hasanhodzic, 2010).2 In one particular study, Allen and Karjalainen (1999) use genetic algorithm to search for profitable technical trading rules along S&P 500 index. They did not find profitable trading rules after accounting for transaction costs. In this paper, we show that a modified version of their algorithm can perform an overall search for anomalies and learn profitable trading rules.
The contribution of this paper is three-fold. First, we introduce an anomaly searching mechanism based on genetic algorithm that can be opted for additional objective functions. In our case, we direct the algorithm to search for positive and significant alphas with low transaction costs assuming an underlying four-factor Fama and French asset pricing model. Second, we document three new trend following anomalies that exhibit cross-sectional anomalistic performance. Third, we explore the performance of asset pricing models, CAPM, three- and four-factor Fama and French models, to price simulated trading rules (in the terminology of Karapandza and Marin (2014), uninformed trading rules). We find CAPM to be the best pricing model; however, in general, these models perform poorly in pricing trading rules. This finding calls for improvement in asset pricing models in the context of technical analysis.
To search for anomalies, we face several challenges. First, the objective function that is significant alphas corresponding to an underlying asset pricing model is non-differentiable; therefore, we cannot employ conventional methods such as gradient-based method to find optimal solutions. Second, the search space may have several local optima and therefore, we may stuck with a statistically insignificant anomaly in our search life. Third, the size of search space is large; depending on the functions and input variables, we are faced with a huge solution space. To respond to these challenges, we employ genetic algorithm as the base of our search mechanism. Genetic algorithm is a machine learning algorithm that recently attracted attention for its application in financial economics (Allen and Karjalainen, 1999).
Adopting the principles of natural evolution to search for optimum solutions, it is founded upon the perception of “the strongest survive”. In simple terms, genetic algorithm starts with a randomly generated set of solutions and apply the concept of evolution to generate stronger population sets. It continues this routine to find the strongest member that survives until the final generation. With regard to technical trading rules, in the first generation, a set of trading rules are created randomly and saved in the population set. The genetic algorithm produces new populations via cross-over and mutation operators. In the cross-over operator, two new trading rules are generated by combining the existing rules in the population. An additional mutated population is computed by combining a new generated trading rule and an existing rule in the population. In each generation, the trading rules with insignificant alphas or high transaction costs are programmed to be removed from the population. This process is repeated for a predetermined number of times.
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