Kernel methods for short-term portfolio management

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Abstract

Portfolio optimization problem has been studied extensively. In this paper, we look at this problem from a different perspective. Several researchers argue that the USA equity market is efficient. Some of the studies show that the stock market is not efficient around the earning season. Based on these findings, we formulate the problem as a classification problem by using state of the art machine learning techniques such as minimax probability machine (MPM) and support vector machines (SVM). The MPM method finds a bound on the misclassification probabilities. On the other hand, SVM finds a hyperplane that maximizes the distance between two classes. Both methods prove similar results for short-term portfolio management.

Introduction

The objective of this study is to develop a model for stock selection by using state of the art machine learning techniques, such as minimax probability machine (MPM) and support vector machines (SVMs). Stock selections decisions are derived from earning announcements and volatility of stocks around the earning time. The majority of the studies on stock markets and earning announcements focus on the information content and timeliness- measured by changes in the characteristics of stock return distribution (e.g. mean, variance, and serial correlation) and trading volume—when corporate earnings are announced to the market (Eilifsen, Knivsflae, & Sættem, 2001). Numerous studies, including Ball and Brown, 1968, Chari et al., 1988, Easton and Zmijewski, 1989, Gennotte and Truemann, 1996, and Kross & Schroeder (1984), find that stock prices respond positively to announcements of increase in earnings and negatively to announcements of decrease in earnings for the USA firms. Beaver (1968) argued that earnings announcements possess information content if stock price volatility and/or trading volume increase around the time of the announcement (see also Atiase, 1985, Bamber, 1987, Bamber et al., 1997, Barron, 1995, Holthausen and Verrecchia, 1990). According to this view, stock prices reflect the market's aggregated (or average) interpretation of the information, while trading volume measures investor activity, and thus reflects differential beliefs among investors.

Three previous studies have examined short-term price movements around earnings announcements—Chari et al. (1988), covering the 1976–1984 period, Ball & Kothari (1991), covering the years 1980–1988, and Trueman et al. (2003) covering January 1998 to August 2000. There are two primary differences between the findings of the first two studies and the findings of Trueman et al. (2003). First, while the stocks in the first two studies' samples do increase in price prior to earnings announcements, there is no consistent price movement (either positive or negative) afterwards. Second, the magnitude of the pre-announcement returns they found is very small in comparison to what the third study reports (less than one tenth in size). Furthermore, those returns are significant only for the day before and the day of the earnings announcement.

Quarterly earnings announcement is probably one of the most highly anticipated events and receives significant media and investor attention. Research consistently shows that the market assimilates more and more of the information in earnings as the announcement date approaches (see Kothari, 2001; for a survey of this research starting with Ball & Brown, 1968). Hence, the extent to which an earnings announcement will provide ‘useful’ information to market participants should be a function not only of the nature of information released but also when it is released. Firms tend to release good news earnings reports earlier than those containing bad news (Chambers and Penman, 1984, Kross and Schroeder, 1984). If this is the case, then the longer a firm goes without reporting its earnings, the less positive (or, alternatively, more negative) will investors expect the ultimate earnings news to be. This implies that a firm should experience negative stock returns from the end of its fiscal quarter up until the time of its earnings announcement. When the earnings are finally released by the manager, the stock price should rise.

Based on these studies, we propose a classification model with two classes; ‘buy a certain stock whose earning/eps is higher than some threshold’ and ‘do not buy a certain stock if its earning is less than some certain threshold’. The threshold value is subjective and depends on the investor. As far as we know, there have been no studies that propose a classification model by using the earning announcements and anomalies. Data mining techniques such as SVMs, MPM and multilayer perceptron (MLP) would be good candidates addressing this problem instead of using classical statistical techniques.

Data mining is the process of discovering and analyzing hidden patterns in data sets. It has wide application areas from engineering to commerce. Most widely used data mining techniques in finance are artificial neural networks (ANNs), SVMs and their variations. Bankruptcy prediction, portfolio management (choosing individual stocks for portfolio), option pricing, and forecasting indices or individual stock prices are typical application areas in finance (Chen et al., 2003, Dourra and Siy, 2002, Galindo, 1998, Hutchinson et al., 1994, Trafalis and Ince, 2000).

The classification problem is to learn a discriminating hyperplane or hypersurface, which separates two classes from examples by minimizing the generalization error (Vapnik, 1995). MPM attempts to control misclassification probabilities for two-class classification problems. Specifically it minimizes the worst case (maximum) probability of misclassification of future data points under all possible choices of class densities with a given mean and covariance matrix, which is positive definite. MPM minimizes directly an upper bound on the generalization errors (Lanckriet, El Ghaoui, Bhattacharyya, & Jordan, 2002). In contrast to MPM, SVMs achieve low generalization error by maximizing an associate quantity termed margin that describes the distance between two classes.

In this study, we will provide a framework for short-term portfolio selection problem by using MPM and SVMs. This can be done by analyzing the behavior of the stocks around their earning announcement. We believe that some variables such as volume, difference between expected eps and actual eps, and expectation have big effect on return. Several studies have shown that the stock market is inefficient during the earning announcement in terms of individual stocks.

The paper is organized as follows: in 2 Minimax probability machine, 3 Support vector machines we present the basics of the MPM and SVM techniques, respectively; in Section 4, a short-term portfolio classification model is explained; computational results are given in Section 5; and finally, Section 6 concludes the paper.

Section snippets

Minimax probability machine

The MPM attempts to control misclassification probabilities for two-class (binary) classification problems. It minimizes the worst case (maximum) probability of misclassification of future data points under all possible choices of class densities with a given mean and covariance matrix (Lanckriet et al., 2002). MPM uses the following theorem, by Popescu & Bertsimas (2001):supy(y¯,y)Pr{yS}=11+d2,and,d2=infyS(yy¯)Ty1(yy¯),where y is a random vector, S is a given convex set, and supremum

Support vector machines

The classification problem can be defined by using the following intuition. Consider a two class pattern recognition problem with a training sample D={xi,yi}i=1l, where xiRn and yi∈{−1,1}, is the total number of observations, and n is the, input dimension. Our goal is the find a decision function which is given in Eq. (9) that separates the two classes with minimum error.f(x)=sign(<w,x>+b)where sign(x)=1 if x0 and sign(x)=−1 if x<0, is the vector normal to the separating hyperplane, bR is

Classification model for earning announcement

Our motivation in this research is to investigate how we could use the earning anomalies in a short-term classification problem. The price changes and trading volume reactions have been investigated by several researchers. Morse (1983) observes the large price reactions to accounting reports for 2 days following the Wall Street Journal announcement and unusual volume trading during the 3 days following the announcements. The short-term price movements have been examined by several researchers.

Experiments

Data analysis is one of the most important approaches in order to discover some patterns in the financial market. Our dataset contains 679 observations. Four consecutive quarterly EPS, stock price at the first day after the earning announcement, and the difference between the actual and expected eps and surprise (0–1) are used as inputs. The output is computed as follows: If the five day return is greater than five percent, the corresponding stock is in the ’BUY’ class (1), otherwise, it is in

Conclusion

In this paper, we develop and describe an intelligent short-term portfolio management model based on the volatility around the earning announcements. We assume that the efficient market hypothesis is not valid around the earning time for individual companies. Especially, one can make excess returns around the earning season by trading individual stocks after their earning announcements. Since, the volatility is very high around this time, one needs to develop a technique to minimize the risk or

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