ISSN 1392 – 2785 Inzinerine Ekonomika-Engineering Economics, 2010, 21(3), 244-254 Calibration of Bollinger Bands Parameters for Trading Strategy Development in the Baltic Stock Market Audrius Kabasinskas, Ugnius Macys Kaunas University of Technology K. Donelaicio st. 73, LT-44029, Kaunas, Lithuania e-mail: [email protected], [email protected] In recent decades there was a robust boom in "Bollinger plotter" was developed using the most investment sector in Lithuania, as more people chose to popular mathematical toolbox MatLab in order to solve invest money in investment funds rather than keep money in stated problems. Application is capable of charting the closet. The Baltic States Market turnover has increased Bollinger Bands and 6 other technical indicators with from 721 MEUR in 2000 to 978 MEUR in 2008 (with peak desired period of time. This software is not a fully 2603 MEUR in 2005). When difficult period appeared in automated decision making system, as decisions are global markets, a lot of attention was dedicated towards the usually made based on value judgment. managing of investments. Investment management firms in Since the stock returns usually have distributions with Lithuania gain significance in personal as well as in fat tails, then less than 95% of data fit in the Bollinger business section increasingly; even though these firms are trading channels. However the Bollinger bands trading considerably young (the first one in Lithuania was signals were supported by additional indicators (e.g. %b), established in year 2000). so the loss of data is not significant. Successful investment begins with the financial Our calibration results show that short term investor analysis of stock, asset or index, which you are going to should apply 10 days moving average and use a trading invest. Professionals can be divided into two groups as far channel with the width of 1.8 standard deviations, for the as this point is concerned: supporters of fundamental Bollinger bands. analysis and the supporters of technical analysis. Fundamental analysts try to determine a company’s value Keywords: Bollinger bands, trading bands, short term, by looking at the balance sheet, cash flow statement and investment, portfolio optimization, parameter income statement. Technicians, on the other hand, assume calibration, Baltic stock market, standard that all these fundamentals are accounted for in the stock’s deviation, moving average, technical analysis. price and analyses charts of price movements and various indicators derived from the price and volume. Technical Introduction analysis suffered major criticism when Fama (1965) Lately, the number of investors in Lithuania was presented his efficient-market hypothesis (EMH), which growing rapidly, and they entrusted their savings to states that past prices cannot be used to profitably predict investment funds. People realized that over time money future prices. However, many researches showed that loses its value when it lies in a drawer or a bank account EMH is not adequate in many aspects. With this and therefore, decided to take some minimal risks and background the “Quantitative Behavioral Finance” theory invest some free capital with the hope of the benefit. was introduced (see recent works of Gunduz Caginalp, In the meantime, during the difficult economic Vernon Smith, David Porter, Don Balenovich, Vladimira situation, a lot of investors are focused on optimal Ilieva, Ahmet Duran, and Ray Sturm). This theory includes investment management. Although Lithuanian investment some topics of classical theories, but mainly it is based on management companies are still young (the first behavioral analysis of market agents and helps to investment management company established in Lithuania understand behavioral biases in conjunction with in 2000), but they play a larger role every year in both valuation. This means that there is no reason to criticize personal and business financial management structures. To the technical analysis, but in difficult cases (e.g. crises) it have successful investment, it is necessary to perform should be supplemented by behavioral analysis of agents. comprehensive and very accurate analysis of the market, In this paper some methods of technical analysis are used index or stock company. The analysts usually are divided to create an investment strategy trading in Baltic States in to 2 different schools: fundamental analysts and stock market. technical analysts. Fundamentalists analyze company The main objectives of this research are: adapt financial performance from their submitted reports to Bollinger Bands to the Baltic market, determine which estimate the company's value. The supporters of technical investment period with – long term or short term – analysis consider that all these figures are reflected in stock Bollinger Bands is more efficient, research the efficiency of price and focuse only on the share price changes, i.e. their Bollinger Bands depending on the parameters. In this analysis is based on graphical analysis. The latter theory paper the optimal parameters are calibrated and the was criticized by economists in the context of 1960–1970, expected profit is estimated without the information about when Professor E. Fama introduced his famous efficient the transaction costs. -244- Audrius Kabasinskas, Ugnius Macys. Calibration of Bollinger Bands Parameters for Trading Strategy Development in the Baltic Stock Market market hypothesis (see Fama, 1965, 1965 and Fama & This paper is organized as follows. In the first section Miller, 1972). This theory states that all past information is we give some methodology of Bollinger and other trading reflected in today's price, so it is impossible to predict the bands. Section 2 deals with the methodology of the direction of price movement basing it on historical data. selection of optimal parameters of Bollinger bands. Section Nowadays this theory is replaced by so called “Behavioral 3 explains the nature of the selected data and related Finance” (see, e.g. Baltussen, 2009), which states that the problems. In the section 4 we give some empirical results stock price is a reflection of traders (agents) behavior. of calibration of Bollinger bands parameters and conclude Furthermore, Mandelbrot (1963, 1964) has showed that the with conclusions and discussions. daily stock price returns are not normally distributed and the effective market hypothesis is not adequate. Nowadays, Trading bands many scientists claim that the daily stock returns fit the so called α -stable distribution (Kabašinskas et al, 2009, The trading bands are curves plotted as envelopes in the Kabasinskas et al, 2010, Rachev et al, 2005, Belovas et al, graph of security price. Hurst (1970) was first to apply 2006, etc.) and may be modeled by GARCH time series trading bands in investment analysis. The author suggested techniques. to graph continuous curves over and down from original stock Nonparametric adequacy hypothesis H0: "Return of the price. By this technique analysts tried to evaluate cycles stock is normally distributed" was tested for each of the (seasonality) of the share price (Bollinger 1992, 2001). selected stocks from the Baltic stock market (see Next improvement was introduced in mid 1970’s. The Kabašinskas et al, 2009, and Belovas et al, 2006). The price shell was formed shifting moving average up and Kolmogorov-Smirnov criterion rejected the null hypothesis down by a fixed constant. This technique remains popular for all the data. Theoretically if the width of trading as it is a simple way to draw trading bands. Figure 1 channel is chosen to be of two standard deviations, (upper) illustrates a 21 day moving average with a trading approximately 95% of data should fit into this trading bands shifted up and down by 4%. channel. However, it is wrong to rely on this assumption as returns of the stocks are not normally distributed (see Kabašinskas et al, 2009, and Rachev et al, 2005). It is likely that less than 95% of data fit in the trading channel as returns usually have fat tailed distributions. This means, that there are more data points in the far tails of the distribution than normal distribution, and empirical tests supports this assumption (Kabašinskas et al, 2009, Kabašinskas et al, 2010, and Belovas et al, 2006b). However, Liu et al. (2006) proved that Black–Scholes model really possesses the Bollinger band property of real stock market when K=2. The price of a security is a consensus between a buyer and seller. Whether a trader decides to buy or sell depends on his expectations. If a price is expected to rise, the trader would buy, and if a price is expected to decrease, the trader would sell. Technical analysis encounters greatest challenge because of a human factor. As expectations of an individual person are neither easily measurable nor predictable, all automated decision making systems remain inconsistent (Achelis, 2000). The management of the investment requires cool mind and objectively assessment of all circumstances, because emotions often lead to the edge of the abyss. However, in our work we analyze the investment methods that are based on technical analysis principles. We will analyze the possibilities of application of one of the technical analysis methods – the Bollinger bands methods (Bollinger, 1992 and 2001) for the investment in the Baltic stock market. Bollinger bands method is widely used, however, not so thoroughly studied in a scientific way (see Ryazanova Oleksiv, 2008). In Lithuania this problem is not studied at all. Therefore our main objective of this study is Figure 1. Evolution of the trading bands with TEO1L stocks to examine the scientific and empirical validity of the method mentioned above. Usually the efficiency of It is trivial to draw this kind of bands. First 21 day Bollinger bands varies depending on the selected moving average is calculated and drawn. Then upper band parameters. So in this paper we will focus on this problem. is moving averages times 1.04 and lower band is moving As also we will determine which investment - long-term or average times 0.96.