Investment Analysis by the Use of the Markov Chain of Process - Research Paper Example

Mathematics Research Paper Lecturer: Introduction Hypothesis, prediction and Idea My paper seeks to determine investment analysis by the use of the Markov Chain of process. This involves the determination of the market performance of a given security or currency under preset conditions by use of the Markov chain as a financial modelling tool. My hypotheses are; i. H0 or the null hypothesis, the preset determinant has a positive or negative effect on the exchange rate of a given currency pair. ii. H1 or the alternative hypothesis, the preset determinant does not affect the exchange rate of the given currency pair From the hypotheses formulated above, use of the Markov Chain as a financial instrument will result in the null hypothesis which states that the preset determinant definitely has an effect on the exchange rate of the given currency pair. If the null hypothesis holds, then I will have proven to a mathematical extent that the Markov Chain of processes can be used as a financial modelling tool. If the alternative hypothesis holds, then I will have failed to prove my understanding of the Markov chain as a probable tool in financial modelling. The field of Markov chains has been widely used in the management field of science as follows: 1. Human resources planning model 2. Pyramid Maslows model on human needs 3. As a Model to predict price changes. 4. Changes in brand by customer product 5. Behaviour of customer receivables This is at least as noted by Hamed Alipoor.T. Etal, Application of Markov Chain in Forecasting Demand of Trading Company. Milan Svoboda and Ladislav Lukáš in their report; Application of Markov chain analysis to trend prediction of stock indices, noted that the prediction of financial market is a complex task since the distribution of financial time series is changing over a period of time. There is also never ending debate as to whether these markets are predictable or not. In other words, they are called efficient markets (EMH) if being unpredictable ones, and vice versa. In the recent years, investors have started to show interest in trading on stock markets indices as it provides an opportunity to hedge their market risk, and at the same time if offers a good investment opportunity for speculators and arbitrageurs. Data and Theory The necessary data for this project will be price related stock or currency exchange data from the respective markets. The project will involve collecting daily prices of the chosen type of data over a period of time say one month. This data will be sourced from any relevant sources in the worldwide web. The main principle of using Markov chain to predict is to build Markov forecasting model that predicts the state of an object in a certain period of time in the future by virtue of probability vector of the initial state and state transition probability matrix, Deju Zhang, Study on Forecasting the Stock Market Trend Based on Stochastic Analysis Method Deju describes the whole process as follows, 1. Obtaining the transition matrix In a balanced system, if probability of the system from state i to j is P ij , then the set of transition probability vector in system state form a transfer matrix, written by P –[P ij] m x n, Where transfer matrix must be a probability matrix which its operation rules is the same as conventional matrix. 2. State probability matrix The average transition process of Markov chain only depends on the system’s initial state and the transfer matrix, where the system’s initial state is a line matrix posed by the probability vector, written by S(0)- [ S(0)ij]1xn When the systems initial state is known, let probability matrix in a state k be k S after k th transferring. By the Chapman-Kolmogorov equation we have S (k+ 1) - S (k) *P Then we can obtain the following recursive formula: S (1) - S (0)* P, S (2) - S (1) * P – S (0) * P2 S (k) - S (k+ 1) * P -, ..., - S (0) * P Such that, S k+ 1 - S(0) * P k+ 1 According to this recursive formula, we achieve the forecast based on the interpretation of dynamic system. Results Zhang further examines the whole idea of financial forecasting by Markov chain by saying that the analysis of the moving changes on Markov chain is mainly based on the state and relationship of limited Markov process in chain, to predict the future situation of chain. According to the characteristics of the composition of process of Markov chain, we may make the following assumptions in order to apply Markov chain forecasting model to stock market analysis. i. The operation of the stock market only is impacted by random factors such as the global or regional economic, politics, and society and so on, and macro policy of securities management department is stable and manipulated impact of investors is negligible. ii. Up or down movement of the stock market in a given day just depended on state before the closing day, but it had little to do with the past, so the market over the past was negligible. iii. The probability which stock market from one state i skips to another state j by the same time interval has nothing with moment of the state i . In his research he also found out that when analyzing and forecasting process by Markov Chain, we should have the following steps: a. Construct state and determine the corresponding state probability b. Write a state transition probability matrix by the state transfer c. Derive all kinds of the state vector by the transition probability matrix d. Analyze, predict and make decision in a stable condition. The data collected was as follows and the variables were Closing price as the determinant/objective factor. The data was from the monthly prices of the Yahoo Uk & Ireland FTSE100   High Low Close 01/12/2014 6753.2002 6753.2002 6566.1001 03/11/2014 6773.1001 6773.1001 6722.6001 01/10/2014 6622.7998 6622.7998 6546.5 01/09/2014 6904.8999 6904.8999 6622.7002 01/08/2014 6831.2002 6831.2002 6819.7998 01/07/2014 6875.2998 6875.2998 6730.1001 02/06/2014 6879 6879 6743.8999 01/05/2014 6894.8999 6894.8999 6844.5 01/04/2014 6794.8999 6794.8999 6780 03/03/2014 6827.2002 6827.2002 6598.3999 03/02/2014 6866.3999 6866.3999 6809.7002 01/01/2014 6867.3999 6867.3999 6510.3999 The results when done using the function MMULT in excel for the purposes of working out the Markov process we get the following; Closing price 1 2 6566.1001 547988239 547988239 6722.6001     6546.5     6622.7002     6819.7998     6730.1001     6743.8999     6844.5     6780     6598.3999     6809.7002     6510.3999     From the results on the table, 1 and 2 are equal in all aspects showing that the Markov chain process applied on the monthly data over this period gives a 100% likelihood that the closing price of a stock will determine its highs and lows over the period the market period. Conclusions As the Markov chain has no after-effect, using this method to analyze and predict the stock market index and closing stock price is more effective under the market mechanism. However, Markov chain prediction method is only a probability forecasting methods, the predicted results is simply expressed probability of a certain state of stock prices in the future, rather than be in a absolute state. The operational status of the stock market is subject to the influence of various factors from market, for example, the multiple market forces from both sides, the fundamentals state of the stock itself, macroeconomic policy, trade and economic degrees and psychological factors of investors, (Zhang, June 2009). Therefore it is evident that no single method can accurately predict changes in the stock market every day, Markov chain prediction method is no exception. But we can combine the results of forecasts from using Markov chain to predict with other factors and see it as a basis for decision-making. In this paper, we only explore application of Markov chain in the stock market, and achieve relatively good results. Markov chain can also be spread and applied to other fields, such as the futures market, the bond market and so on. References: 1. Hamed Alipoor .T. etal, Application of Markov Chain in Forecasting Demand of Trading Company. 2. Milan Svoboda and Ladislav Lukáš, Application of Markov chain analysis to trend prediction of stock indices 3. Deju Zhang, Study on Forecasting the Stock Market Trend Based on Stochastic Analysis Method, (June, 2009) Read More