Markov Chain Model Application on Share Price Movement in Stock Market

Abstract

The success of an investor especially in a stock market hinges much on the choice of decision made which in turn depends to a large extent on how well informed one is in stock analysis. The Markov chain model was used to analyse and to make predictions on the three states that exist in stock price change which are share prices increase, decrease or remain unchanged. The two top banks used to illustrate are Guarantee Trust bank of Nigeria and First bank of Nigeria. The six years data used were obtained from 2005 to 2010. The Transition matrix was derived using the Microsoft Excel. Obtaining powers of transition matrices and probability vector analysis using the R Statistical software, equilibrium was attained in about twenty years. It was realized that regardless of a bank current share price, in the long run we could predict that its share price will depreciate with a probability of 0.4229, remain unchanged with probability of 0.2072 and appreciate with a probability of 0.3699. The probability of each of the two banks appreciating is also on the increase, with GTB taking the lead with a probability of 0.4614 at equilibrium, and then FBN with a probability of 0.3799. For a company price to remain the same over a period of time is not a good sign for the company’s performance and considering the probability of unchanged for this sector, we will notice that at equilibrium, the probability of GTB shares remaining the same is 0.0688 which is lower to that of First bank which implies that GTB shares change hands more than the FBN.

Keywords: Stock Market, Transition Matrix, Equilibrium, Probability Vector, Stock Prediction