A Simulation Study: Obtaining a Sufficient Sample Size of Discrete-Time Markov Chains of Investment in a Short Frequency of Time

Abstract

This paper deals with the problem of determining the sufficient sample size needed to estimate the transition matrix in the Markov chain. In particular, this paper focuses on systems with insufficient data or a short frequency of time caused by the difficulty of acquiring data. This study developed a Markov chain simulation technique that achieves a sufficient sample and can be used to estimate the size of the transition probability, despite having a short frequency of time. It also shows how this technique can be used in the short-, medium-, and long-term, and how a sufficient sample size can be found in these three situations. More specifically, this study illustrates the proposed simulation Markov chain model that estimates the transition probability matrix of the return of assets (ROA) in the industrial sector in Malaysia between 2007 and 2018. In this study, we present a method of determining an adequate sample size using a Markov chain simulation model. This model uses data from a number of companies in the industrial sector in Malaysia in order to study the performance of ROA and assist investors in making investment decisions. However, each company only has yearly ROA values. In other words, the frequency of the values is low, which makes studying the performance of ROA in the industrial sector more difficult. This could be the case because companies don't publish financial yearly reports, or because they are emerging companies that don't have adequate financial reports to calculate their ROA. This study was able to compensate for the lack of data through the number of companies used.