Trading with securities and stock indices is becoming increasingly popular among investors. Stock exchange trading allows investors to hedge their market risk while also providing a good investment opportunity, and in some cases, they can take advantage of arbitration conditions. The Johannesburg Securities Exchange (JSE) is the world's 16th largest stock exchange and the largest of Africa's 22 stock exchanges. Market capitalization stood at R4 029 billion at the end of December 2003, up from R1 160 billion five years earlier. In this project, we aim to investigate methods to model and predict exchange value sequences for the JSE stock. In doing so, we employ Markov Chains, which is commonly used in this context, and benchmark our model with other popular machine learning techniques. We find that Markov Chains are very effective in this context, given its capacity to model time series data.