作者Malkiel将随机漫步的概念和理论进行了扩展，提出了一种观点，即安全的主动交易是以下命题。正是由于交易成本的随机性，价格变动才说明作者提出的命题(Chitenderu, Maredza and Sibanda, 2014)。通过对不同的股票市场指数进行投资，买入并持有交易管理的理念，并将其与短期交易策略进行技术分析比较，认为这是一种较好的交易策略。
According to the random walk theory, a stock’s existing market price is a result of chance rather than the summation of previous events or the outcome of the model of human behaviour. The random walk theory is considered as a hotly debated subject, and there are many debates occur in this subject among the academic scholars, financial analyst and the investors. The individual prices movement or price changes of an actively traded stock are illustrated to be random and thus any prediction of future price fluctuations must be considered as a faulty exercise (Bougioukou, 2015).
According to the scholars who support the random walk theory, the future movement of the security price is widely unpredictable than the past one. The idea is the key for the random walk theory. In case the present market price of a stock is a full representation of the actual value of the stock, then there is not any way to analysis, which can give an appropriate insight into where the security price will move in future.
The author Malkiel made expansion of the concepts and theory of random walk by provide an argument that the active trading of security is the following proposition. It is because of the transaction cost random characteristics of the price movement which indicates the explanation of the proposition made by the author (Chitenderu, Maredza and Sibanda, 2014). The investment are implemented on different stock market indices to buy and hold philosophies of trade management and it is considered as far better trading strategy by Malkiel with comparing to the short term trading strategies by technical analysis.