Random Walk Theory is a principle used in economics, mathematics and other sciences to describe a statistical process. It postulates that the magnitude and direction of price movements of a security are impossible to predict due to the chaotic nature of the markets. The belief is that the same process that drives future prices of the security is the same process that was used to determine the security's past performance.

The basis of Random Walk Theory is that the magnitude of the next price movement is unpredictable. This is known as price uncertainty. At any given time, the price of a security can go up or down by a large or small amount and in any direction. Therefore, it is impossible to foresee or predict with any accuracy the future changes in a security's price. As such, investors have to rely on their best guess, which is certainly not a reliable approach for maximizing returns.

Random Walk Theory argues that technical and fundamental analysis are both unreliable methods of predicting the future direction of a security. Technical analysis can result in investors buying or selling a security after the move has already occurred meaning they miss out on the best returns. Meanwhile, fundamental analysis relies on collecting and interpreting often-poor quality data, meaning that the data can be misinterpreted.

Overall, Random Walk Theory implies that it is impossible to outperform the market without assuming additional risks. Furthermore, it suggests that investment advisers don't really add value to an investor's portfolio, as they cannot predict the future performance of a security. Therefore, investors are best suited to use a buy-and-hold strategy or an indexed fund based on their risk preferences.

Overall, Random Walk Theory is a useful tool for understanding market volatility and helping investors formulate an optimal long-term strategy. By placing the emphasis on market uncertainty and unpredictability, the theory highlights the need for investors to diversify across multiple assets, rather than trying to pursue a risky strategy in the hope of outperforming the market.