Stock prices periodically dip and go up. We will take a look at the probability distribution of the stock price log returns and try a very simple strategy. This strategy is based on regression towards the mean. This is a concept originally discovered in genetics by Sir Francis Galton. It was discovered that children of tall parents tend to be shorter than their parents. Children of short parents tend to be taller than their parents. Of course, this is a statistical phenomenon and doesn't take into account fundamental factors and trends such as improvement in nutrition. Regression towards the mean is also relevant to the stock market. However, it gives no guarantees. If a company starts making bad products or makes bad investments, regression towards the mean will not save the stock.

Let's start by downloading the historical data for a stock, for instance, AAPL. Next, we calculate the daily log returns (http://en.wikipedia.org/wiki/Rate_of_return) of the close...