# Studying the anomalies mathematically

The efficient market theory which says that there’s nothing in the data, let’s say price data, which will indicate anything about the future, because the price is sort of always right, the price is always right in some sense. But that’s just not true. According to the famous mathematician, James Simons, there's some mathematical ways to predict prices. There's some anomalies in the data we could study. These are not big anomalies, since otherwise people could see them quickly and predict them. Then these anomalies have to be small and put together can allow to predict well the stock market. I know the mathematics behind is basically statistical, but I do not know where to start.

What types of anomalies can James Simons refer to build his models? How could we study, predict them mathematically?

• This is a bit too broad and my knowledge is a bit too lacking to write a good answer. However I can point you to the book Inside the Black Box by Rishi Narang that gives descriptions of typical quant strategies involving momentum, mean reversion, and correlation. Simons and his firm Ren Tech were pioneers in the field of quant strategies and remain some of the most successful investors ever. Strategies using information other than prices and correlations, such as looking at the order flow and scraping news articles are common now as well. – spaceisdarkgreen Aug 13 '17 at 22:43

Hedging is another good strategy. For example a $-1$ or close to $-1$ correlation of the share prices of two rival companies (Apple and Microsoft was used once as an example). If one goes up, the other one goes down and vice-versa. Investing in both will reduce the risk of huge losses compared to investing only in one.