Using Entropy to Measure Risk in US Stock Prices

Name: Latif Fetahaj

Mentor: Glenn Miller

Abstract: In this project we use the concept of entropy, specifically as defined in information theory, to rate various securities in terms of their risk. Entropy quantifies how much is not known in an event, uncertainty. A difference between entropy and information is that entropy measures the unknown, and information is the known part. Information allows us to make a more accurate prediction about a future event, in this case the stock market. We use two approaches to test the data. First, we look for patterns in when the security increased in price (coded as 1) or decreased (coded as 0). In the second approach we tested the data in 5 levels, considering changes in the stock price as a dramatic decrease (coded as 0), slight decrease (1), relatively unchanged (2), slight increase (3), and dramatic increase (4). The first approach did not significantly reduce the entropy compared to a random sequence, whereas the second approach gives us more information making the stock price for certain companies more predictable, that is less risky, than others.