# Math Graduate Student Seminar

*,*Department of Mathematics

*,*Caltech

*,*

Did you know that from 1926-1979 the stocks of small companies earned on average about 3 times more per year than the stocks of large companies? More specifically, small company stock prices grew 15% per year on average, whereas large company stock prices grew only 5% per year on average. What a huge difference!

How on earth is this possible? Surely over the course of 50 years people would have noticed this pattern. Surely they would have all run to buy small company stocks and run to sell big company stocks. Surely this would have caused market prices to adjust and made the pattern disappear. Evidently this is not what happened.

It turns out that there are tons of patterns like these in the stock market. Asset pricing theory is the area of finance that tries to understand why these patterns exist. I'll present an introduction to the field, focusing on two models: the Capital Asset Pricing Model (CAPM) and the Fama-French 3 Factor Model (FF3). I'll dabble in both the theory (math) and the empirical facts (statistics and data).

No background is needed to understand this talk.