Goursat’s Lemma is an elementary, but perhaps niche, result in group theory classifying subdirect products of the product of two groups. In this talk, I will review what this lemma says, and describe how it can be used to deduce the irreducibility of Galois representations.

Stock market traders who trade because of information they possess reveal that information to the rest of the market in the process of bidding: if the information is positive they bid up the price, and if it is negative they lower it.   New information constantly develops and is brought to the market in this way, and because it influences prices, it ultimately influences the allocation of investments by firms.  

 

Using a new approach, we estimate the flow of this information and the price of that information (different from the stock price), and thus its value, for each stock, and then sum up this value across all stocks, obtaining an estimate of the total value of the dynamic flow of information in the stock market as a whole. This requires digesting the records of millions of stock orders (including cancelled orders, not just executed trades) to construct the dynamic limit order book and estimate the information flow and value from its structure.  

 

Our results support the notion that the cross-correlation of price impact across stocks is consistent with the CAPM: there is a single systematic component of price impact, and this is driven by the volatility of the systematic component of the stock market. This result suggests that by separating the underlying information into two components, systematic and idiosyncratic, informed traders distinguish between productive assets that have a systematic impact on the economy and those that can be diversified.