We survey the nascent literature on machine learning in the study of financial markets. We highlight the best examples of what this line of research has to offer and recommend promising directions for future research. This survey is designed for both financial economists interested in grasping...

We propose a statistical model of differences in beliefs in which heterogeneous investors are represented as different machine learning model specifications. Each investor forms return forecasts from their own specific model using data inputs that are available to all investors. We measure...

The extant literature predicts market returns with "simple" models that use only a few parameters. Contrary to conventional wisdom, we theoretically prove that simple models severely understate return predictability compared to "complex" models in which the number of parameters exceeds the...

We theoretically characterize the behavior of machine learning asset pricing models. We prove that expected out-of-sample model performance--in terms of SDF Sharpe ratio and test asset pricing errors--is improving in model parameterization (or "complexity"). Our empirical findings verify the...

We have seen in the past decade a sharp increase in the extent that companies use data to optimize their businesses. Variously called the `Big Data' or `Data Science' revolution, this has been characterized by massive amounts of data, including unstructured and nontraditional data like text and...

Despite the clear success of forecast combination in many economic environments, several important issues remain incompletely resolved. The issues relate to selection of the set of forecasts to combine, and whether some form of additional regularization (e.g., shrinkage) is desirable. Against...

We survey the recent literature on learning in financial markets. Our main theme is that many financial market phenomena that appear puzzling at first sight are easier to understand once we recognize that parameters in financial models are uncertain and subject to learning. We discuss phenomena...

This paper studies the predictability of ultra high-frequency stock returns and durations to relevant price, volume and transactions events, using machine learning methods. We find that, contrary to low frequency and long horizon returns, where predictability is rare and inconsistent,...

Optimal investment of firms implies that expected stock returns are tied with the expected marginal benefit of investment divided by the marginal cost of investment. Winners have higher expected growth and expected marginal productivity (two major components of the marginal benefit of...