Quantal Response Statistical Equilibrium (QRSE) models the joint probability distribution of asset returns and entropy constrained buy/sell decisions of investors and in doing so offers a behavioral foundation for many of the stylized facts we commonly observe in the distributions of asset returns and economic data such as fat-tails, excess peakedness, and skew. In a QRSE market model, investors condition the distribution of probabilistic buy/sell decisions on the extent to which investments offer above or below average returns. By modeling both returns and actions as probabilistic, QRSE is able to explain the marginal distributions of asset returns as the result of two opposing forces: 1) informational shocks that act as an underlying “natural” source of dispersion; 2) the tendency of investors to buy low/sell high that causes a mean-reversion dynamic, which decreases the entropy of the returns distribution we actually observe.
In this thesis, I introduce three new QRSE distributions each derived using the Maximum Entropy Principle. The first is a simple three parameter symmetric QRSE distribution that can fit and, therefore, provide a behavioral foundation for many commonly observed distributions including the Laplace, Gaussian, Logistic, and Student's T distributions. I then introduce a generalized maxent QRSE framework for expanding the assumptions of the basic model. I use this framework to derive two additional QRSE models that allow for skew: one that assumes skew is an implicit characteristic of the underlying data generating process and one that assumes that skew is due to asymmetric buy/sell preferences of investors. I also include two empirical applications. First, I apply QRSE to cross-sectional US equity returns. Second, I apply QRSE to 10 year US Treasury yields in a multiple equilibrium setting using a QRSE hidden Markov model.
|Advisor:||Foley, Duncan K.|
|Commitee:||Scharfenaker, Ellis, Semmler, Willi, dos Santos, Paulo|
|School:||The New School|
|School Location:||United States -- New York|
|Source:||DAI-A 79/12(E), Dissertation Abstracts International|
|Keywords:||Economics, Financial econometrics, Information theory, Maximum entropy, Quantal response statistical equilibrium, Rational inattention|
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