Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions
Department of Economics
The structure of many models in economics and finance depends on majorization properties of convolutions of distributions. In this paper, we analyze robustness of these properties and the models based on them to heavy-tailedness assumptions. We show, in particular, that majorization properties of linear combinations of log-concavely distributed signals are reversed for very long-tailed distributions. As applications of the results, we study robustness of monotone consistency of the sample mean, value at risk analysis and the model of demand-driven innovation and spatial competition as well as that of optimal bundling strategies for a multiproduct monopolist in the case of an arbitrary degree of complementarity or substitutability among the goods. The implications of the models remain valid for not too heavy-tailed distributions. However, their main properties are reversed in the very thick-tailed setting.
Market Efficiency, Bayes' Rule and the Recency Bias
Ph.D. Candidate in Financial Economics
Yale School of Management
There is a large psychological and behavioral literature that claims that Bayes' rule is not a valid model of the human decision process. The strongest evidence proposed in financial markets against Bayes' rule is long-term overreaction (De Bondt and Thaler (1985)) and excess volatility (Shiller (1981)). Under a random walk model of market efficiency simulations support these claims. I propose a random walk with noise model as an intuitively appealing alternative for market efficiency. I demonstrate that within a Bayesian framework that both these market anomalies are consistent and predicted under a random walk with noise, resolving some long-standing debates. The intuition is simple. Under a random walk prices must adjust fully and immediately to new information. This constraint binds price behavior and causes violations of many observed market phenomenon. However, under a random walk with noise, there is an extra degree of freedom, the signal to noise ratio, which breaks this overly restrictive constraint of immediate and full reaction. My model allows me to be the first to empirically estimate the signal to noise ratio in the market. I find a significant level of noise with the variance of noise about 5 times that of information.
Some Remarks about the Methodology and the Mythology of Financial Markets
Department of Mathematics and Statistics
Many aspects of modern finance stem from the belief that, generally, one can think of daily rates of return from stocks as independent samples from one and the same (stock specific) probability law. I will briefly review some of the key statistical tests that have been used in the past to justify this claim and will show with a concrete example that the results from these tests are just as compatible with time series that exhibit self-regulatory behavior and are therefore very different from random walks. Another common belief among some practitioners is that, unless the returns behave as random walks, there will be fortunes to be made on the stock market out of nothing. This is quite surprising, because the conditions under which markets allow or do not allow arbitrage have been studied extensively in the last 20 years and it has long been established that very general models for stock prices are arbitrage free. I will briefly review the principles from which such conditions can be derived and will propose an alternative to the random walk model for stock returns.