Nonlinear Price Dynamics of S&P 100 Stocks

The methodology presented provides a quantitative way to characterize investor behavior and price dynamics within a particular asset class and time period. The methodology is applied to a data set consisting of over 250,000 data points of the S&P 100 stocks during 2004-2018. Using a two-way fixed-effects model, we uncover trader motivations including evidence of both under- and overreaction within a unified setting. A nonlinear relationship is found between return and trend suggesting a small, positive trend increases the return, while a larger one tends to decrease it. The shape parameters of the nonlinearity quantify trader motivation to buy into trends or wait for bargains. The methodology allows the testing of any behavioral finance bias or technical analysis concept

Slow-Fast Analysis of a Multi-Group Asset Flow Model with Implications for the Dynamics of Wealth

The multi-group asset flow model is a nonlinear dynamical system originally developed as a tool for understanding the behavioral foundations of market phenomena such as flash crashes and price bubbles. In this paper we use a modification of this model to analyze the dynamics of a single-asset market in situations when the trading rates of investors (i.e., their desire to exchange stock for cash) are prescribed ahead of time and independent of the state of the market. Under the assumption of fast trading compared to the time-rate of change in the prescribed trading rates we decompose the dynamics of the system to fast and slow components. We use the model to derive a variety of observations regarding the dynamics of price and investors’ wealth, and the dependence of these quantities on the prescribed trading rates. In particular, we show that strategies with constant trading rates, which represent the well-known constant-rebalanced portfolio (CRP) strategies, are optimal in the sense that they minimize investment risks. In contrast, we show that investors pursuing non-CRP strategies are at risk of loss of wealth, as a result of the slow system not being integrable in the sense that cyclic trading rates do not always result in periodic price variations

Does Price Efficiency Increase with Trading Volume? Evidence of Nonlinearity and Power Laws in ETFs

Whether efficiency increases with increasing volume is an important issue that may illuminate trader strategies and distinguish between market theories. This relationship is tested using 124,236 daily observations comprising 68 large and liquid U.S. equity exchange traded funds (ETFs). ETFs have the advantage that efficiency can be measured in terms of the deviation between the trading price and the underlying net asset value that is reported each day. Our findings support the hypothesis that the relationship between volume and efficiency is nonlinear. Indeed, efficiency increases as volume increases from low to moderately high levels, but then decreases as volume increases further. The first part tends to support the idea that higher volume simply facilitates transactions and maintains efficiency, while the latter part, i.e., even higher volumes, supports the ansatz that increased volume is associated with increased speculation that ignores valuation and decreases efficiency. The results are consistent with the hypothesis that valuation is only part of the motivation for traders. Our methodology accounts for fund heterogeneity and contemporaneous correlations. Similar results are obtained when daily price volatility is introduced as an additional independent variable

The Set of Hemispheres Containing a Closed Curve on the Sphere

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you\u27ve traveled less than 2πR. Does your path, γ, have to lie in some hemisphere? This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that the curve must be contained in the Northern Hemisphere. This type of proof not only answers the existence question, but also yields a specific hemisphere that contains your path. We, however, thought the problem lent itself nicely to integral geometry, which required us to consider the space whose points are hemispheres. This led to a different existence proof and to a solution of the more general question: can you describe and measure the set of all hemispheres that contain γ? An outline of the remainder of this paper follows. In Section 2 we introduce terminology and definitions. The existence of at least one hemisphere containing γ is proved using the ideas of integral geometry in Section 3. Classifying sets of such hemispheres for a single arc, a geodesic triangle, and a geodesic quadrilateral is accomplished in Section 4. Section 5 contains a discussion of convexity on the sphere and how it relates to our question. Our main theorem is stated and proved in Section 6

Let’s Chat... When Communication Promotes Efficiency in Experimental Asset Markets

The growing prevalence of stock market chat rooms and social media suggests communication between traders may affect market outcomes. Using data from a series of laboratory experiments, we study the causal effect of trader communication on the price efficiency of markets. We show that communication allows markets to convey private information more effectively. This effect is most pronounced when the communication platform publicizes a reputation score that might identify a person as not being truthful. This illustrates the need for market designers to consider social interactions when designing market institutions to leverage the social motives that foster information aggregation

Information Aggregation and the Cognitive Make-up of Traders

We assess the effect of the cognitive make-up of traders on the informational efficiency of markets. We put forth that cognitive skills, such as cognitive reflection, are crucial for ensuring the informational efficiency of markets because they endow traders with the ability to infer others’ information from prices. Using laboratory experiments, we show that information aggregation is significantly enhanced when (i) all traders possess high levels of cognitive sophistication and (ii) this high level of cognitive sophistication is common information for all traders. Our findings shed light on the cognitive and informational constraints underlying the efficient market hypothesis

Nonlinear Dynamics and Stability In a Multigroup Asset Flow Model

The multigroup asset flow model for asset price dynamics incorporates distinct motivations, e. g., trend and fundamentals (value) and assessments of value by different groups of investors. The stability and bifurcation properties are established for the curve of equilibria. We prove that if all trader groups focus on fundamentals, then all equilibria are stable. For systems in which there is one fundamental and one momentum (trend) group, we establish conditions for stability. In particular, an equilibrium that is stable becomes unstable as the time scale on which momentum investors focus diminishes. The computations examine the excursions, which we define as the maximum deviation in price of the trajectory from its initial price located near the curve of equilibria

Trading Volume and Public Information in an Experimental Asset Market with Short-Horizon Traders

We examine the joint impact of investors’ trading horizons and public information on trading volume. We hypothesize that public information leads to relative homogenization in the traders’ beliefs about the fundamental value of an asset and this reduces their disagreement regarding the fundamental value. Since the long-horizon traders’ trade is motivated by the fundamental value, such reduced disagreement leads to a reduction in trading volume. We further hypothesize that public information leads to polarization in the traders’ beliefs about other traders’ beliefs about the fundamental value and this polarization increases disagreement regarding other traders’ beliefs about the fundamental value. Since short-horizon traders’ trade is motivated by other traders’ beliefs about the fundamental value, such increased disagreement leads to an increase in trading volume. We test these hypotheses in an experimental asset market and find strong evidence in their support

Revisiting Information Aggregation in Asset Markets: Reflective Learning & Market Efficiency

The ability of markets to aggregate disperse information leading to prices that reflect the fundamental value of an asset is key to assessing the often-debated efficiency of markets. We study information aggregation in the experimental environment originally created by Plott and Sunder (1988). Contrary to the current belief, we find that markets do not aggregate information. The model that best describes our data, as well as data on information aggregation subsequent to Plott and Sunder (1988), is prior information (Lintner, 1969). That is, traders use their private information but fail to use market prices to infer other traders’ information. We argue that reflecting on asset prices to infer others’ information requires specific skills related to the concept of cognitive reflection. We develop a learning model in which only a subset of the traders possess this reflective capacity. We show, using both simulations and laboratory experiments, that information aggregation can only be achieved when the market is populated by highly reflective traders and this high level of cognitive reflection is commonly known to all of the traders

The Nonlinear Price Fynamics of US Equity ETFs

We investigate the price dynamics of large market-capitalization U.S. equity exchange-traded funds (ETFs) in order to uncover trader motivations and strategy. We show that prices of highly liquid ETFs can deviate significantly from their daily net asset values. By adjusting for changes in valuations, we report the impact of non-classical variables including price trend and volatility using data from 2008 to 2011. We find a cubic nonlinearity in the trend suggesting that traders are not only aware of the underreaction of others, but also self-optimize by anticipating others\u27 reactions, and sell when the uptrend is stronger than usual