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Can competition between forecasters stabilize asset prices in learning to forecast experiments?
Abstract
We conduct a learning to forecast asset pricing experiment that assumes that financial advisors and professional forecasters attract more investors when their price forecasts are more accurate. The competition between forecasters implies that the impact of their forecasts on realized market prices evolves endogenously. We investigate how these endogenous impacts affect price dispersion and mispricing relative to the fundamental price. Our results show that the effect of endogenous impacts depends on (i) the type of market dynamics (stable/unstable) and (ii) the sensitivity of impacts with respect to forecast accuracy (low/high). Compared to the baseline treatment, where impacts are constant and independent of forecast accuracy, price dispersion and mispricing is somewhat lower in stable markets when impacts are moderately sensitive to forecast accuracy. In contrast, impacts that are strongly sensitive to forecast accuracy can further destabilize unstable markets, amplifying price dispersion and mispricing.
... Gill and Prowse (2016) show that more cognitively able subjects choose numbers closer to equilibrium, converge more frequently to equilibrium, and earn more. Kopányi et al. (2019) investigate how price dynamics in a learning to forecast (LtF) asset pricing experiment are influenced by financial advisors who attract more investors by forecasting more accurately and are able to influence market prices asymmetrically. Successful financial advisors attract more money and therefore they have a greater impact on market prices. ...
... However, we create an extrinsic asymmetry among subjects in terms of their ability to affect the target. Kopányi et al. (2019) is closely related to ours in terms of both the types of markets it models and the asymmetric impact of the players on the outcome. Our model can also be motivated by the fact that in financial markets, there are investment advisors who manage different account sizes and their impact on the markets differ accordingly. ...
... Our model can also be motivated by the fact that in financial markets, there are investment advisors who manage different account sizes and their impact on the markets differ accordingly. Kopányi et al. (2019) use experimental LtF asset markets in which the impact of players and prices are endogenously determined. We use guessing games to model these markets where the impact of players is different but fixed. ...
This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing r>1 replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (r=1r=1) imitates the strong player (r>1). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases the discrepancy in choices (defined as the squared distance of choices from the winning number) in both games.
... By contrast, in our design, heterogeneity is driven solely by the differing strengths of players to influence the target without any informational asymmetry. Kopányi et al. (2019) investigate how price dynamics in a learning to forecast (LtF) asset pricing experiment are influenced by financial advisors who attract more investors by forecasting more accurately and are able to influence market prices asymmetrically. They motivate their model with the observations that the effects of market participants on market prices may partially depend on past successes. ...
... Our model can also be motivated by the fact that in financial markets, there are investment advisors who manage different account sizes and their impact on the markets differ accordingly. Kopányi et al. (2019) use experimental LtF asset markets in which the impact of players and prices are endogenously determined. We use guessing games to model these markets where the impact of each player is taken as fixed. ...
This paper theoretically and experimentally investigates the behavior of asymmetric players in guessing games. The asymmetry is created by introducing k > 1 replicas of one of the players. Two-player and restricted N-player cases are examined in detail. Based on the model parameters, the equilibrium is either unique in which all players choose zero or mixed in which the weak player (k = 1) imitates the strong player (k > 1). A series of experiments involving two and three-player repeated guessing games with unique equilibrium is conducted. We find that equilibrium behavior is observed less frequently and overall choices are farther from the equilibrium in two-player asymmetric games in contrast to symmetric games, but this is not the case in three-player games. Convergence towards equilibrium exists in all cases but asymmetry slows down the speed of convergence to the equilibrium in two, but not in three-player games. Furthermore, the strong players have a slight earning advantage over the weak players, and asymmetry increases discrepancy in choices (defined as the squared distance of choices from the winning number) in both games.
... In a related bandit experiment, Hanaki et al. (2018) show that providing information about the decisions of others can help maximize profit, while in an exponential bandit problem, Hoelzemann and Klein (2021) find an increase in free-riding on the information produced by partners. Alternatively, one can also study how almost continuoustime affects the evolution of prices in learning-to-forecast experiments (Hommes, 2005, and recently Arifovic andPetersen, 2017 andKopányi, 2019). We leave these ideas for future research. ...
We design an experiment to study how reversible entry decisions are affected by public and private payoff disclosure policies. In our environment, subjects choose between a risky payoff, which evolves according to an autoregressive process, and a constant payoff. The treatments vary the information disclosure rule on the risky payoff, such that in the public information treatment the risky payoff is always observable, while in the private information treatment, the risky payoff is observable only to the participants who enter the market. We find that under private information, market entry is higher, which suggests that subjects engage in exploration and place value on information.
This paper explores the robustness of laboratory expectation formation and public signal credibility to external uncertainty shocks and online experimentation. We exploit the recent pandemic as a source of exogenous background uncertainty in a New Keynesian learning-to-forecast experiment (LtFE) where participants receive projections of varying precision about future inflation. We compare results from identical LtFE completed immediately before the onset of the pandemic, soon after (online), and well after (online and in-person). Baseline LtFEs with no communication are robust to both factors. However, both background uncertainty and online experimentation impact how subjects use public signals. The pandemic led to a decreased appetite for and tolerance of overly precise communication while increasing the efficacy of projections that also convey uncertainty. Subjects became more averse to central bank forecast errors after the onset of the pandemic if the central bank conveyed a precise outlook but not if it conveyed forecast uncertainty.
We study the effects of the investment horizon on asset price volatility using a Learning to Forecast laboratory experiment. We find that, for short investment horizons, participants coordinate on self-fulfilling trend-extrapolating predictions. Price deviations are then reinforced and amplified, possibly leading to large bubbles and crashes in asset prices. For longer investment horizons such bubbles do not emerge and price volatility tends to be lower. This is due to the fact that, for longer horizons, there is more dispersion in participants’ forecasts, and participants extrapolate trends in past prices to a lesser extent. We also show that, independent of the investment horizon, if the initial history of asset prices is already relatively stable before participants start their prediction task, price volatility remains small, with prices close to their fundamental values for the duration of the experiment.
This paper provides original empirical evidence on the emerging practice by central banks of communicating uncertainty in their inflation projections. We compare the effects of point and density projections in a learning-to-forecast laboratory experiment where participants’ aggregated expectations about one- and two-period-ahead inflation influence macroeconomic dynamics. Precise point projections are more effective at managing inflation expectations. Point projections reduce disagreement and uncertainty while nudging participants to forecast rationally. Supplementing the point projection with a density forecast mutes many of these benefits. Relative to a point projection, density forecasts lead to larger forecast errors, greater uncertainty about own forecasts, and less credibility in the central bank’s projections. We also explore expectation formation in individual-choice environments to understand the motives for responding to projections. Credibility in the projections is significantly lower when strategic considerations are absent, suggesting that projections are primarily effective as a coordination device. Overall, our results suggest that communicating uncertainty through density projections reduces the efficacy of inflation point projections.
Asset markets like stock markets are characterized by positive feedback through speculative demand. But the supply of housing is endogenous, and adds negative feedback to the housing market. We design an experimental housing market and study how the strength of the negative feedback, i.e., the price elasticity of supply, affects market stability. In the absence of endogenous housing supply, the experimental markets exhibit large bubbles and crashes because speculators coordinate on trend-following expectations. When the positive feedback through speculative demand is offset by the negative feedback of elastic housing supply the market stabilizes and prices converge to fundamental value. Individual expectations and aggregate market outcome are well described by the heuristics switching model. Our results suggest that negative feedback policies may stabilize speculative asset bubbles.
This experiment compares the price dynamics and bubble formation in an asset market with a price adjustment rule in three treatments where subjects: (1) submit a price forecast only; (2) choose quantity to buy/sell and (3) perform both tasks. We find deviation of the market price from the fundamental price in all treatments, but to a larger degree in treatments (2) and (3). Mispricing is therefore a robust finding in markets with positive expectation feedback. Some very large, recurring bubbles arise, where the price is three times larger than the fundamental value, which were not seen in former experiments.
Adaptive and eductive learning are two widely used ways of modeling the process by which agents learn a rational expectation equilibrium (REE). In this paper we report an experiment where we exploit differences in the conditions under which adaptive and eductive learning converge to REE so as to investigate which approach provides the better description of the learning behavior of human subjects. Our results suggest that the path by which the system converges appears to be a mixture of both adaptive and eductive learning model predictions.
We investigate expectation formation in a controlled experimental environment. Subjects are asked to predict the price in a standard asset pricing model. They do not have knowledge of the underlying market equilibrium equations, but they know all past realized prices and their own predictions. Aggregate demand for the risky asset depends upon the forecasts of the participants. The realized price is then obtained from market equilibrium with feedback from six individual expectations. Realized prices differ significantly from fundamental values and typically exhibit oscillations around, or slow convergence to, this fundamental. In all groups participants coordinate on a common prediction strategy. Copyright 2005, Oxford University Press.
Recent work on complex adaptive systems for modelling financial markets is surveyed. Financial markets are viewed as evolutionary systems between different, competing trading strategies. Agents are boundedly rational in the sense that they tend to follow strategies that have performed well, according to realized profits or accumulated wealth, in the recent past. Simple technical trading rules may survive evolutionary competition in a heterogeneous world where prices and beliefs coevolve over time. The evolutionary model explains stylized facts, such as fat tails, volatility clustering and long memory, of real financial series. Although our adaptive belief systems are very simple, they can match the autocorrelation patterns of returns, squared returns and absolute returns of 40 years of S&P 500 data. Some recent laboratory work on expectation formation in an asset pricing framework is also discussed.
In recent 'learning to forecast' experiments with human subjects (Hommes, et al. 2005), three different patterns in aggregate asset price behavior have been observed: slow mono-tonic convergence, permanent oscillations and dampened fluctuations. We construct a simple model of individual learning, based on performance based evolutionary selection or reinforcement learning among heterogeneous expectations rules, explaining these dif-ferent aggregate outcomes. Out-of-sample predictive power of our switching model is higher compared to the rational or other homogeneous expectations benchmarks. Our results show that heterogeneity in expectations is crucial to describe individual forecast-ing behavior as well as aggregate price behavior.
We evaluate why individuals invest in high-fee index funds. In our experiments, subjects each allocate $10,000 across four
S&P 500 index funds and are rewarded for their portfolio's subsequent return. Subjects overwhelmingly fail to minimize fees.
We reject the hypothesis that subjects buy high-fee index funds because of bundled nonportfolio services. Search costs for
fees matter, but even when we eliminate these costs, fees are not minimized. Instead, subjects place high weight on annualized
returns since inception. Fees paid decrease with financial literacy. Interestingly, subjects who choose high-fee funds sense
they are making a mistake.
We study learning in an individual choice price forecasting task in which subjects must learn coefficients of two independent variables in stationary linear stochastic processes. The 99 subjects each forecast in 480 trials with feedback. Learning is tracked by fitting individual forecasts to the independent variables. Results: (1) Learning is fairly consistent with respect to objective values, but with slight tendency toward overresponse. (2) Learning is noticeably slower than the Marcet-Sargent ideal. Two striking treatment effects are tendencies toward (3) overresponse with high background noise and (4) underresponse with asymmetric coefficients. Copyright 2002, Oxford University Press.
Adaptively rational equilibrium is introduced, where agents adapt their beliefs by choosing from a finite set of predictor functions. Agents make a rational predictor choice, based upon a publically available performance measure such as realized past profits. This results in an adaptive belief system, where predictor choice is coupled to the market equilibrium dynamics. As a typical example, the cobweb model with rational versus naive expectations is analyzed. If the market is locally unstable and rational expectations are costly to obtain, a high intensity of choice for predictor selection leads to chaos and strange attractors.
Evolutionary games are introduced as models for repeated anonymous strategic interaction: actions (or behaviors) which are more "fit," given the current distribution of behaviors, tend over time to displace less fit behaviors. Cone fields characterize the continuous-time processes compatible with a given fitness (or payoff) function. For large classes of dynamics, it is shown that all stable steady states are Nash equilibria and that all Nash equilibria are steady states. The biologists' evolutionarily stable strategy condition is shown to be less closely related to the dynamic equilibria. Economic examples and a literature survey are also provided. Copyright 1991 by The Econometric Society.
We present a large-group experiment in which participants predict the price of an asset, whose realization depends on the aggregation of individual forecasts. The markets consist of 21 to 32 participants, a group size larger than in most experiments. Multiple large price bubbles occur in six out of seven markets. The bubbles emerge even faster than in smaller markets. Individual forecast errors do not cancel out at the aggregate level, but participants coordinate on a trend-following prediction strategy that gives rise to large bubbles. The observed price patterns can be captured by a behavioral heuristics switching model with heterogeneous expectations.
We present a laboratory experiment designed to investigate the effect of the fee structure on mutual fund choice. We find that subjects tend to ignore periodic and small operating expenses fees and base their decisions on gross, instead of net, returns. A fee in the form of a, much larger, front-end load leads to lock-in into one of the funds. It is used by some subjects as a commitment device, but exacerbates the decision errors of other subjects. Although past returns do not convey information about future returns, return chasing helps explain subjects’ behavior.
Capital Asset Pricing Model (CAPM) alpha explains hedge fund flows better than alphas from more sophisticated models. This suggests that investors pool together sophisticated model alpha with returns from exposures to traditional (except for the market) and exotic risks. We decompose performance into traditional and exotic risk components and find that while investors chase both components, they place greater relative emphasis on returns associated with exotic risk exposures that can only be obtained through hedge funds. However, we find little evidence of persistence in performance from traditional or exotic risks, which cautions against investors' practice of seeking out risk exposures following periods of recent success.
Data obtained from monthly Gallup/UBS surveys from 1998 to 2007 and from a special supplement to the Michigan Surveys of Consumer Attitudes and Behavior, run in 22 monthly surveys between 2000 and 2005, are used to analyze stock market beliefs and portfolio choices of household investors. We show that the key variables found to be positive predictors of actual stock returns in the asset-pricing literature are also highly correlated with investor's subjective expected returns, but with the opposite sign. Moreover, our analysis of the microdata indicates that subjective expectations of both risk and returns on stocks are strongly influenced by perceptions of economic conditions. In particular, when investors believe macroeconomic conditions are more expansionary, they tend to expect both higher returns and lower volatility. This is difficult to reconcile with the canonical view that expected returns on stocks rise during recessions to compensate household investors for increased exposure or sensitivity to macroeconomic risks. Finally, the relevance of these investors' subjective expectations is supported by the finding of a significant link between their expectations and portfolio choices. In particular, we show that portfolio equity positions tend to be higher for those respondents that anticipate higher expected returns or lower uncertainty.
This paper discusses aspects of recruiting subjects for economic laboratory experiments, and shows how the Online Recruitment System for Economic Experiments can help. The software package provides experimenters with a free, convenient, and very powerful tool to organize their experiments and sessions.
Do laboratory subjects correctly perceive the dynamics of a mean-reverting time series? In our experiment, subjects receive historical data and make forecasts at different horizons. The time series process that we use features short-run momentum and long-run partial mean reversion. Half of the subjects see a version of this process in which the momentum and partial mean reversion unfold over 10 periods ('fast'), while the other subjects see a version with dynamics that unfold over 50 periods ('slow'). Typical subjects recognize most of the mean reversion of the fast process and none of the mean reversion of the slow process.
We analyze time series of investor expectations of future stock market returns from six data sources between 1963 and 2011.
The six measures of expectations are highly positively correlated with each other, as well as with past stock returns and
with the level of the stock market. However, investor expectations are strongly negatively correlated with model-based expected
returns. The evidence is not consistent with rational expectations representative investor models of returns.
The article presents a temporary equilibrium framework for macroeconomic analysis that allows for a wide range of possible specifications of expectations but reduces to a standard new Keynesian model in the limiting case of rational expectations. This common framework is then used to contrast the assumptions and implications of several different ways of relaxing the assumption of rational expectations. As an illustration of the method, the implications of alternative assumptions for the selection of a monetary policy rule are discussed. Other issues treated include the conditions required for Ricardian equivalence and for existence of a deflation trap.
We review bubble measures which are commonly used in the experimental asset market literature. It seems sensible to require
that measures of mispricing should (i) relate the fundamental value and price, (ii) be monotone in the difference between
fundamental value and price, and (iii) be independent of the total number of periods and the absolute level of fundamental
value. We show that none of the measures currently used fulfills all these criteria. To facilitate comparability across different
experimental settings with different parameterizations we propose two alternative measures which fulfill all evaluation criteria.
The measure for mispricing, RAD (relative absolute deviation), is calculated by averaging absolute differences between the
(volume-weighted) mean price and the fundamental value across all periods and normalizing it with the absolute value of the
average FV of the market. The measure for overvaluation, RD (relative deviation), is calculated analogously, but uses raw
difference between (volume-weighted) mean prices and fundamental values. Hence, it provides information on whether the mispricing
stems from over- or undervaluation of the asset.
KeywordsExperimental economics-Asset market-Bubble-Bubble measure
JEL ClassificationC90-D84-G14
We present results on expectation formation in a controlled experimental environment. In each period subjects are asked to predict the next price of a risky asset. The realized market price is derived from an unknown market equilibrium equation with feedback from individual forecasts. In most experiments prices deviate from the benchmark fundamental and bubbles emerge endogenously. These bubbles are inconsistent with rational expectations and seem to be driven by trend chasing behavior or “positive feedback expectations” of the participants. We also analyze individual predictions of participants and find that participants within a group tend to coordinate on a common prediction strategy.
The evolution of many economic variables is affected by expectations that economic agents have with respect to the future development of these variables. We show, by means of laboratory experiments, that market behavior depends to a large extent on whether realized market prices respond positively or negatively to average price expectations. In the case of negative expectations feedback, as in commodity markets, prices converge quickly to their equilibrium value, confirming the rational expectations hypothesis. In the case of positive expectations feedback, as is typical for speculative asset markets, large fluctuations in realized prices and persistent deviations from the benchmark fundamental price are likely. We estimate individual forecasting rules and investigate how these explain the differences in aggregate market outcomes.
This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their ‘beliefs’ in each period in a boundedly rational way, according to a ‘fitness measure’ such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (‘rational animal spirits’). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.
In repeated number guessing games choices typically converge quickly to the Nash equilibrium. In positive expectations feedback experiments, however, convergence to the equilibrium price tends to be very slow, if it occurs at all. Both types of experimental designs have been suggested as modeling essential aspects of financial markets. In order to isolate the source of the differences in outcomes we present several new experiments in this paper. We conclude that the feedback strength (i.e. the ‘p-value’ in standard number guessing games) is essential for the results.
The authors present a simple overlapping generations model of an asset market in which irrational noise traders with erroneous stochastic beliefs both affect prices and earn higher expected returns. The unpredictability of noise traders' beliefs creates a risk in the price of the asset that deters rational arbitrageurs from aggressively betting against them. As a result, prices can diverge significantly from fundamental values even in the absence of fundamental risk. Moreover, bearing a disproportionate amount of risk that they themselves create enables noise traders to earn a higher expected return than rational investors do. The model sheds light on a number of financial anomalies. Copyright 1990 by University of Chicago Press.
We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
This paper studies the flows of funds into and out of equity mutual funds. Consumers base their fund purchase decisions on prior performance information, but do so asymmetrically, investing disproportionately more in funds that performed very well the prior period. Search costs seem to be an important determinant of fund flows. High performance appears to be most salient for funds that exert higher marketing effort, as measured by higher fees. Flows are directly related to the size of the fund's complex as well as the current media attention received by the fund, which lower consumers' search costs. Copyright The American Finance Association 1998.
We study the existence and robustness of expectationally driven price volatility in experimental overlapping generation economies. In the theoretical model under study there exist "pure sunspot" equilibria which can be "learned" if agents use some adaptive learning rules. Our data show the existence of expectationally driven cycles, but only after subjects have been exposed to a sequence of real shocks and "learned" a real cycle. In this sense, we show evidence of path-dependent price volatility. Journal of Economic Literature, Classification Numbers: C62, C92, F17, E32, E44.
This paper reports an experimental study of expectation formation and revision in a time series context. In an adaptive expectations framework, it is shown that the speed of adjustment seems to fall in turning point periods. Expectations are considered as probability density functions, and a scoring system is devised and employed that gives subjects an incentive to report a measure of the dispersion of these functions. This measure, which is inversely related to the confidence with which expectations are held, seems to be inversely related to past forecasting performance.
We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
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