Risk-averse Traders Research Articles

Price Interpretability of Prediction Markets: A Convergence Analysis

Prediction markets are renowned for their accuracy in forecasting. However, it is not fully clear how the predication market aggregates the traders’ beliefs. In “Price Interpretability of Prediction Markets: A Convergence Analysis,” Gao, Wang, Wu, and Yu introduce a novel multivariate utility (MU)-based mechanism that consolidates various existing automated market-making schemes. This mechanism establishes convergence results for markets consisting of risk-averse traders with diverse beliefs who interact repeatedly with the market maker. Furthermore, the study delivers analytical and numerical insights into the limiting price across different market models. Building on these results, the authors offer an efficient approximation scheme for the limiting price, shedding light on how traders’ beliefs shape market prices. These discoveries provide valuable guidance to market designers, enabling them to refine and optimize market-making mechanisms for more efficient opinion elicitation.

Optimal trading and competition with information in the price impact model

Information drives trading and hence affects price dynamics. We study how an informed trader optimally trades, how multiple traders compete with each other, and how their competition affects price dynamics as well as their inventories in the linear price impact model framework. We formulate the informed trading problem as a stochastic optimal control problem and a stochastic differential game in different cases. By virtue of different methods, problems are solved explicitly in all cases. In the case of a single trader, the risk-averse informed trader trades less in the beginning and then speeds up to reduce exposure to the volatility of dynamic information. In addition, the risk-averse trader reveals information more slowly and thus contributes less to price efficiency. When multiple risk-neutral traders compete with information, regardless of the competition structure, they tend to trade more rapidly in the early stage to fill orders at a good price. Competition and the presence of a leader help promote price efficiency, and competition also leads to the empirically observed mean-reverting behavior of price dynamics and order flows. Furthermore, among risk-averse informed traders, inventory management triggers predatory trading and active information leakage during informed trading, and the positions of traders with the same level of risk aversion tend to be identical and mean-reverting to zero under multiple rounds of competition.

Learning equilibrium in bilateral bargaining games

Bilateral bargaining of a single good among one buyer and one seller describes the simplest form of trade, yet Bayes–Nash equilibrium strategies are largely unknown. Only for the average mechanism in the standard independent private values model with independent and uniform priors, we know that there is a continuum of equilibria. However, a non-uniform prior distribution already leads to a system of non-linear differential equations for which closed-form bidding strategies cannot be derived. Recent advances in equilibrium learning provide a numerical approach to equilibrium analysis, which can push the boundaries of existing results and allow for the analysis of environments that have been considered intractable so far. We study Neural Pseudogradient Ascent (NPGA) and Simultaneous Online Dual Averaging (SODA), two new equilibrium learning algorithms for Bayesian auction games with continuous type and action spaces. Although the environment is simple to describe, the continuum of equilibria makes it challenging for equilibrium learning algorithms. Empirically, NPGA finds the payoff-maximizing linear equilibrium, while SODA also finds non-differentiable step-function equilibria. Interestingly, the algorithms also find equilibrium with non-uniform priors and risk-averse traders for which we do not know an analytical solution. We show that the game is not globally monotone, but we can prove local convergence for a model with uniform priors and linear bid functions.

Herding with leading traders: Evidence from a laboratory social trading platform

We provide novel evidence about herd behavior and its impact on asset price bubbles in an experimental financial market. We find that traders imitate quotes of those with the highest wealth increases as ranked on the leader-boards, despite that no traders possess private value-related information and that wealth increases are not due to trading skills. Most remarkably, we find that herd behavior does not produce more price bubbles and the awareness of information asymmetry leads to fewer bubbles as risk-averse traders become more cautious and do not quote prices too far from the fundamental value. We also find that participants with financial training have a lower herding tendency and markets with these participants exhibit less mispricing.

Does risk sorting explain overpricing in experimental asset markets?

Sorting according to the gender or cognitive abilities of the traders has been investigated as a potential source of overpricing in asset markets. Here we study if sorting according to risk attitudes matters, motivated by the fact that filtering out risk-averse investors is practiced widely in Europe and is in line with the Markets in Financial Instruments Directive (MiFID) of the EU.Despite the central role of risk attitude in the literature, our study is the first that sorts participants into markets by risk tolerance and tests its effect on overpricing. We show that risk sorting can explain overpricing only partially: Markets with the most risk-tolerant traders exhibit larger overpricing than markets with the most risk-averse traders. In our study, risk aversion does not correlate with gender or cognitive abilities, bringing in an additional factor to understand overpricing.

RETRACTED: Risk-averse trading strategy for a hybrid power plant in energy and carbon markets to maximize overall revenue

A risk-averse bidding platform has been proposed in this paper to a hybrid power plant (HPP) that participates as a price-taker player in energy, reserve, and ancillary services markets. A carbon trading market is also being discussed, where the HPP can buy and sell additional carbon credits required for the project. The HPP strikes a balance between selling additional carbon credits and generating more power by gas-fired microturbine. The uncertainty of electricity prices is involved using scenario-based stochastic programming. Penalty charges incurred as a result of variation of renewable generation to manage their uncertainty. For multi-step power markets, the suggested optimization framework derives quantity-price curves using the proposed mixed-integer linear programming. The results indicated that considering carbon quota restricts the operation of microturbines and reduces their revenue by about 60%. On the flip side, the available carbon credits make a considerable revenue for the renewable dominant HPP and increase the total expected profit by 30% and cover the loss of revenue of microturbines. The CVaR is applied to maximize the profit over the 25% of scenarios with the least profit resulting in a 5% reduction of the total revenue under a risk-averse strategy.

Risk-Sensitive Optimal Execution via a Conditional Value-at-Risk Objective

We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. The trader encounters a trade-off between the transaction costs incurred due to market impact and the volatility risk of holding the position. Our formulation begins with a continuous-time and infinite horizon variation of the seminal model of Almgren and Chriss (2000), but we define as the objective the conditional value-at-risk (CVaR) of the implementation shortfall, and allow for dynamic (adaptive) trading strategies. In this setting, we are able to derive closed-form expressions for the optimal liquidation strategy and its value function. Our results yield a number of important practical insights. We are able to quantify the benefit of adaptive policies over optimized static policies. The relevant improvement depends only on the level of risk aversion: for moderate levels of risk aversion, the optimal dynamic policy outperforms the optimal static policy by 5-15%, and outperforms the optimal volume weighted average price (VWAP) policy by 15-25%. This improvement is achieved through dynamic policies that exhibit "aggressiveness-in-the-money": trading is accelerated when price movements are favorable, and is slowed when price movements are unfavorable. From a mathematical perspective, our analysis exploits the dual representation of CVaR to convert the problem to a continuous-time, zero-sum game. We leverage the idea of the state-space augmentation, and obtain a partial differential equation describing the optimal value function, which is separable and a special instance of the Emden-Fowler equation. This leads to a closed-form solution. As our problem is a special case of a linear-quadratic-Gaussian control problem with a CVaR objective, these results may be interesting in broader settings.

Optimal trade execution with uncertain volume target

In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as in the power market, in which the volume to be traded can only be estimated and becomes more accurate when approaching a specified delivery time. During the course of execution, a trader should then constantly adapt their trading strategy to meet their fluctuating volume target. In this paper, we develop a model that accounts for volume uncertainty and we show that a risk-averse trader has benefit in delaying their trades. More precisely, we argue that the optimal strategy is a trade-off between early and late trades in order to balance risk associated with both price and volume. By incorporating a risk term related to the volume to trade, the static optimal strategies suggested by our model avoid the explosion in the algorithmic complexity usually associated with dynamic programming solutions, all the while yielding competitive performance.

The Value of USDA Announcements in the Electronically Traded Corn Futures Market: A Modified Sufficient Test with Risk Adjustments

AbstractThe paper assesses the value of USDA information in the electronic corn futures markets. While recent research has documented large price volatility spikes after USDA announcements, increased volatility does not directly translate into value. Using multiple newly developed risk‐premium measures and intraday data, we extend the Carter and Galopin approach based on estimating the risk‐adjusted profits that accrue to advanced USDA information. Using the 2010–2020 period, the analysis demonstrates that USDA announcement surprises have economic value, with WASDE surprises from NASS‐WASDE joint events being always valuable under all risk preferences. While the value is sensitive to these preferences, risk is relatively small because prices usually move in the direction of the market surprise which minimises losses. NASS surprises also contain value, though less than WASDE and only for the less risk averse traders. While overall risk is generally small, the intensified volatility right after the announcement points to the presence of noise and to the inadequacy of inferring the value of public information through price variability alone.

Learning from prices: information aggregation and accumulation in an asset market

Can prices convey information about the fundamental value of an asset? This paper considers this problem in relation to the dynamic properties of the fundamental (whether it is constant or time-varying) and the structure of information available to agents. Risk-averse traders receive two potential signals each period: one exogenous and private and the other, prices, endogenous and public. Prices aggregate private information but include aggregate noise. Information can accumulate over time both through endogenous and exogenous signals. With a constant fundamental, the precision of both private and public cumulative information increases over time but agents put progressively more weight on the endogenous signals, asymptotically disregarding private ones. If the fundamental is time-varying, the use of past private signals complicates the role of prices as a source of information, since it introduces endogenous serial correlation in the price signal and cross-correlation between it and innovations in the fundamental. A modified version of the Kalman filter can still be used to extract information from prices and results show that the precision of the endogenous signals converges to a constant, with both private and public information used at all times.

Risk aversion, public disclosure, and partially informed outsiders

In this paper, we examine the impact of public disclosure and partially informed outsiders on a risk-averse insider’s trading behavior, market efficiency, and market depth. In our model, under disclosure requirements, except for the final auction, market depth is the same at every auction. When informed outsiders are risk-neutral, in contrast to the case of a risk-averse insider with no informed outsiders, the insider is more concerned about the uncertainty about future price risk. When the number of informed outsiders increases, market liquidity improves, and the insider increases the variance of her random component to conceal her trading strategy. However, since the insider is relatively more risk-averse, she pays less attention to doing this on her own. Besides, the order flow provided by informed outsiders and randomly added by the insider injects additional liquidity into the market. When informed outsiders are risk-averse, compared to risk-neutral informed outsiders, an insider is most concerned about trading risks brought by informed outsiders at the beginning of trading. Furthermore, whether the trader is an insider or informed outsider, the more risk-averse trader has lower expected profits. Moreover, outsiders’ greater risk aversion leads to a smaller market depth.

Learning From Prices: Information Aggregation and Accumulation in an Asset Price Model

Can prices convey information about the fundamental value of an asset? This paper considers this problem in relation to the dynamic properties of the fundamental (whether it is constant or time-varying) and the structure of information available to agents. Risk-averse traders receive two potential signals each period: one exogenous and private and the other, prices, endogenous and public. Prices aggregate private information but include aggregate noise. Information can accumulate over time both through endogenous and exogenous signals. With a constant fundamental, the precision of both private and public cumulative information increases over time but agents put progressively more weight on the endogenous signals, asymptotically disregarding private ones. If the fundamental is time-varying, the use of past private signals complicates the role of prices as a source of information, since it introduces endogenous serial correlation in the price signal and cross-correlation between it and innovations in the fundamental. A modified version of the Kalman filter can still be used to extract information from prices and results show that the precision of the endogenous signals converges to a constant, with both private and public information used at all times.

Market or limit orders?

In this paper we investigate the problem of optimal order placement of an asset listed on an exchange using both market and limit orders in a simple model of market dynamics. We seek to understand under which settings it is optimal to place limit or market orders. Limit orders typically lower transaction costs but increase the risk of incomplete order execution, whereas market orders typically have higher transaction costs but are guaranteed to be executed. Rather than considering order book dynamics to determine if a limit order is executed we rely on price dynamics for this. We look at implementation shortfall in this setup with market impact of trading and propose a dynamic program to find the optimal placement of both market and limit orders for risk-neutral and risk-averse traders. With this we find a bound on the expected cost of trading and show that a trader who behaves optimally should always expect to pay less to trade less. We then solve the dynamic program numerically and examine optimal order placement strategies. We find that the decision between market and limit orders is sensitive to price volatility, risk aversion, and trading costs.

Does Risk Sorting Explain Bubbles?

A recent stream of experimental economics literature studies the factors that contribute to the emergence of financial bubbles. We consider a setting where participants sorted according to their degree of risk aversion trade in experimental asset markets. We show that risk sorting is able to explain bubbles partially: Markets with the most risk-tolerant traders exhibit larger bubbles than markets with the most risk averse traders. In our study risk aversion does not correlate with gender or cognitive abilities, so it is an additional factor that helps understand bubbles.

The Valuation of Cryptocurrencies in Single-Asset and Multiple-Asset Models

Cryptocurrencies are virtual currencies employed in blockchain transactions. They are particularly worthy of theoretical examination, given the limited academic literature on the subject. This paper constructs valuation models of bitcoin and altcoins, both as single investments and components of mutliple-asset portfolios. As single investments, cryptocurrencies are valued at the confluence of Legendre utility functions, with Esscher transformed Geometric Levy pricing processes. As part of portfolios, cryptocurrencies are contained in traditional Markowitz portfolios which are varied by increasing the proportion of the riskless asset, shorting the risky asset, or adding currency options. Theoretical formulations show that Markowitz models combined with bitcoin, located on the Capital Market Line (which we term CML portfolios), have low returns, mainly due to the presence of the riskless asset. Such portfolios are appropriately suited to the investment goals of risk-averse traders, while overlooking the preferences of risk-takers. To satisfy less risk-averse investors, we propose a high-return portfolio with 9 asset choices, consisting of risky assets, cryptocurrencies, US dollars, soybean futures, Treasury bond futures, oil futures, currency options on the US dollar, currency options on the Mexican peso, and technology, or biotechnology stocks. Laplace transforms are employed to suppress volatility, skewness, or kurtosis of returns, which empirical studies have found to contribute to tail risk contained in outliers in fat-tailed distributions.

Strategic trading with risk aversion and information flow

We analyze a dynamic auction model in which competitive risk-averse traders optimally exploit their long-lived homogeneous private information regarding the value of an asset. The asset's terminal value depends on both the traders' initial signal and a sequence of zero-mean information shocks — private and/or public — that arrive at each auction. Traders balance the risks of noise trade imbalances, which can be avoided by trading early, and the risks of these persistent shocks, which can be avoided by trading later. Despite competition among the informed traders, observed trade patterns can resemble a “waiting game” rather than a “rat race.”

Neural Correlates of Direct Access Trading in a Real Stock Market: An fMRI Investigation.

Background: While financial decision making has been barely explored, no study has previously investigated the neural correlates of individual decisions made by professional traders involved in real stock market negotiations, using their own financial resources.Aim: We sought to detect how different brain areas are modulated by factors like age, expertise, psychological profile (speculative risk seeking or aversion) and, eventually, size and type (Buy/Sell) of stock negotiations, made through Direct Access Trading (DAT) platforms.Subjects and methods: Twenty male traders underwent fMRI while negotiating in the Italian stock market using their own preferred trading platform.Results: At least 20 decision events were collected during each fMRI session. Risk averse traders performed a lower number of financial transactions with respect to risk seekers, with a lower average economic value, but with a higher rate of filled proposals. Activations were observed in cortical and subcortical areas traditionally involved in decision processes, including the ventrolateral and dorsolateral prefrontal cortex (vlPFC, dlPFC), the posterior parietal cortex (PPC), the nucleus accumbens (NAcc), and dorsal striatum. Regression analysis indicated an important role of age in modulating activation of left NAcc, while traders' expertise was negatively related to activation of vlPFC. High value transactions were associated with a stronger activation of the right PPC when subjects' buy rather than sell. The success of the trading activity, based on a large number of filled transactions, was related with higher activation of vlPFC and dlPFC. Independent of chronological and professional age, traders differed in their attitude to DAT, with distinct brain activity profiles being detectable during fMRI sessions. Those subjects who described themselves as very self-confident, showed a lower or absent activation of both the caudate nucleus and the dlPFC, while more reflexive traders showed greater activation of areas involved in strategic decision making.Discussion: The neural correlates in DAT are similar to those observed in other decision making contexts. Trading is handled as a well-learned automatic behavior by expert traders; for those who mostly rely on heuristics, cognitive effort decreases, and transaction speed increases, but decision efficiency lowers following a poor involvement of the dlPFC.

Information and Competition with Symmetry

This paper investigates the strategic foundations for rational expectations equilibrium. In the model, risk-averse traders with two signals — private information and endowment shocks — submit demand schedules to trade a risky asset. Traders are divided into groups. Within groups, traders share common signals; signals are different across different groups. Either traders become price takers or the price becomes fully revealing, but not both, as the number of competitors per group goes to infinity. As the number of groups goes to infinity, neither price taking nor fully revealing prices are obtained. Measuring competition by the quantity traded as a fraction of that traded by a price-taker, we show that optimal exercise of market power has opposite implications for competition and price informativeness.

Evaluating the efficacy of regionalisation in limiting high-risk livestock trade movements

Many countries implement regionalisation as a measure to control economically important livestock diseases. Given that regionalisation highlights the difference in disease risk between animal subpopulations, this may discourage herd managers in low-risk areas from purchasing animals from high-risk areas to protect the disease-free status of their herds. Using bovine tuberculosis (bTB) in New Zealand as a case example, we develop a novel network simulation model to predict how much the frequency of cattle movements between different disease control areas (DCAs) could theoretically change if herd managers adopted the safest practices (preferentially purchasing cattle from areas with the lowest risk of bTB), if herd managers adopted the riskiest practices (preferentially purchasing cattle from areas with the greatest risk of bTB), or if herd managers made trade decisions completely at random (purchasing cattle without consideration for bTB disease risk). A modified configuration wiring algorithm was used in the network simulation model to preserve key temporal, spatial, and demographic attributes of cattle movement patterns. The simulated frequencies of cattle movements between DCAs in each of the three behavioural scenarios were compared with the actual frequency of cattle movements that occurred between 1st July 2010 and 30th June 2011. Our results showed that the observed frequency of cattle movements from high-risk areas into low-risk areas was significantly less than if trade decisions were made completely at random, but still significantly greater than if herd managers made the safest possible trade decisions. This suggests that while New Zealand cattle farmers may have adopted risk-averse trading behaviour in response to regionalisation, there are other underlying factors driving livestock trade, such as established supplier-buyer relationships and heterogeneous individual perceptions towards disease risk, which may reduce the potential efficacy of regionalisation as a disease control strategy. Physical constraints and socio-psychological factors that determine herd managers’ livestock trading behaviour warrant further studies to better understand how herd managers respond to future livestock disease regulations. The flexibility of a network re-wiring framework presented in this study allows such a behavioural response to be incorporated into a disease simulation model, which will in turn facilitate a better evaluation of disease control strategies.

Central Counterparties and Strategic Reduction of Systemic Risk

This paper studies a dynamic network economy, where risk averse traders trade multi-laterally over the counter but cannot commit to fulfil their short positions. We show that, although the level of trade is below the first-best, bilateral clearing with collateral can provide an allocation superior to those without collateral. However, with use of collateral, the optimal bilateral clearing contract leads to multiple equilibria, one of which is a scenario of systemic default where defaulting one’s trading partner will trigger the victim to default his trading partners, and so on, causing the spread of contagious default. We show that a simple arrangement with central counterparty clearing (CCP) can eliminate the systemic risk of default contagion, and raise the level of trade, but at the cost of higher level of collateral. We show that whether CCP is essential depends on the opportunity cost of collateral, the discount rate, and the traders’ endowment and risk aversion.