Distribution Of Returns Research Articles

Long-span multi-layer spillovers between moments of advanced equity markets: The role of climate risks

In this paper, we examine the potential spillovers between returns, volatility, skewness and kurtosis of developed stock markets under the lenses of rare disaster events, proxied by climate risks. The aforementioned moments based on model-implied distributions of stock returns are derived from the quantile autoregressive distributed lag mixed-frequency data sampling (QADL-MIDAS) method, using a long span of data. The empirical findings are as follows: firstly, spillovers are significant within- and across stock markets for each of the four moments. Secondly, based on a nonparametric causality-in-quantiles approach, changes in temperature anomalies, have the predictive power to shape the entire conditional distribution of various metrics of spillover involving single- and multiple-layers of returns and risks layers. In sum, we show that the multi-layer approach offers a comprehensive and nuanced view of how stock market-related information is transmitted across the stock markets of advanced economies, carrying implications for investors and policymakers.

An L-Moment Approach for Portfolio Choice under Non-Expected Utility

Abstract We develop and apply a novel semi-parametric estimation method based on L-moments. Unlike conventional moments, L-moments are linear in the data and therefore robust to outliers. The estimation method provides a series expansion that quickly converges to the underlying return distribution and can be used when conventional moments do not exist. An extensive empirical analysis of portfolio choice under non-expected utility demonstrates the effectiveness of our approach. Empirical results show that our method copes well with estimation risk, yields stable portfolio returns, and reaps the information content of moment returns beyond order four.

Taming Data‐Driven Probability Distributions

ABSTRACTWe propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. By allowing complex time series patterns to be learned from a data‐rich environment, our approach is useful for decision making that depends on the uncertainty of a large number of economic outcomes. In particular, it is informative for agents facing asymmetric dependence of their loss on the outcomes of possibly non‐Gaussian and nonlinear variables. We demonstrate the usefulness of the proposed approach on two different datasets where a machine learns patterns from the data. First, we illustrate the gains in predicting stock return distributions that are heavy tailed and asymmetric. Second, we construct macroeconomic fan charts that reflect information from a high‐dimensional dataset.

Entropy corrected geometric Brownian motion

The geometric Brownian motion (GBM) is widely used for modeling stochastic processes, particularly in finance. However, its solutions are constrained by the assumption that the underlying distribution of returns follows a log-normal distribution. This assumption limits the predictive power of GBM, especially in capturing the complexities of real-world data, where deviations from log-normality are common. In this work, we introduce entropy corrections to the GBM framework to relax the log-normality constraint and better account for the inherent structures in real data. We demonstrate that as the deterministic components within the data increase, entropy decreases, leading to refinements in GBM’s predictive accuracy. Our approach shows significant improvements over conventional GBM in handling distributions that deviate from log-normal behavior, as demonstrated through both a simple dice roll experiment and real-world financial data. Beyond just financial modeling, this research also opens up new avenues for generating synthetic data that better captures real-world complexity, enhancing applications in fields like machine learning and statistical modeling.

Information Asymmetric Cooperative Public Choice Games

This paper introduces information asymmetry, cooperation and payoff compensation mechanism into public choice games, and establishes an analytical frame for information asymmetric cooperative public choice games. This paper examines the coalition formation and the distribution of the cooperative payoff under the equilibrium public choice (if it does exist) in an information asymmetric public choice game under unanimity rule and those in an information asymmetric public choice game under majority rule, respectively. Arrow [1951] and Sen [1970] assumed that there is no cooperation and payoff compensation mechanism in a public choice game, and showed that rational individuals with individual sovereignty could not reach consensus on any public choice. This paper shows that, even in a public choice game of information asymmetry, the cooperation and payoff compensation mechanism may lead to the coalition equilibrium, the achievement of equilibrium public choice, and the distribution equilibrium of cooperative payoff of the coalition which supports the equilibrium public choice, whether the public choice games are under unanimity rule or under majority rule.

Information-constrained coordination of economic behavior

We analyze a coordination game with information-constrained players. The players' actions are based on a noisy compressed representation of the game's payoffs in a particular case, where the compressed representation is a latent state learned by a variational autoencoder (VAE). Our generalized VAE is optimized to trade off the average payoff obtained over a distribution of possible games against a measure of the congruence between the agent's internal model and the statistics of its environment. We apply our model to the coordination game in the experiment of Frydman and Nunnari (2023), and show that it offers an explanation for two salient features of the experimental evidence: both the relatively continuous variation in the players' action probabilities with changes in the game payoffs, and the dependence of the degree of stochasticity of players' choices on the range of game payoffs encountered on different trials. Our approach also provides an account of the way in which play should gradually adjust to a change in the distribution of game payoffs that are encountered, offering an explanation for the history-dependent play documented by Arifovic et al. (2013).

Evolution of cooperation in heterogeneous populations with asymmetric payoff distribution.

The emergence and maintenance of cooperation is a complex and intriguing issue, especially in the context of widespread asymmetries in interactions that arise from individual differences in real-world scenarios. This study investigates how asymmetric payoff distribution affects cooperation in public goods games by considering a population composed of two types of individuals: strong and weak. The asymmetry is reflected in the fact that strong players receive a larger share of the public pool compared to weak players. Our results demonstrate that asymmetric payoff distribution can promote cooperation in well-mixed populations and trigger the co-evolution of cooperation between sub-populations of strong and weak players. In structured populations, however, the effect of asymmetric payoff distribution on cooperation is contingent on the proportion of strong players and the extent of their payoff share, which can either foster or inhibit cooperation. By adjusting the interaction probability between strong and weak players based on their spatial arrangement on lattice networks, we find that moderate interaction probabilities most effectively maintain cooperation. This study provides valuable insights into the dynamics of cooperation under asymmetric conditions, highlighting the complex role of asymmetrical interactions in the evolution of cooperation.

Risk parity portfolio optimization under heavy‐tailed returns and dynamic correlations

Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat‐tailed and heteroscedastic with regime switching dynamic correlations. The conditional return distribution is modeled by an elliptical multi‐variate generalized hyperbolic distribution, allowing for fast parameter estimation via an expectation‐maximization algorithm, and a semi‐closed form of the risk contributions. A new method for efficient computation of non‐Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish–Fisher‐type approximations. Accounting for fat‐tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis or the COVID shock. While risk parity portfolios are rather robust to the misuse of the Gaussian distribution, a sophisticated time series model can improve risk‐adjusted returns, strongly reduces drawdowns during periods of market stress and enables to use a holistic risk model for portfolio and risk management.

Food-fuel nexus beyond mean-variance: New evidence from a quantile approach

This paper investigates the dynamic relationship between crude oil, ethanol, and corn markets across various quantiles of return distributions, as well as at higher statistical moments. Using a quantile vector autoregression model and data from 2007 to 2022, we find that the cross-market linkages are quantile dependent, with the strongest connections observed in the tails of the distribution. A shock to the oil market significantly impacts ethanol and corn returns under extreme bearish and bullish conditions. Positive shocks to the corn market reduce ethanol returns when the ethanol market is highly bullish, but this effect becomes positive in the left tail of the distribution. We also identify significant co-movement in higher statistical moments between these markets. Extreme excess kurtosis in the food-fuel nexus is more likely to occur with high financial market uncertainty, a bullish stock market, contracting industrial production, and a strong US dollar. In addition to these variables, credit spreads, futures market liquidity, futures term structure, and hedging pressure also influence kurtosis in individual markets within the nexus.

Choices under uncertainty and the investment horizon

AbstractMean–Variance (M–V) is the most popular investment rule employed by both practitioners and researches. For a short-planned investment horizon, this rule generally conforms with expected utility paradigm. However, for a relatively long horizon, generally more than one year, the distributions of returns become positively skewed, hence the M–V rule loses ground. As the horizon increases, by the M–V rule one needs (mistakenly) to increase the weight of bonds in the stock–bond portfolio, e.g., almost 100% in bonds for a 30-year horizon. Expected utility maximization recommending almost 100% in stocks for long horizons. This, gap is of crucial importance, because life expectancy is increasing, implying longer investment horizons. For long horizons the mean–coefficient-of-variance rule conforms with expected utility, as the distributions are close to log-normal. For intermediate horizons one should employ stochastic dominance or direct expected utility maximization.

Path Tracing-Inspired Modeling of Non-Line-of-Sight SPAD Data.

Non-Line of Sight (NLOS) imaging has gained attention for its ability to detect and reconstruct objects beyond the direct line of sight, using scattered light, with applications in surveillance and autonomous navigation. This paper presents a versatile framework for modeling the temporal distribution of photon detections in direct Time of Flight (dToF) Lidar NLOS systems. Our approach accurately accounts for key factors such as material reflectivity, object distance, and occlusion by utilizing a proof-of-principle simulation realized with the Unreal Engine. By generating likelihood distributions for photon detections over time, we propose a mechanism for the simulation of NLOS imaging data, facilitating the optimization of NLOS systems and the development of novel reconstruction algorithms. The framework allows for the analysis of individual components of photon return distributions, yielding results consistent with prior experimental data and providing insights into the effects of extended surfaces and multi-path scattering. We introduce an optimized secondary scattering approach that captures critical multi-path information with reduced computational cost. This work provides a robust tool for the design and improvement of dToF SPAD Lidar-based NLOS imaging systems.

Deformation of volatility curves of the Russian stock market on the example of margined options on futures contracts on the RTS index

We reassess the Russian stock market behavior in terms of the relationship between risk parameters and return on assets in connection with global structural changes in 2022. The subject of this study is volatility curves calculated from quotes of exchange options on RTS index futures. The purpose of the study is to analyze the relationship between volatility curves and the distribution of returns in 2015–2022, to analyze changes in the structure of this relationship in 2022, to assess the applicability of the GARCH model and to develop new investment and hedge strategies on the Russian stock market. The issue of interpreting the dynamics of volatility curves is disputable however, it was theoretically developed in the theory of valuation of derivative financial instruments. As a result of the study, unrelated structures of the distribution of returns and volatility curves for the RTS composite index were found throughout the entire period concerned, regardless of the presence of external shocks. It is concluded that in the Russian stock market, investors prefer protective options rather than speculative ones, despite the negative asymmetry of the distribution of RTS index returns. And despite the greater weight of positive returns in their distribution in each period under consideration, due to the technical features of the functioning of return indicators, the negative asymmetry of the return distribution does not necessarily correlate with growing volatility curves.

Asymmetric Laplace scale mixtures for the distribution of cryptocurrency returns

AbstractRecent studies about cryptocurrency returns show that their distribution can be highly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. To accommodate all these peculiarities, we propose the asymmetric Laplace scale mixture (ALSM) family of distributions. Each member of the family is obtained by dividing the scale parameter of the conditional asymmetric Laplace (AL) distribution by a convenient mixing random variable taking values on all or part of the positive real line and whose distribution depends on a parameter vector $$\varvec{\theta }$$ θ providing greater flexibility to the resulting ALSM. Advantageously concerning the AL distribution, our family members allow for a wider range of values for skewness and kurtosis. For illustrative purposes, we consider different mixing distributions; they give rise to ALSMs having a closed-form probability density function where the AL distribution is obtained as a special case under a convenient choice of $$\varvec{\theta }$$ θ . We examine some properties of our ALSMs such as hierarchical and stochastic representations and moments of practical interest. We describe an EM algorithm to obtain maximum likelihood estimates of the parameters for all the considered ALSMs. We fit these models to the returns of two cryptocurrencies, considering several classical distributions for comparison. The analysis shows how our models represent a valid alternative to the considered competitors in terms of AIC, BIC, and likelihood-ratio tests.

Robust dynamic contracts with multiple agents

We develop a continuous-time dynamic multi-agent contracting model in which the principal is unsure about the distributions of the project's terminal payoffs and worries about model misspecification. With model uncertainty, workers' wages depend on the outputs of other unrelated projects and the optimal contracts exhibit overdetermination. We demonstrate an inverse U-shaped relationship between the extent of overdetermination and group size. Moreover, model uncertainty induces wage compression, especially in small firms as the empirical evidence demonstrates. Finally, expanding the group size increases the average project value by mitigating the negative impacts of ambiguity.

Moral wiggle room and group favoritism among political partisans.

How does the availability of excuses for self-interested behavior impact group favoritism? We report the results of a preregistered experiment, conducted on the eve of the 2022 midterm elections, in which American political partisans made payoff distribution choices for themselves and a partner who was known to be a co-partisan or opposing partisan. Under full information, participants exhibit significant group favoritism. However, when the payoff consequences for one's partner are initially hidden, participants exploit this excuse to act selfishly regardless of who their partner is and ignorance rates are identical for in-group and out-group members. As a result, moral wiggle room has a significantly larger impact on selfish behavior for those interacting with co-partisans than opposing partisans, leading to a reduction in group favoritism.

Impact of Sharia‐Based Screening on Equity Risk: International Evidence

ABSTRACTThis paper investigates the impact of mainstream Sharia‐based screening methodologies on equity risk. The study is based on the daily returns of 23 pairs of stock indices belonging to different index providers, namely Dow Jones, FTSE, and S&P. For risk measurement, the study uses five Value at Risk (VaR) methods. Moreover, the conditional VaR (CVaR) is used to analyze the tail behavior of return distributions. The results show that Sharia‐based screening is a source of significant differences in risk. There is strong evidence that Islamic stock indices (ISIs) tend to be less risky than their conventional peers. Also, the screening process allows for keeping extreme negative returns at a lower level relative to unscreened indices. The analysis during the Dotcom and Subprime crises shows that, globally, the results are time‐invariant. In sum, Islamic screening is tantamount to prudential rules that lead to low‐risk portfolios; it is, in its essence, a risk‐reduction strategy. Findings suggest that Sharia‐compliant stocks would be of great attractiveness to risk‐averse investors. They will find their claim in this asset class, as its riskiness is relatively low. For banks, a lower VaR of Islamic investing implies fewer capital requirements for market risk when holding portfolios that include Sharia‐compliant stocks. Fewer capital requirements will enhance the banks' ability to invest and make profits, which will, in turn, result in reducing the cost of capital.

Zero‐beta risks and required returns: ESG and CAPM

AbstractWe ask how idiosyncratic zero‐beta risks (e.g., the risk of litigation or R&D failing) affect the firm's cost of capital under capital asset pricing model (CAPM). Surprisingly, perhaps, CAPM theory reveals that adding an idiosyncratic risk to the firm's payoff distribution will usually although not necessarily increase the firm's cost of capital. Lintner's famous original CAPM expositions revealed that the firm's CAPM cost of capital is a function of the ratio of the covariance of its cash payoff with the market to its payoff mean. Lintner proved that an idiosyncratic risk that affects the firm's payoff covarianceper unit of meanis“priced” in the sense that it necessarily alters the firm's CAPM discount rate. We explain and clarify Lintner's argument using elementary CAPM equations and numerical examples.

Risk conscious investment

The risk conscious investor is defined as the maximizer of a conservative valuation or a dynamic nonlinear expectation. Both the static and dynamic problems are addressed using distortions of tail probabilities or distortions of tail measures. The multivariate static problem is solved in the context of the multivariate bilateral gamma model. For the dynamic model states and their transitions are modeled in two ways. The first defines states by a parametric model for the return distribution with transitions described by a continuous-time finite state Markov chain between the distributional possibilities. In the second model states are represented by the first four power variations with transitions given by (OU) equations for modeling stochastically the first four power variations as Tempered Fractional Lévy Processes (TFLP). Numerical solutions for policy functions are implemented in trading 768 equity assets over seven years ending December 2021.

Energy firms in China towards resilience: A dynamic quantile connectedness approach

Α comprehensive understanding of the energy and technology sectors is imperative for the implementation of effective climate and industrial policies. This study investigates the quantile interconnectedness between the top five energy equities and the top five technology equities, listed on the Shanghai Stock Exchange 50 Index (SSE50), based on market capitalization. Employing the Quantile VAR methodology, we uncover significant interconnectedness across various quantiles of the return distribution for both energy and technology equities. This implies that price fluctuations within one sector can have a significant effect on the other. Furthermore, our analysis reveals directional connectedness, where energy equities consistently influence technology equity prices throughout the entire period of investigation. Additionally, a heightened degree of interconnectedness is observed during periods of extreme market movements, i.e. in the upper and lower tails of the return distribution. This suggests a more integrated system during stressed conditions, where all equities under investigation exhibit a magnified influence on each other, potentially leading to amplified volatility spillovers. These findings provide valuable insights for investors, portfolio managers, and policymakers, enabling them to develop more informed investment strategies and construct robust risk management frameworks.

Exploring decision-making: experimental observations on project selection and the impact of justification pressure

AbstractIn this experimental investigation, we explore the impact of justification on project choices. Introducing a novel element, we implement asymmetric payoff schemes commonly employed in business, signifying distinct payoff distributions for the firm (principal) and the manager (agent). The agent has to choose one project from two options that differ in their risk-return profiles. The outcomes of our experiment substantiate our hypothesis, indicating that a mandate for justification decreases the probability of agents selecting the project with higher risk and return. The degree of this reduction appears to hinge on the nature of justification. Increased profit shares for the agent or a project recommendation from the principal can partially counterbalance the distortion in the project choice.