Distribution Of Returns Research Articles

Skewness-seeking behavior and financial investments

AbstractRecent theoretical and empirical advancements highlight the pivotal role played by higher-order moments, such as skewness, in shaping financial decision-making. Nevertheless, contemporary experimental research predominantly relies on limited-outcome lotteries, an oversimplified representation distant from real-world investment dynamics. To bridge this research gap, we conducted a rigorously pre-registered experiment. Our study delves into individuals’ preferences for investment opportunities, examining the influence of skewness of continuous probability distributions of returns. We document an inclination towards positively skewed outcome distributions. Furthermore, we uncovered a substitution effect between risk appetite and the sign of skewness. Finally, we unveiled a robust positive correlation between skewness-seeking behavior and a propensity for speculative behavior. Simultaneously, a distinct negative correlation surfaced between skewness-seeking behavior and the perceived risk associated with positive skewness.

Emergent invariance and scaling properties in the collective return dynamics of a stock market.

A key metric to determine the performance of a stock in a market is its return over different investment horizons (τ). Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across the individual stocks in the market, and do not track statistics about the joint distributions of returns conditioned on different stocks, which would be useful for optimizing inter-stock asset allocation strategies. As a step towards this goal, we study emergent phenomena in the distributions of returns as captured by their pairwise correlations. In particular, we consider the pairwise (between stocks i, j) partial correlations of returns with respect to the market mode, ci,j(τ), (thus, correcting for the baseline return behavior of the market), over different time horizons (τ), and discover two novel emergent phenomena: (i) the standardized distributions of the ci,j(τ)'s are observed to be invariant of τ ranging from from 1000min (2.5 days) to 30000min (2.5 months); (ii) the scaling of the standard deviation of ci,j(τ)'s with τ admits good fits to simple model classes such as a power-law τ-λ or stretched exponential function [Formula: see text] (λ, β > 0). Moreover, the parameters governing these fits provide a summary view of market health: for instance, in years marked by unprecedented financial crises-for example 2008 and 2020-values of λ (scaling exponent) are substantially lower. Finally, we demonstrate that the observed emergent behavior cannot be adequately supported by existing generative frameworks such as single- and multi-factor models. We introduce a promising agent-based Vicsek model that closes this gap.

Quantifying endogenous and exogenous shocks to financial sector systemic risk: A comparison of GFC and COVID-19

In this study, we use segregated endogenous and exogenous shocks to large banks’ returns to compare the effect of each on financial sector systemic risk. We use the copula-CoVaR methodology and GARCH (1,1) with time-varying moments to model the marginal distribution function and bivariate probability distribution of the tail returns. We find that endogenous risk dominates exogenous risk in the financial system. A comparison of the 2008 global financial crisis and COVID-19 reveals that the crisis aggravates only as exogenous shocks to the system persist. Additionally, we find that large banks reduce the total risk of the system in normal times but increase the risk of the financial system in crisis times. Our findings have important implications for policymakers, investors, and portfolio managers.

Explaining the Stylized Facts of Foreign Exchange Markets with a Simple Agent-based Version of Paul de Grauwe’s Chaotic Exchange Rate Model

AbstractWe propose a simple agent-based version of Paul de Grauwe’s chaotic exchange rate model. In particular, we assume that each speculator follows his own technical and fundamental trading rule. Moreover, a speculator’s choice between these two trading philosophies depends on his individual assessment of current market circumstances. Our agent-based model setup is able to explain a number of important stylized facts of foreign exchange markets, including bubbles and crashes, excess volatility, fat-tailed return distributions, serially uncorrelated returns and volatility clustering. A stability and bifurcation analysis of its deterministic skeleton provides us with useful insights that foster our understanding of exchange rate dynamics.

Option Pricing with the Logistic Return Distribution

The Black–Scholes model and many of its extensions imply a log-normal distribution of stock total returns over any finite holding period. However, for a holding period of up to one year, empirical stock return distributions (both conditional and unconditional) are not log-normal, but rather much closer to the logistic distribution. This paper derives analytic option pricing formulas for an underlying asset with a logistic return distribution. These formulas are simple and elegant and employ exactly the same parameters as B&S. The logistic option pricing formula fits empirical option prices much better than B&S, providing explanatory power comparable to much more complex models with a larger number of parameters.

Dynamic currency hedging with non-Gaussianity and ambiguity

This paper introduces a non-Gaussian dynamic currency hedging strategy for globally diversified investors with ambiguity. It provides theoretical and empirical evidence that, under the stylized fact of non-Gaussianity of financial returns and for a given optimal portfolio, the investor-specific ambiguity can be estimated from historical asset returns without the need for additional exogenous information. Acknowledging non-Gaussianity, we compute an optimal ambiguity-adjusted mean-variance (dynamic) currency allocation. Next, we propose an extended filtered historical simulation that combines Monte Carlo simulation based on volatility clustering patterns with the semi-parametric non-normal return distribution from historical data. This simulation allows us to incorporate investor's ambiguity into a dynamic currency hedging strategy algorithm that can numerically optimize an arbitrary risk measure, such as the expected shortfall. The out-of-sample backtest demonstrates that, for globally diversified investors, the derived non-Gaussian dynamic currency hedging strategy is stable, robust, and highly risk reductive. It outperforms the benchmarks of constant hedging as well as static/dynamic hedging approaches with Gaussianity in terms of lower maximum drawdown and higher Sharpe and Sortino ratios, net of transaction costs.

Salience theory value spillovers between China’s systemically important banks: evidence from quantile connectedness

Analyzing the interdependencies among financial institutions is critical for designing systemic risk monitoring mechanisms; however, most existing research focuses on the first moment of the return distribution, which falls into the conventional models of choice under risk. Previous literature has observed the scarcity of investors’ attention and processing power, which makes the traditional theory of choice under risk more vulnerable and brings the salience theory that accommodates investors’ cognitive limitations to our attention. Motivated by evidence of salience theory value (STV) containing unique information not captured by traditional higher-order moments, we employ a quantile connectedness approach to examine the STV interconnectedness of China’s systemically important banks (C-SIBs). The quantile approach allows us to uncover the dynamic STV interconnectedness of C-SIBs under normal, bearish, and bullish market conditions and is well-suited to extreme risk problems. Our results show that the C-SIBs system is asymmetrically interconnected across quantiles and at higher levels under bullish than bearish market conditions. Principally, a bank’s performance in the C-SIBs system depends on its systemic importance and market conditions. Furthermore, the comparative analysis indicates that STV could provide more information than higher-order moments in capturing the dynamic change in the C-SIBs system and detecting some market events more precisely. These results have important implications for policymakers and market participants to formulate regulatory policy and design risk management strategies.

Evaluation of strategy portfolios

People usually create a portfolio in order to diversify the risk coming from individual investments. To get a high yield with a good level of diversification, investors usually seek professional advice from portfolio managers. However, the true performance of an optimized portfolio usually depends on the correctness of the estimates of the distribution of future returns, which is often a matter of luck rather than skill. Thus, the optimization models may not be better than randomly selected portfolios. Our aim is to find how the so-called strategy portfolios, i.e., portfolios obtained by some decision optimized for a long-run horizon, perform compared to a benchmark, namely, a random investment, under specific market conditions. For this purpose, we evaluate several portfolio strategies over two periods of crisis: the subprime mortgage crisis and the Covid-19 pandemic, as well as run a moving window analysis over a longer horizon. In each case, the results are compared with the performance of random-weight portfolios. We find that if the strategy is minimization, the portfolios perform well; however, for the maximization of the objectives, the results are rather mixed.

Martingale defects in the volatility surface and bubble conditions in the underlying

AbstractThe martingale theory of bubbles enables testing for asset price bubbles by analyzing option prices. As recently shown by Piiroinen et al. (Asset price bubbles: an option-based indicator, 2018), the SABR model is a strict local martingale when its parameterization implies a positive correlation between stock and option prices. We operationalize this theoretical result and analyze stock price bubbles in 2576 stocks over 26 years. Martingale defect conditions are absorbed quickly by options markets, but identify high proportions in significant and permanent changes in distribution of price returns, option trading activity, short interest in the underlying, and institutional ownership. These results confirm many common assumptions about stock price bubbles. These bubbles are temporally clustered, and tend to occur in periods of positive market development. Martingale defects are rare in market corrections, which indicates that they are a result of overoptimistic speculation.

Persistence of return distribution sequence in financial markets

The analysis of return distribution is an important topic in risk management and investment practice. This study analyzes time-varying distribution sequences and characterizes persistence with topological correlation coefficients (TCC), where the distribution consists of cross-sectional returns. We used some models to show that TCC can effectively analyze persistence, and found that both the autocorrelation structure and volatility clustering of time series can lead to the persistence of the distribution sequence. We analyzed the persistence of the return distribution sequences in the Chinese market and the US market. The calculation shows that some sequences have significant persistence. In addition, we analyzed factors that affect the persistence, where model-based analysis provides a baseline for comparison. The analysis shows that neither autocorrelation structure nor volatility clustering can fully explain persistence, so the generation mechanism of persistence is complex. In particular, dynamic analysis shows that persistence is time-varying and that there are significant differences between the two markets. This study provides a way to study distribution sequences, which can help analyze the predictability of distributions.

Improved Hedge Fund Portfolio Optimization Using 2-Step Covariance Matrix and Fund Transaction Costs

This study focuses on fund portfolio investments in the Chinese market. The application of classic portfolio optimization methods encounters several issues when applied to fund portfolios. For example, issues such as the non-normal distribution of returns on funds or fund portfolios, turnover rate limitations in fund investments, and liquidity constraints of fund assets, which can lead to transaction costs and opportunity costs, are prevalent challenges. The existence of these issues can compromise the effectiveness of classic portfolio optimization methods like Mean-Variance Optimization. This may result in a reduction of accuracy in determining the portfolios optimal weights, a deviation of actual trading results from the models optimal expectation, and may even render the optimal weights impractical in real-world scenarios. To address these challenges, this paper integrates the 2-Step covariance matrix method (2-Step method) and the measurement of fund transaction costs into the portfolio optimization process. The paper finds that the 2-Step method, compared to the baseline, can indeed improve the risk-return indicators of the potimal fund portfolio. The inclusion of the transaction cost can effectively control the turnover frequency of the portfolio. Even after accounting for these costs, the 2-Step method continues to exhibit a significant improvement effect compared to the baseline.

Are VaR models effective in capturing downside risk in alternative investment funds? Insights from a cross-country study

In this paper, we analyze the downside risk of alternative investment funds (AIFs) in a cross-country setting over a period of 2015–2021, using popular Value-at-Risk (VaR henceforth) models, and test the efficacy of such models in capturing the volatility posed by these funds. We estimate VaR in the presence of three error distributions, including normal distribution, Student’s t distribution, and GED distribution. Using weekly return data of 991 AIFs from 28 countries, over the period 2015–2021, we find that most of the funds, irrespective of country representation, exhibited a significant proportion of their weekly returns to be negative. To statistically validate our findings we use three backtesting approaches, i.e., Jorion’s failure rate, Kupiec’s proportion of failure (POF) tests and Christoffersen’s independence test. Our findings indicate the presence of significant downside risk for AIFs, which these popular VaR models are unable to capture. These findings highlight the need for investors and fund managers to be cautious when relying solely on popular VaR models to manage downside risk in AIF and suggest that further research is needed to develop more effective risk management strategies for AIF, particularly in light of their complex structure and asymmetric return distributions.

Distributional Policy Gradient With Distributional Value Function.

In this article, we propose a distributional policy-gradient method based on distributional reinforcement learning (RL) and policy gradient. Conventional RL algorithms typically estimate the expectation of return, given a state-action pair. Furthermore, distributional RL algorithms consider the return as a random variable and estimate the return distribution that can characterize the probability of different returns resulted by environmental uncertainties. Thus, the return distribution provides more valuable information than its expectation, leading to superior policies in general. Although distributional RL has been investigated widely in value-based RL methods, very few policy-gradient methods take advantage of distributional RL. To bridge this research gap, we propose a distributional policy-gradient method by introducing a distributional value function to the policy gradient (DVDPG). We estimate the distribution of policy gradient instead of the expectation estimated in conventional policy-gradient RL methods. Furthermore, we propose two policy-gradient value sampling mechanisms to do policy improvement. First, we propose a distribution-probability-sampling method that samples the policy-gradient value according to the quantile probability of return distribution. Second, a uniform sample mechanism is proposed. With our sample mechanisms, the proposed distributional policy-gradient method enhances the stochasticity of the policy gradient, improving the exploration efficiency and benefiting to avoid falling into local optimal solutions. In sparse-reward tasks, the distribution-probability-sampling method outperforms the uniform sample mechanism. In dense-reward tasks, the two sample mechanisms perform similarly. Moreover, we show that the conventional policy-gradient method is a special case of the proposed method. Experimental results on various sparse-reward and dense-reward OpenAI-gym tasks illustrate the efficiency of the proposed method, outperforming baselines in almost environments.

Analyzing market sentiment based on the option-implied distribution of stock returns

Analyzing market sentiment based on the option-implied distribution of stock returns

Optimal Hedging of Assets with Pathological Distributions of Returns

Optimal Hedging of Assets with Pathological Distributions of Returns

Is peace a human phenomenon?

Peace is a hallmark of human societies. However, certain ant species engage in long-term intergroup resource sharing, which is remarkably similar to peace among human groups. We discuss how individual and group payoff distributions are affected by kinship, dispersal, and age structure; the challenges of diagnosing peace; and the benefits of comparing convergent complex behaviours in disparate taxa.

Decision-Making With Speculative Opponent Models.

Opponent modeling has proven effective in enhancing the decision-making of the controlled agent by constructing models of opponent agents. However, existing methods often rely on access to the observations and actions of opponents, a requirement that is infeasible when such information is either unobservable or challenging to obtain. To address this issue, we introduce distributional opponent-aided multiagent actor-critic (DOMAC), the first speculative opponent modeling algorithm that relies solely on local information (i.e., the controlled agent's observations, actions, and rewards). Specifically, the actor maintains a speculated belief about the opponents using the tailored speculative opponent models that predict the opponents' actions using only local information. Moreover, DOMAC features distributional critic models that estimate the return distribution of the actor's policy, yielding a more fine-grained assessment of the actor's quality. This thus more effectively guides the training of the speculative opponent models that the actor depends upon. Furthermore, we formally derive a policy gradient theorem with the proposed opponent models. Extensive experiments under eight different challenging multiagent benchmark tasks within the MPE, Pommerman, and starcraft multiagent challenge (SMAC) demonstrate that our DOMAC successfully models opponents' behaviors and delivers superior performance against state-of-the-art (SOTA) methods with a faster convergence speed.

Option Pricing with the Logistic Return Distribution

Option Pricing with the Logistic Return Distribution

Value at Risk Estimation for Non-Gaussian Distributions

This paper presents a methodology for computing Value at Risk for Önancial as- sets that does not follow a normal distribution of return. A back-testing approach have been applied in order to select the best theoretical non-Gaussian distributions that can explain the behavior of the empirical data. In this study, Cauchy, Laplace, Logistic and Beta dis- tributions have been considered. As benchmark, historical distribution, and Extreme Value Theory (EVT) method have been used. The experiment suggests di§erences in estimation of over 5 times between one method and another.

Collaborative Green Innovation of Livestock Product Three-Level Supply Chain Traceability System: A Value Co-Creation Perspective

To enhance the health and stability of livestock product supply chains, it is imperative to augment product sustainability and satisfy food safety requirements through collaborative green innovation. Digital traceability technology amalgamates information and resources from stakeholders in the supply chain, facilitating knowledge sharing and product tracking throughout the entire process to purify the supply chain environment. Augmenting communication and trust among supply chains paves the way for green innovation, thereby yielding value-added benefits. Consequently, this paper formulates a simulation model for manufacturers, retailers, and consumers—three pivotal stakeholders in the traceability process of livestock products—from a value co-creation standpoint. It also incorporates a contract penalty mechanism to probe the collaborative green innovation process among various entities involved in the livestock product supply chain. System simulation is employed to emulate the evolution path of collaborative green innovation in the livestock product supply chain under the value co-creation perspective. Subsequently, a stepwise penalty mechanism, green incentive mechanism, and fair distribution mechanism are proposed for stakeholders to actualize collaborative green innovation and value creation. The findings reveal that: (1) the collaborative green behavior between suppliers, retailers, and consumers is influenced by factors such as value co-creation excess returns, innovative technology costs like traceability, cost sharing among stakeholders, and a certain threshold of government penalties. (2) A balanced distribution of excess returns and cost-sharing among stakeholders fosters the evolution of a green collaborative state in the supply chain, thereby achieving sustainable development with value chain enhancement and ecological optimization.