Distribution Of Returns Research Articles

Extremely stablecoins

In this research, I explore the factors driving extreme fluctuations in stablecoin prices concerning financial and cryptocurrency market indices. Through quantile models, I reveal the directional predictability of diverse financial variables, capturing extreme price variations and return distribution fluctuations. The outcomes highlight asymmetric pricing reactions and the impact of stablecoin stability mechanisms. The varying effects observed in stablecoin and cryptocurrency behavior imply a broader market link and potential fragility. Notably, intermediary constraints and stablecoin liquidity exhibit predictive power for subsequent price shifts in both tails, providing insights into the complex dynamics within cryptocurrency and stablecoin markets.

Финансовое заражение российского фондового рынка от европейского в период пандемии COVID-19

This paper investigates the transmission of financial contagion from the European to the Russian stock market during the COVID-19 pandemic. Financial contagion refers to the spread of instability and shocks across individual countries, sectors, or markets during a crisis, where the relationship between returns and volatility of different assets goes beyond normal interactions. Using the construction of extended autoregressive models, we test the contagion of the RTSI composite index from the EURO STOXX 50 index, with the US dollar exchange rate and the spot price of Urals crude oil serving as control variables. The calculation of the moving coefficient of variation in assets prices allows us to distinguish the pre-crisis, crisis and post-crisis periods, for which three separate autoregressive models are built. The contagion of the Russian stock market from the European stock market in these models is identified in two ways: 1) based on the growth and significance of estimated coefficient for the tested variable (STOXX 50 index return) during the crisis; 2) through an increase in the contribution of the tested variable to the explained variance of the dependent variable (RTSI return). In addition, we tested contagion based on the method of central co-moments of the distribution of returns, skewness and volatility of the tested and dependent variable. The analysis has convincingly demonstrated the existence of a financial contagion effect from the European stock market to the Russian stock market in the short term — strengthening of the impact of the European STOXX 50 index on the Russian RTSI index in the acute phase of the pandemic. Understanding the factors contributing to the spread of market shocks in the context of financial globalization can help policymakers to implement effective financial regulatory measures and maintain long-term financial stability in line with national interests. For investors, it helps to identify potential risks and opportunities, enabling optimal hedging and diversification response strategies.

Python for financial engineers: Mastering four moments in portfolio management

This research conducts a comprehensive analysis aimed at optimizing portfolios comprising 14 stocks listed on the Moroccan stock exchange. Our journey culminates in the construction of portfolios that are meticulously designed to maximize returns while prudently managing risk. These portfolios are the result of an exhaustive Monte Carlo simulation that explored over three million unique portfolio combinations. The simulations take into account the skewness and kurtosis of the return distributions, offering investors a robust framework for decision-making. We collected historical data for theses 14 stocks on the Moroccan market exchange by accessing 5 years' worth of historical data from investing.com.We explore the concepts of Modern Portfolio Theory (MPT), which forms the backbone of our approach, and we employ the power of mathematics and Python programming to bring forth insights that can inform sound investment decisions. The primary focus of this study centers on the incorporation of higher statistical moments from the returns of key financial indices, with a particular emphasis on their skewness and kurtosis characteristics. To achieve this goal, various evaluative criteria derived from these statistical parameters are introduced and thoroughly investigated. Within this research framework, we confront a spectrum of optimization challenges, including the maximization of skewness, and minimization of kurtosis.

Conventional and downside CAPM with higher-order moments: Evidence from emerging markets

Research background: Conventional CAPM is a well-known and tested theory on various capital markets. It was also repeatedly rejected as a model of capital pricing. This article proposes a different approach to both CAPM testing and the use of other risk measures. In addition, research is global, including emerging countries. Purpose of the article: This paper investigates the standard CAPM, and this model is based on higher moments of the return distribution for the global emerging market. In addition, this paper aims to compare the conventional and downside CAPM versions using the beta coefficient and co-moments. Methods: Contrary to the classical unconditional tests for the risk premium, conditional relationships are also estimated considering the market portfolio condition. Moreover, the studies considered conventional and downside approaches to risk measures. The cross-sectional regressions are based on the Fama-MacBeth (F-M) procedure and panel models. Findings & value added: The findings contribute to the debate on whether beta coefficient and higher order co-moments in conventional and downside approaches can explain the cross-sectional emerging indices returns. The unconditional models using all measures do not significantly describe the cross-sectional volatility of returns. The cross-sectional regressions in up and down-market based on both the classic F-M procedure and panel models show that the beta and co-kurtosis risk premium is significant and depends on market conditions. The risk premium for co-skewness is not valid, and the direction of the relationships is opposite than expected. Research also demonstrates that the test results of CAPM relationships are not robust to the presence of outliers and shocks resulting from the Covid-19 pandemic in the context of risk-return space. Research provides strong support for the importance of downside risk in the context of standard CAPM and, above all, higher co-moments.

Empirical Evidence on the Validity of the Conditional Higher Moment Capm in the Bombay Stock Exchange

Various researchers criticized the assumption of a normal distribution of returns in the traditional Capital Asset Pricing Model (CAPM), leading to the recognition of the non-normal distribution of returns and the mean and variance were insufficient to characterize the distribution of returns completely which led the researchers to look for higher order moments. The present study investigated empirical validity of the conditional higher order moment Capital Asset Pricing Model (CAPM) in the context of the Indian stock market, specifically the Bombay Stock Exchange utilizing the data from sectoral indices for the period from April 2011 to March 2021. To test the four moment CAPM empirically, the specification derived from Bollerslev et al. (1988) has been used in the study. The study's findings reveals that the higher moment i.e. conditional coskewness and cokurtosis hold significant pricing implications and do have an impact on returns in the Indian stock market. The explanatory power of the model showed an increase as compared to the unconditional CAPM as the R-square value obtained was greater than the latter model. The results of the study were found to be mixed and inconclusive. Hence, the conditional higher moment CAPM cannot be validated in the Indian context.

АДАПТАЦІЙНЕ УПРАВЛІННЯ ПОКАЗОМ РЕКЛАМНИХ РОЛИКІВ В СОЦІАЛЬНИХ МЕРЕЖАХ ЗА СХЕМОЮ БАГАТОРУКОГО БАНДИТА

In a rapidly changing marketing environment, to ensure the success of an advertising campaign, it is necessary to minimize the time from the idea of advertising to the implementation of communication. There is a need for simultaneous advertising, study and adjustment of communication processes. Accordingly, it is necessary to make a certain sequence of decisions, the sum of which ensures the right balance between learning and earning. One of the most convenient adaptation mechanisms for practical implementation is the two-armed bandit scheme. A two-armed bandit is a model of multiple choices of one of two alternatives with an a priori unknown distribution of payoffs between them. Each alternative is associated with one arm of the bandit. As a result of the choices made, the probabilistic distribution of payoffs is identified by step to step and used to exploit the best alternative. In practice, there may be more alternatives, in which case the multiple decision problem is maped to the multi-armed bandit scheme. A new multi-armed bandit-based model for advertising control in social networks is proposed. The idea is that multiple advertisements are displayed simultaneously, and the frequency of display of each depends on its performance - from the level of viewer retention to the contact frame. Based on the retention rates, a certain share of resources is redistributed among the commercials on a daily basis. Simple and effective formulas for the reassignment of resources are proposed, taking into account both the current unevenness of retention rates and the statistics of video demonstrations. A simulation of the control model for a 35-day campaign for three commercials is performed. The performance of the control model is demonstrated both under steady-state conditions and in the case of a viral message insertion. The phase trajectories show how the response of the system to the insertion of a viral message changes with different control parameters.

Empirical Evidence on the Validity of the Unconditional Higher Moment CAPM in the Bombay Stock Exchange

The traditional Capital Asset Pricing Model (CAPM) assumed a normal distribution of returns, which was criticized by various researchers who recognized the non-normal distribution of returns in the Sharpe-Lintner CAPM. The introduction of unconditional higher moments, namely co-skewness and co-kurtosis, as additional measures of systematic risk may enhance the model's explanatory power, especially when the distribution function of stock returns is asymmetric. The present study empirically investigates the applicability of unconditional higher order moment CAPM and the impact of higher moments in the Indian stock market i.e. Bombay Stock Exchange using the data of sectoral indices for the period from April 2011 to March 2021. To test the four moment CAPM empirically, the specification given by Fang and Lai has been used in the study. The findings of the present study revealed that the higher moments (coskewness and cokurtosis) are significantly priced and have impact on the returns in the Indian stock market. The market risk premium for covariance was found to be insignificant. Further the hypothesis related to intercept term was accepted and market risk premiums were rejected. The results showed an increase in the explanatory power of the model as compared to the unconditional CAPM as the R-square value of the model was obtained better than the latter model. The mixed and inconclusive findings contradicted the model in the Indian context. The alternate models like the Fama-French three factor and five factor model should be exploited in the Indian context as those models have been rarely used in the Indian context.

On co-dependent power-law behavior across cryptocurrencies

Using daily returns on large-cap altcoins, this paper uses power-law functions to model cryptocurrency-specific exposure to events exhibiting potentially large standard deviations. Since our analysis provides evidence for power-law behavior in the returns on cryptocurrencies, co-fractality analysis is employed to explore potential co-dependencies in the heavy-tailed part of return distributions. The findings indicate that the potential arrival of events exhibiting large standard deviations in Bitcoin returns can hardly be diversified using other sample altcoins. Other altcoins exhibit very similar features in terms of co-dependencies. Further results show that co-fractal behavior is not specific to any subsample.

Social Justice and the Old-Age Pension System in the Slovak Republic

The aim of the contribution is to examine how eligible voters in the 2020 parliamentary election perceive social justice in relation to the old-age pension system in the Slovak Republic. The sub-objective is to analyse possible significant differences in the perception of social justice among eligible voters in the 2020 parliamentary election in relation to the old-age pension system in terms of their political orientation. 701 respondents (349 women and 352 men) responded to questions asking about their political orientation as eligible voters in the parliamentary election in Slovakia in 2020 and the degree of perceived social justice in relation to the old-age pension system of the Slovak Republic. The results showed the fair distribution of deposits and returns is important for the respondents’ perception of social justice in relation to the old-age pension system of the Slovak Republic. The analyses showed that respondents with different political orientations had different opinions on the extent to which the calculation of the old-age pension should depend on the amount of income.

Beyond Expected Return: Accounting for Policy Reproducibility When Evaluating Reinforcement Learning Algorithms

Many applications in Reinforcement Learning (RL) usually have noise or stochasticity present in the environment. Beyond their impact on learning, these uncertainties lead the exact same policy to perform differently, i.e. yield different return, from one roll-out to another. Common evaluation procedures in RL summarise the consequent return distributions using solely the expected return, which does not account for the spread of the distribution. Our work defines this spread as the policy reproducibility: the ability of a policy to obtain similar performance when rolled out many times, a crucial property in some real-world applications. We highlight that existing procedures that only use the expected return are limited on two fronts: first an infinite number of return distributions with a wide range of performance-reproducibility trade-offs can have the same expected return, limiting its effectiveness when used for comparing policies; second, the expected return metric does not leave any room for practitioners to choose the best trade-off value for considered applications. In this work, we address these limitations by recommending the use of Lower Confidence Bound, a metric taken from Bayesian optimisation that provides the user with a preference parameter to choose a desired performance-reproducibility trade-off. We also formalise and quantify policy reproducibility, and demonstrate the benefit of our metrics using extensive experiments of popular RL algorithms on common uncertain RL tasks.

Optimal Impact Portfolios with General Dependence and Marginals

Using Induced Order Statistics to Construct Optimal Impact Portfolios with General Dependence and Marginals We develop a mathematical framework for constructing optimal impact portfolios and quantifying their financial performance by characterizing the returns of impact-ranked assets using induced order statistics and copulas. Our results apply to any joint distribution of impact factors and residual returns, making them broadly applicable to a wide range of contexts. We develop significant extensions of the theory of induced order statistics, with which we are able to characterize the distribution of residual returns of individual assets ranked by the impact factor. Our framework provides a toolkit for practitioners to construct impact portfolios and quantify their performance based on real data. This allows impact investors to achieve higher risk-adjusted returns than those with impact portfolios constructed using simpler heuristics such as negative or positive screening.

Portfolio optimisation of international real estate investment trusts market during COVID-19: A behavioural perspective

This paper employs the cumulative prospect theory to investigate how deviation from rational investor asset selection improves portfolio optimisation. Firstly, asset portfolios are constructed by utilising the cumulative prospect theory, which captures investors’ psychology and risk tolerance and is herein referred to as a behavioural portfolio (BF). Secondly, the cluster technique is also used to build behavioural-centred investment portfolios that capture all the relevant moment properties of the asset return distribution as well as investors’ psychological dynamics and risk appetite, herein called the cluster moment behavioural portfolio (CMBF). The constructed portfolios are optimised by copula and differential evolution techniques. The analysis of optimisation of the constructed portfolios indicates that for behavioural portfolios (BF), in all phases of our sample period, portfolios with higher behavioural scores outperformed those with lower behavioural scores. And in the cluster moment behavioural portfolio (CMBP), for the pre-COVID and the COVID phases, the portfolios with lower behavioural scores outperform those with higher behavioural scores; however, for the full sample phase, the portfolio with a higher behavioural score outperforms the portfolio with the lower behavioural scores. The optimisation results of all the constructed portfolios largely favour portfolios with higher behavioural scores over those with lower scores. The results offer investment suggestions to guide investors with varying risk tolerance levels and those who deviate from the rational investor on how they can enhance their portfolio optimisation.

Evaluating Density Forecasts Using Weighted Multivariate Scores in a Risk Management Context

AbstractScoring rules are commonly applied to assess the accuracy of density forecasts in both univariate and multivariate settings. In a financial risk management context, we are mostly interested in a particular region of the density: the (left) tail of a portfolio’s return distribution. The dependence structure between returns on different assets (associated with a given portfolio) is usually time-varying and asymmetric. In this paper, we conduct a simulation study to compare the discrimination ability between the well-established scores and their threshold-weighted versions with selected regions. This facilitates a comprehensive comparison of the performance of scoring rules in different settings. Our empirical applications also confirm the importance of weighted-threshold scores for accurate estimates of Value-at-risk and related measures of downside risk.

Frequent winners explain apparent skewness preferences in experience-based decisions

Do people's attitudes toward the (a)symmetry of an outcome distribution affect their choices? Financial investors seek return distributions with frequent small returns but few large ones, consistent with leading models of choice in economics and finance that assume right-skewed preferences. In contrast, many experiments in which decision-makers learn about choice options through experience find the opposite choice tendency, in favor of left-skewed options. To reconcile these seemingly contradicting findings, the present work investigates the effect of skewness on choices in experience-based decisions. Across seven studies, we show that apparent preferences for left-skewed outcome distributions are a consequence of those distributions having a higher value in most direct outcome comparisons, a "frequent-winner effect." By manipulating which option is the frequent winner, we show that choice tendencies for frequent winners can be obtained even with identical outcome distributions. Moreover, systematic choice tendencies in favor of right- or left-skewed options can be obtained by manipulating which option is experienced as the frequent winner. We also find evidence for an intrinsic preference for right-skewed outcome distributions. The frequent-winner phenomenon is robust to variations in outcome distributions and experimental paradigms. These findings are confirmed by computational analyses in which a reinforcement-learning model capturing frequent winning and intrinsic skewness preferences provides the best account of the data. Our work reconciles conflicting findings of aggregated behavior in financial markets and experiments and highlights the need for theories of decision-making sensitive to joint outcome distributions of the available options.

Multiportfolio Optimization: A Fairness-Aware Target-Oriented Model

Problem definition: We consider a multiportfolio optimization problem in which nonlinear market impact costs result in a strong dependency of one account’s performance on the trading activities of the other accounts. Methodology/results: We develop a novel target-oriented model that jointly optimizes the rebalancing trades and the split of market impact costs. The key advantages of our proposed model include the consideration of clients’ targets on investment returns and the incorporation of distributional uncertainty. The former helps fund managers to circumvent the difficulty in identifying clients’ utility functions or risk parameters, whereas the latter addresses a practical challenge that the probability distribution of risky asset returns cannot be fully observed. Specifically, to evaluate the quality of multiple portfolios’ investment payoffs in achieving targets, we propose a new class of performance measures, called fairness-aware multiparticipant satisficing (FMS) criteria. These criteria can be extended to encompass distributional uncertainty and have the salient feature of addressing the fairness issue with the collective satisficing level as determined by the least satisfied participant. We find that, structurally, the FMS criteria have a dual connection with a set of risk measures. For multiportfolio optimization, we consider the FMS criterion with conditional value-at-risk being the underlying risk measure to further account for the magnitude of shortfalls against targets. The resulting problem, although nonconvex, can be solved efficiently by solving an equivalent converging sequence of tractable subproblems. Managerial implications: For the multiportfolio optimization problem, the numerical study shows that our approach outperforms utility-based models in achieving targets and in out-of-sample performance. More generally, the proposed FMS criteria provide a new decision framework for operational problems in which the decision makers are target-oriented rather than being utility maximizers and issues of fairness and ambiguity should be considered. Funding: This work was supported by the Hong Kong Research Grants Council [Grants 14210821, 16204521], Leading Talent Program of Guangdong Province [Grant 2016LJ06D703], and the National Natural Science Foundation of China [Grants 71971187, 72171156, 72231002, 72331009]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0363 .

The Impacts of the Interest Rate, the Exchange Rate, and the Market Index on the Stock Returns of the Brazilian Banks

Abstract This paper aims to analyze the impact of interest rate, exchange rate, and market on the returns and volatility of the stocks of banks listed on the Brazilian Stock Exchange. This analysis used two statistical models: the linear model estimated using Ordinary Least Squares and the ARCH/GARCH time series volatility models. The econometric studies considered the daily data of 15 financial institutions listed on the stock exchange during the period from January 2009 to December 2021. Regarding the market effect, the Ibovespa index for the period was considered; for the interest rate, the CDI (Certificate of Interbank Deposit) was used; and, about the exchange rate, the dollar rate was adopted as a reference. The results indicate that the distribution of stock returns is asymmetrical, with an elongated tail on the right. It was observed, based on the econometric model applied, that the daily returns of the shares are significantly influenced by the market, and the interest rate exerts the least impact on the returns. These findings are relevant to the scientific community exploring the topic and provide valuable insights for bankers, analysts, market investors, regulatory authorities, and society in the decision-making process. JEL classification numbers: C32, G00, G21. Keywords: Banking, Interest rates, Exchange rate, Bank stocks.

Liquidity‐adjusted value‐at‐risk using extreme value theory and copula approach

AbstractIn this study, we propose the application of the GARCH‐EVT‐Copula model in estimating liquidity‐adjusted value‐at‐risk (L‐VaR) of energy stocks while modeling nonlinear dependence between return and bid‐ask spread. Using the L‐VaR framework of Bangia et al. (1998), we present a more parsimonious model that effectively captures non‐zero skewness, excess kurtosis, and volatility clustering of both return and spread distributions of energy stocks. Moreover, to measure the nonlinear dependence between return and spread series, we use multiple copulas: Clayton, Gumbel, Frank, Normal, and Student‐t. Based on the statistical backtesting and economic loss functions, our results suggest that the GARCH‐EVT‐Clayton copula is superior and most consistent in forecasting L‐VaR compared with other competing models. This finding has several implications for investors, market makers, and daily traders who appreciate the importance of liquidity in market risk computation.

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.