Distribution Of Stock Returns Research Articles

Ambiguity, Limited Market Participation, and the Cross-Sectional Stock Return

Using expected utility under uncertain probability theory (EUUP, Izhakian, 2017; 2020), we study whether the ambiguity related to individual stocks is priced in the Chinese A-share market and the mechanism behind the ambiguity premium phenomenon. Theoretically, when the asset price is within a specific range, ambiguity-averse investors refrain from participating in trading. As asset ambiguity increases, high ambiguity-averse investors exit the market, with those with lower aversion remaining in the market (limited market participation phenomenon). Investors who remain in the market due to lower ambiguity aversion are willing to accept a low ambiguity premium. Empirically, we measure monthly ambiguity using the volatility of daily stock return distributions within a month and find the following: (1) The equal-weighted average returns of the most ambiguous portfolios (top 20%) are significantly lower than those of the least ambiguous portfolios (bottom 20%). (2) Ambiguity still significantly negatively affects the cross-sectional stock return after controlling for common firm characteristics. (3) The higher the ambiguity, the lower the future trading activity, supporting our theoretical predictions. These findings reveal the mechanism of the negative ambiguity premium in the Chinese A-share market. This study provides new ideas for building a factor-pricing model suitable for the A-share market and a fresh perspective for preventing systemic financial risk.

The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

Stock Liquidity and Return Distribution in Emerging Market

Purpose: This study aims to illustrate the relationship between the liquidity of a stock and the return distribution of all companies listed on the Indonesian Stock Exchange. Design/methodology/approach: The correlation between stock liquidity and return distribution, represented using skewness and kurtosis methods, was determined by the author through two-way tests using line regression (fixed cross-section regression) and machine learning (random forest regressor) for Indonesia data Stock exchange from 2014 to 2023. Findings: The results indicate a connection between stock liquidity and return distribution. When evaluating stock liquidity, the zero return days technique gives a more significant relationship, while the kurtosis of return method gives a more significant return distribution. It is impossible to determine with absolute certainty whether the correlation is positive or negative; it depends on how stock liquidity and return distribution are measured. Research limitations/implications: The correlation between stock liquidity and return distribution cannot be characterized as an absolute relationship due to the intricacy and variety of approaches used to measure it. Practical implications: The kurtosis of return has a better relationship with stock liquidity, and “zero return day” and “relative spread” are still more strongly correlated with the return distribution. Originality/value: As the first study to use machine learning and linear regression to examine the relationship between stock liquidity and return distribution, this paper expands the body of knowledge. Second, it examines which return distribution – skewness or kurtosis – has a stronger correlation with stock liquidity. Third, we examine which liquidity metrics—relative spread, Amihud liquidity, price impact ratio, and zero return days—are most related to the return distribution.

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.

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.

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

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

Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

Proper description of the return distribution is crucial for investment practitioners. The underestimation of the tail risk may lead to severe consequences, even for assets with moderate fluctuations. However, many empirical studies found that the distribution tails of many financial assets drop off more slowly than the Gaussian distributions. Therefore, we intend to model and calibrate the heavy tails observed in financial fluctuations in this study. By maximizing the Varma entropy with value-at-risk and expected shortfall constraints, we obtain the probability distribution of stock return and observe that the tail of stock return distribution is a power law. Since the variance of the real stock portfolio may be a random variable, using the mean-VaR-ES constraints to maximize the Varma entropy effectively avoids the problem of assuming that the variance is a constant value under the traditional mean-variance constraint. Therefore, the deduced theoretical model would be more consistent with the real market. Using high-frequency data from China’s stock markets, we calibrate our theoretical model and give the concrete form of probability density distribution p(x) for different time intervals. The calibration results show that the tail of the stock return distribution is a power law with most of the power-law orders between −2 and −7. We prove the robustness of our results by calibrating the Varma entropy for S&P 500 of the USA stock market and different stock market indices in China’s A-share market. Our research’s findings not only offer a theoretical perspective for researchers but also give investing professionals a theoretical foundation on which to base their decisions.

An Analysis of the Schrodinger Equation Model for the Distribution Rate of Stock Returns

Quantum mechanics is a theory that describes the behavior of particles in the microscopic world. If the stock index can be considered an object on a macro scale, then every stock of a stock index is an object on a micro-scale. The stock price can be analogous to being a particle. This study aimed to obtain the density distribution of stock returns. Modeling stock returns distribution using a Schrodinger equation model with the assumption that stock is a particle in the good delta potential function so that stock returns as analogous to particles can be known. The Schrodinger equation can calculate stock returns expressed as an exponential distribution. The stock return density distribution using Schrodinger equation model has a higher kurtosis value than the kurtosis value in the normal distribution. The kurtosis value is the degree of the peak height of a distribution. The stock price data used is the stock price data of PT. United Tractors Tbk. and PT. Unilever Indonesia Tbk. during 2013-2018. This study shows the stock price of PT. Unilever Indonesia Tbk. has a more stable average stock price return with a more negligible risk of loss than the stock price of PT. United Tractors Tbk.

Revisiting the relationship between idiosyncratic risk and stock returns: a quantile regression analysis in the context of an emerging market

PurposeThe relationship between idiosyncratic risk and stock return has been debated for decades; this study reexamined this relationship in the Pakistani stock market by using the quantile regression approach along with the prospect theory.Design/methodology/approachThe present study is quantitative, and secondary data obtained from an emerging market are used. The quantile regression method allows the estimates of idiosyncratic risk to vary across the entire distribution of stock returns, i.e. the dependent variable. In this study, the standard deviation of regression residuals from the Fama and French three-factor model was used to measure idiosyncratic risk. Convenience sampling is employed; the sample consists of 82 firms listed on the KSE-100 index, with 820 annual observations for the ten years from 2011 to 2020. After computing results by using quantile regression, the study's findings, ordinary least squares (OLS) and least sum of absolute deviation (LAD) regression techniques are also compared.FindingsThe quantile regression estimation results indicate that idiosyncratic risk is positively correlated with stock returns and that this relationship is contingent on whether prices are rising or falling. Consistent with the prospect theory, the finding suggests that stock investors tend to avoid risk when they anticipate a loss but are more willing to take risks when they anticipate a profit. The results of the OLS and LAD regressions indicate that the method typically employed in previous studies does not adequately describe the relationship between idiosyncratic risk and stock return at extreme points or across the entire distribution of stock return.Originality/valueThese empirical findings shed new light on the relationship between idiosyncratic risk and stock return in Pakistani stock market literature.

Investor Opinion Formation and the Distribution of Stock Returns

Investor Opinion Formation and the Distribution of Stock Returns

Performance evaluation of investment with DEA models under pure jump processes

SummaryPortfolio optimization is a selection of the best combination of financial assets that maximizes the return and minimizes the risk. As the stock return distributions exhibit skewness, kurtosis, and heavy‐tailedness, for asset performance evaluation through the data envelopment analysis (DEA), we assume that the asset returns follow a pure jump Lévy process. For this purpose, two risk measures are provided as value‐at‐risk (VaR) and conditional VaR (CVaR). To deal with negative values, the range directional measure (RDM) model is utilized in the appropriate Lévy process, and inefficiency measurements are compared. Moreover, the asset price jumps have significant effects on the input and output of DEA models, risk measures, mean returns, and efficiency scores. In this regard, there are two optimization problems integrating DEA based on the variance gamma (VG) Lévy process, in which the input and output are stochastic. One of these two problems is a multi‐objective optimization model that evaluates more reliable efficiency scores than the other models. For this purpose, the VG parameters are estimated through the moments estimation method in order to analyze seven companies listed in the Tehran stock exchange (TSE). Finally, the Kolmogorov–Smirnov goodness‐of‐fit test is conducted. The results indicate that the VG model fits properly and is well suited to assets returns.

Forecasting liquidity‐adjusted VaR: A conditional EVT‐copula approach

AbstractThis study models the joint distribution of individual stock returns and bid‐ask spreads using combined EGARCH‐EVT and combined GP‐INGARCH‐EVT processes for the marginals, and bivariate copulas for the dependence structure. We use the proposed approach to first simulate returns and spreads of individual stocks from different countries and regions, and then forecast the Liquidity‐adjusted Value‐at‐Risk (L‐VaR) measure according to three types of L‐VaR models. The backtesting results suggest that the proposed simulated L‐VaR models perform better than the competing L‐VaR/VaR models in forecasting L‐VaR. It is also observed that the simulated L‐VaR models perform better than the competing L‐VaR/VaR models in predicting the economic downturn.

Encoded Value-at-Risk: A machine learning approach for portfolio risk measurement

Measuring risk is at the center of modern financial risk management. As the world economy is becoming more complex and standard modelling assumptions are violated, the advanced artificial intelligence solutions may provide the right tools to analyse the global market. In this paper, we provide a novel approach for measuring market risk called Encoded Value-at-Risk (Encoded VaR), which is based on a type of artificial neural network, called Variational Auto-encoders (VAEs). Encoded VaR is a generative model which can be used to reproduce market scenarios from a range of historical cross-sectional stock returns, while increasing the signal-to-noise ratio present in the financial data, and learning the dependency structure of the market without any assumptions about the joint distribution of stock returns. We compare Encoded VaR out-of-sample results with twelve other methods and show that it is competitive to many other well-known VaR algorithms presented in the literature.

Reliability of maximum spanning tree identification in correlation-based market networks

Maximum spanning tree is a popular tool in market network analysis. Large number of publications are devoted to the maximum spanning tree calculation and its interpretation for particular stock markets. Usually one use market data to calculate Pearson correlations between stock returns and construct a compete weighted graph, where weights of edges are given by calculated correlations. Then maximum spanning tree of the obtained network is calculated and its market interpretation is discussed. However, Pearson correlation is not only one similarity measure which can be used for market network analysis. Different measures of similarity will generate different market networks, and, as a consequence, different maximum spanning trees. The main goal of the present paper is to analyze the key points of this difference. We show that this is related with uncertainty (reliability) of maximum spanning tree identification in different networks. We study uncertainty in the framework of the concept of random variable network (RVN). We consider different correlation based networks in the large class of elliptical distributions. We show that true maximum spanning tree is the same in three correlation networks: Pearson correlation network, Fechner correlation network, and Kendall correlation network. It means, that from theoretical point of view there is no difference between maximum spanning trees in these networks. The observed difference between maximum spanning trees in different networks can be, therefore, explained by uncertainty of maximum spanning tree identification by observations. We argue that among different measures of uncertainty the FDR (False Discovery Rate) is the most appropriated to measure uncertainty (reliability) of maximum spanning tree identification. We investigate FDR of Kruskal algorithm for maximum spanning tree identification and show that reliability of maximum spanning tree identification is different in these three networks. In particular, for Pearson correlation network the FDR essentially depends on distribution of stock returns. We prove that for market network with Fechner correlation the FDR is non sensitive to the assumption on stock’s return distribution. Some interesting phenomena are discovered for Kendall correlation network. Our experiments show that FDR of Kruskal algorithm for maximum spanning tree identification in Kendall correlation network weakly depend on distribution and at the same time the value of FDR is almost the best in comparison with maximum spanning tree identification in other networks.

Clustering-enhanced stock price prediction using deep learning

In recent years, artificial intelligence technologies have been successfully applied in time series prediction and analytic tasks. At the same time, a lot of attention has been paid to financial time series prediction, which targets the development of novel deep learning models or optimize the forecasting results. To optimize the accuracy of stock price prediction, in this paper, we propose a clustering-enhanced deep learning framework to predict stock prices with three matured deep learning forecasting models, such as Long Short-Term Memory (LSTM), Recurrent Neural Network (RNN) and Gated Recurrent Unit (GRU). The proposed framework considers the clustering as the forecasting pre-processing, which can improve the quality of the training models. To achieve the effective clustering, we propose a new similarity measure, called Logistic Weighted Dynamic Time Warping (LWDTW), by extending a Weighted Dynamic Time Warping (WDTW) method to capture the relative importance of return observations when calculating distance matrices. Especially, based on the empirical distributions of stock returns, the cost weight function of WDTW is modified with logistic probability density distribution function. In addition, we further implement the clustering-based forecasting framework with the above three deep learning models. Finally, extensive experiments on daily US stock price data sets show that our framework has achieved excellent forecasting performance with overall best results for the combination of Logistic WDTW clustering and LSTM model using 5 different evaluation metrics.

Dynamic portfolio formulation using bitcoin and LQ45 stocks

This research aims to evaluate whether dynamic portfolios consisting of bitcoin and LQ45 stocks outperform portfolios composed solely of LQ45 stocks, especially during the Covid-19 pandemic. Accordingly, we use the time-series data of eight stocks and bitcoin from January 1, 2020, to December 31, 2020. We then run the DCC-GARCH method to analyze better the dynamic correlation between assets and the abnormalities of stock return distributions. The findings demonstrate that bitcoin is negatively correlated with LQ45 stocks, and hence, it can be used to hedge against stock assets. Further, we measure the portfolio performance of bitcoin-hedged and unhedged stock portfolios using the Jensen Index, Treynor Index, Sharpe Index, Sortino Ratio, and Omega Ratio. These measures consistently indicate that bitcoin-hedged stocks outperform unhedged stocks. In sum, our study concludes that incorporating bitcoin into portfolio formation improves portfolio performance.

Hypothesis Test of Weak Form of Market Efficiency in Some Selected Stocks

The present study attempted to examine the weak-form of market efficiency of a sample of 33 daily stock returns belonging to seven specific sectors in the National Stock Exchange of India for the period from May 18, 2020 – May 12, 2021. The study’s objective was to examine normality and randomness in data series of stock returns for this period. In order to get the desired results, it used means, standard deviation, skewness, kurtosis, Jarque – Bera test, and runs test. The normality test results found that the data of 31 equity stock prices were not normally distributed except for the two stock prices. The outcome of the runs test was that the distribution of daily stock returns of 30 select companies followed a random walk and was the weak-form efficient market.

Armageddon and the stock market: US, Canadian and Mexican market responses to the 1962 Cuban Missile Crisis

The threat of nuclear annihilation has never been higher than in 1962, when US President Kennedy and Soviet Premier Khruschev engaged in brinkmanship over the placement of Soviet missiles in Cuba during October 16−28. Although the resolution of the crisis was followed by a sustained recovery in the US, Canadian and Mexican stock markets, the stock market impact of the crisis itself, at first glance, seems relatively limited. Notwithstanding the fact that empirical analysis of 1962 US market data reveal a significant break on October 23, 1962, which is the day after President Kennedy’s television address about the Cuban Missile Crisis, the drop on this day was smaller than prior one day declines seen in the earlier part of the year. When we focus on the 1 % left tail of the distribution of stock returns, that is, just the very largest and least probable negative returns, a different story emerges, however. US uncertainty is now seen to have a significant negative impact on returns across each of the US, Canadian and Mexican markets. Moreover, the size of the negative response to the rise in uncertainty is comparable in all three cases notwithstanding the fact the pre-crisis Mexican stock market trajectory had been very different from that seen in the United States and Canada.

Learning Probability Distributions in Macroeconomics and Finance

We propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. Being able to learn complex patterns from a data rich environment, our approach is useful for a decision making that depends on uncertainty of large number of economic outcomes. Specifically, it is informative to agents facing asymmetric dependence of their loss on outcomes from possibly non-Gaussian and non-linear variables. We show the usefulness of the proposed approach on the two distinct datasets where a machine learns the pattern from data. First, we construct macroeconomic fan charts that reflect information from high-dimensional data set. Second, we illustrate gains in prediction of stock return distributions which are heavy tailed, asymmetric and suffer from low signal-to-noise ratio.

Pricing Cyber Security Insurance

Cybersecurity breaches may be correlated due to geography, similar infrastructure, or use of a third-party contractor. We show how a logistic regression may be used to estimate the probability of an attack where breaches may be correlated among firms up and down the supply chain. We also show how a Poisson regression may be used to estimate the number of records breached. Losses arising from cybersecurity breaches have an unknown distribution. We propose the stock price reaction to a breach as an objective measure of the loss in wealth sustained by the firm due to a breach. This loss measure reflects the immediate and long-term effects of a breach, including reputational effects and other intangible impacts that are otherwise more difficult to quantify. We examine stock returns for 258 cybersecurity breach announcements over 2011-2016 in order to obtain the empirical loss distribution. We find a five-day abnormal return of -1.44%. Seventy-one percent of these 258 announcements result in a negative abnormal return, and a gamma distribution provides an excellent fit to these losses. In addition to introducing a predictive model for correlated losses, our study shows how insurers can use either the empirical stock return distribution of losses or the per record cost of a breach in the pricing of cyberinsurance.