Distribution Of Stock Returns Research Articles

Whether stock market provides high returns: evidence from skewness of individual stocks in China

PurposeThis paper studies whether individual stocks provide higher returns than government bond in the Chinese market.Design/methodology/approachThe authors compare individual stock returns and government bond returns in the Chinese market.FindingsThe authors find that more than half of individual stocks underperform government bonds over the same period in China, which highlights the important role of positive skewness in the distribution of individual stock returns. The high return of a few stocks is the reason why the stock market return is higher than that of government bond in China.Originality/valueThe results of this paper emphasize that portfolio diversification plays an important role in the Chinese market.

Stock liquidity and return distribution: Evidence from the London Stock Exchange

We investigate the relationship between liquidity and the distribution of returns, for all listed firms on the London Stock Exchange between 2002–2018. We find a strong relationship between the distribution of returns, as measured by skewness and kurtosis, and liquidity.

An Application of Extreme Value Theory to Finance – An Empirical Study of Whether Stock Shape Parameters and the Differences Between Corresponding Actual and BSM Put Option Values Are Positively Correlated

Large stock price movements and financial crises are a common occurrence relative to the belief of normality in markets, and they are becoming more common as the world becomes more interconnected and more technology driven. After large dips in prices and after crises the topic of risk management, specifically tail risk quantification, comes into the focus of not just researchers, but is also put into question by the general public. Recently, Extreme Value Theory, originally targeted at the study of weather and climate, entered the field of risk management and provided a new approach to measuring tail risk, letting the data speak for itself rather than underpinning distributional assumptions as most approaches had done thus far. This thesis employs Extreme Value Theory, specifically the Peaks over Threshold approach or Generalized Pareto Distribution approach, in order to quantify the tail thickness of the left tail of stock return distributions of the S&P 500 index and its constituents. The thesis then assesses the relationship between the tail fatness of the underlying stock and the absolute as well as relative difference between the actual put option value and the put option value according to Black Scholes Merton. The hypothesis is that thicker left tails imply that large negative movements are more probable than under the Gaussian assumption. This in turn could display itself in an undervaluation of put options, in particular deep out of the money put options, as calculated by traditional BSM. In the analysis, neither the absolute nor the relative differences seem to show a relationship to respective shape parameters. However, the averages of the absolute differences of deep out of the money put options do appear to be very small in size, indicating a valuation close to that of the BSM model, while the averages of the relative differences of deep out of the money put options are for the larger part close to 100%, indicating a complete undervaluation of these put options by BSM, regardless of the shape parameter. The lack of relationship between shape parameters and differences begs the question of whether buyers are valuing options correctly and the employed methodology is wrong or whether the thesis methodology is appropriate and buyers are mistaken. A short analysis provides evidence pointing to the latter.

Conditional violation of weak-form market efficiency

PurposeMany prior tests of market efficiency, which occurred decades ago, were limited by data and did not employ methodology to correct for leptokurtosis in the stock return distribution. Furthermore, these studies did not test many aspects of conditional market efficiency. One aspect of a potential conditional violation of market efficiency is whether stock markets are efficient conditional on the level of stock return.Design/methodology/approachThis paper uses quantile regressions to control for leptokurtosis in the stock return distribution and simultaneous quantile regressions to test whether markets are efficient conditional on the level of the market return. This paper uses market-level stock return data to bias against finding significant results in the efficiency tests. Furthermore, the author uses data from 1926 through 2018, providing the longest time period to date under which market efficiency is tested.FindingsThis paper presents evidence that the autoregressive coefficient decreases across return levels in stock market indices. The autoregressive coefficient is positive around highly negative returns and negative or insignificant around highly positive returns, which suggests that when stock returns are low they are more likely to continue lower, and when stock returns are high they are more likely to reverse. Results additionally suggest that market efficiency is not time-invariant and that stock markets have become more efficient over the sample period.Originality/valueThis paper extends the literature by finding evidence of a violation of weak-form market efficiency conditional on the level of stock returns. It further extends the literature by finding evidence that the stock market has become more efficient between 1926 and 2018.

Optimal Stock Investment under Ambiguity about Ambiguity

A prominent approach to modelling ambiguity about stock return distribution is to assume that investors have multiple priors about the distribution and these priors are distributed according to a certain second-order distribution. Realistically, investors may also have multiple priors about the second-order distribution, thus allowing for ambiguous ambiguity. Despite a long history of debates about this idea (Reichenbach [1949], Savage [1954]), there seems to be no formal analysis of investment behavior in the presence of this feature. We develop a tractable portfolio choice framework incorporating ambiguous ambiguity, characterize analytically the optimal portfolio, and examine its properties.

Trade clustering and power laws in financial markets

This study provides an explanation for the emergence of power laws in asset trading volume and returns. We consider a two‐state model with binary actions, where traders infer other traders' private signals regarding the value of an asset from their actions and adjust their own behavior accordingly. We prove that this leads to power laws for equilibrium volume and returns whenever the number of traders is large and the signals for asset value are sufficiently noisy. We also provide numerical results showing that the model reproduces observed distributions of daily stock volume and returns.

Encoded Value-at-Risk: A Predictive Machine for Financial Risk Management

Measuring risk is at the center of modern financial risk management. As the world economy is becoming more complex and standard modeling assumptions are violated, the advanced artificial intelligence solutions may provide the right tools to analyze 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 eleven other methods and show that it is competitive to many other well-known VaR algorithms presented in the literature.

Crowded Trades, Market Clustering, and Price Instability

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock the clustering measure captures the degree of trading overlap among any two investors in that stock. We investigate the effect of crowded trades on stock price stability and show that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability.

Crowded Trades, Market Clustering, and Price Instability

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock the clustering measure captures the degree of trading overlap among any two investors in that stock. We investigate the effect of crowded trades on stock price stability and show that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability.

VALUE AT RISK IN STOCK PORTFOLIO USING T-COPULA: Case Study of PT. Indofood Sukses Makmur, Tbk. and Bank Mandiri (Persero), Tbk.

Value at Risk (VaR) is a measuring tool that can calculate the amount of the worst losses that occur in the stock portfolio with a certain level of confidence and in certain period of time. In general, financial data has a high volatility value, which is caused the variance of residual model is not constant and nonnormally distributed. In this case, Copula-GARCH can be used to calculate the VaR. The Generalized Autoregressive Conditional Heterocedasticity (GARCH) model can resolve the time series models that have non-constant residual variance. This research use the t-Copula to model the dependency structure in the combined distribution of stock returns. The t-copula function is good in terms of reaching the extreme value state that often occurs in the financial data of stock returns and has heavytails. The empirical data uses the stock return data of PT. Indofood Sukses Makmur, Tbk (INDF) and Bank Mandiri (Persero) Tbk (BMRI) in the period of October 8, 2012 - October 8, 2017. In this research, Value at Risk is calculated using the period 1 day ahead at 90% confidence level that is 0.042, at 95% confidence level that is 0.025 and at 99% confidence level that is 0.017 with weight of each stock is 50%.

Asymmetry in the distribution of daily stock returns

When plotting aggregated daily stock returns with absolute value less than x against x, a typical spoon-shaped pattern emerges which indicates a special type of asymmetry. This pattern disappears when individual returns are averaged; it is also absent in stock price indices, which points to explanations based on firm-specific drivers of returns.

Market Impact on financial market integration: Cross-quantilogram analysis of the global impact of the euro

We contribute to the literature by providing a more comprehensive understanding of the impact the euro has had on financial market integration with economies of different characteristics outside and within the European market via inclusion of market conditions influence on the level of financial integration. Our paper employs the recently developed cross-quantilogram (Han et al., 2016) approach to examine quantile dependence between the conditional stock return distributions of Germany and the UK with that of three common currency groups within EMU (Finland, France, and Italy), two global leading markets (the US and Japan), and two of the most promising emerging markets (China and India). We find three key results. First, both the EU membership and the common currency union affect the degree of financial market integration. Nevertheless, disentangling the effects of EU membership from the common currency shows that the common currency group has an additional impact on financial integration, as the degree of dependence is stronger in the common currency group than in the sovereign currency group and other groups. Second, there is a heterogeneous dependence structure, which is strongly observed for the UK and German stock returns with that of developed (the US and Japan) and emerging markets (India and China). Third, cross-quantile correlations change over time, especially in low and high quantiles, indicating that they are prone to jumps and discontinuities in the dependence structure. As far as we are aware, this is the first study in this field employing a cross-quantilogram method to examine the impact of different market conditions on the correlations, making our study a pioneer in the field of stock market integration.

A quantile-copula approach to dependence between financial assets

This article unveils the dependence structure between United States stock prices, crude oil prices, exchange rates, and U.S. interest rates. In particular, we employ linear and nonlinear estimation methods, such as quantile regression and the quantile-copula approach. Over the 1998–2017 period, we find that there is a positive relationship between the dollar value and the S&P 500 stock price, with the exception of the lower and upper tails of the stock return distribution. Further evidence is obtained on the dependence structure between other asset returns. The stock returns are negatively related to oil prices but positively to U.S. interest rates. Our results highlight the way that financial assets are linked, which have implications for risk management and monetary policy.

Effects of the fat-tail distribution on the relationship between prospect theory value and expected return

This study investigates the negative relationship between prospect theory value and expected return considering the fat-tail property of the return distribution. The results of both decile portfolio and cross-sectional regression show evidence supporting the hypothesis related to prospect theory value. However, these results are very sensitive to whether the model includes a short-term reversal factor. In the empirical design combining the hypothesis with the degree of fat-tail of the return distribution, stock groups with the fat-tail return distribution definitely show that prospect theory value has a significant information value for explaining expected return, regardless of whether the short-term reversal and other factors are included in the models. These results suggest that both the fat-tail property in the stock return distribution and the property of the skewed return distribution must be considered in examining the relationship between prospect theory value and expected return. Furthermore, our findings on the effects of the fat-tail property of the return distribution are verified through robustness testing while considering changes in empirical design and using out-of-sample stock markets of the U.S., Japan, and China, as well as the in-sample Korean stock market.

Nonparametric Dynamic Conditional Beta

Abstract This article derives a dynamic beta representation using a Bayesian semiparametric multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model. The conditional joint distribution of excess stock returns and market excess returns is modeled as a countably infinite mixture of normals. This allows for deviations from the elliptic family of distributions. Empirically, we find the time-varying beta of a stock nonlinearly depends on the expected value of excess market returns. The nonlinear dependence is robust to different GARCH specifications as well as more factors in the model. In highly volatile markets, beta is almost constant, while in stable markets, the beta coefficient can depend asymmetrically on the expected market excess return. We extend the model to several factors and find empirical support for a three-factor model with nonlinear factor sensitives.

PERHITUNGAN VALUE AT RISK DENGAN PENDEKATAN THRESHOLD AUTOREGRESSIVE CONDITIONAL HETEROSCEDASTICITY-GENERALIZED EXTREME VALUE

Stock is the most popular type of financial asset investment. Before buying a stock, an investor must estimate the risks which will be received. Value at Risk (VaR) is one of the methods that can be used to measure the level of risk. When investing in stock, if an investor wants to earn high returns, then he must be prepared to face higher risks. Most of stock return data have volatility clustering characteristic or there are cases of heteroscedasticity and the distribution of stock returns has heavy tail. One of the time series models that can be used to overcome the problem of heteroscedasticity is the ARCH/GARCH model, while the method for analyzing heavy tail data is Extreme Value Theory (EVT). In this study used an asymmetrical ARCH model with the Threshold ARCH (TARCH) and EVT methods with Generalized Extreme Value (GEV) to calculate VaR of the stock return from PT Bumi Serpong Damai Tbk for the period of September 2012 to October 2018. The best chosen model is AR([3])–TARCH(1). At the 95% confidence level, the maximum loss an investor will be received within the next day by using the TARCH-GEV calculation is 0.18%.

Do Global Stocks Outperform US Treasury Bills?

We study compound returns to nearly 62,000 global common stocks during the 1990 to 2018 period, documenting that the majority, 56% of US stocks and 61% of non-US stocks, under perform one-month US Treasury bills over the full sample. Focusing on aggregate shareholder wealth creation measured in US dollars, we find that the top-performing 1.3% of firms account for the $US 44.7 trillion in global stock market wealth creation from 1990 to 2018. Outside the US, less than one percent of firms account for the $US 16.0 trillion in net wealth creation. These results highlight the practical implications of the fact that the distribution of long-run stock returns is strongly positively skewed.

Cross-Sectional Learning of Extremal Dependence Among Financial Assets

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint heavy-tailed random vectors featuring not only distinct marginal tail heaviness, but also flexible tail dependence structure. The novelty lies in that pairwise tail dependence between any two dimensions is modeled separately from their correlation, and can vary respectively according to its own parameter rather than the correlation parameter, which is an essential advantage over many commonly used methods such as multivariate $t$ or elliptical distribution. It is also intuitive to interpret, easy to track, and simple to sample comparing to the copula approach. We show its flexible tail dependence structure through simulation. Coupled with a GARCH model to eliminate serial dependence of each individual asset return series, we use this novel method to model and forecast multivariate conditional distribution of stock returns, and obtain notable performance improvements in multi-dimensional coverage tests. Besides, our empirical finding about the asymmetry of tails of the idiosyncratic component as well as the market component is interesting and worth to be well studied in the future.

Analytic solution to the portfolio optimization problem in a mean-variance-skewness model

ABSTRACTIn portfolio theory, it is well-known that the distributions of stock returns are often unimodal asymmetric distributions. Therefore, many researches have suggested considering the skew-normal distribution as an adequate model in quantitative finance. Such asymmetry explains why the celebrated mean-variance theory, which does not account to the skewness of distribution of returns, frequently fails to provide an optimal portfolio selection rule. In this paper, we provide a novel approach for solving the problem of optimal portfolio selection for asymmetric distributions of the stock returns, by putting it into a framework of a mean-variance-skewness measure. Moreover, our optimal solutions are explicit and are closed-form. In particular, we provide an analytical portfolio optimization solution to the exponential utility of the well-known skew-normal distribution. Our analytical solution can be investigated in comparison to other portfolio selection rules, such as the standard mean-variance model. The new methodology is illustrated numerically.

Predicting firm level stock returns: Implications for asset pricing and economic links

We examine the predictive ability of stock price ratios, stock return dispersion and distribution measures for firm level returns. Analysis typically focusses on market level returns, however, for the underlying asset pricing model to hold, firm-level predictability should be present. Additionally, we examine the economic content of predictability by considering whether the predictive coefficient has the theoretically correct sign and whether it is related to future output growth. While stock returns reflect investor expectations regarding future economic conditions, they are often too noisy to act as predictor. We use the time-varying predictive coefficient as it reflects investor confidence in the predictive relation. Results suggest that a subset of stock price ratios have predictive power for individual firm stock returns, exhibit the correct coefficient sign and has predictive power for output growth. Each of these ratios has a measure of fundamentals divided by the stock price and has a positive relation with stock returns and output growth. This implies that as investors expect future economic conditions to improve and earnings and dividends to rise, so expected stock returns will increase. This supports the cash flow channel as the avenue through which stock return predictability arises.