Models of asset returns: changes of pattern from high to low event frequency

In this paper we have analysed asset returns of the New York Stock Exchange and the Helsinki Stock Exchange using various time-independent models such as normal, general stable, truncated Lévy, mixed diffusion-jump, compound normal, Student t distribution and power exponential distribution and the time-dependent GARCH(1, 1) model with Gaussian and Student t distributed innovations. In order to study changes of pattern at different event horizons, as well as changes of pattern over time for a given event horizon, we have analysed high-frequency or short-horizon intraday returns up from 20 s intervals to a full trading day, medium-frequency or medium-horizon daily returns and low-frequency or long-horizon returns with holding period up to 30 days. As for changes of pattern over time, we found that for medium-frequency returns there are relatively long periods of business-as-usual when the return-generating process is well-described by a normal distribution. We also found periods of ferment, when the volatility grows and complex time dependences tend to emerge, but the known time dependences cannot explain the variability of the distribution. Such changes of pattern are also observed for high-frequency or short-horizon returns, with the exception that the return-generating process never becomes normal. It also turned out that the time dependence of the distribution shape is far more prominent at high frequencies or short horizons than the time dependence of the variance. For long-horizon or low-frequency returns, the distribution is found to converge towards a normal distribution with the time dependences vanishing after a few days.     

A duscrete-time model of high-frequency stock returns

A model of intraday financial time series is developed. The model is a dynamic factor model consisting of two equations. First, a rate of return of a ‘stock’ in a single day is assumed to be generated by serveral common factors plus some additive erros (‘intraday equation’). Secondly, the joint distribution of those common factors is assumed to depend on the hidden state of the day, which fluctuates according to a Markov chain (‘day-by-day equation’). Together the equations compose a hidden Markov model.

We investigate properties of the model. Among them is a central limit theorem for cumulative returns, which agrees with the well-known empirical phenomenon in the stock markets that the distributions of longer-horizon returns are closer to the normal. We propose a two-step procedure consisting of the method of principal components and the EM algorithm to estimate the model parameters as well as the unboservable states. In addition, we propose a procedure for predicting intraday returns. Finally, the model is fitted to empirical data, the Standard&Poors 500 Index 5 min return data, to see if the model is capable of describing intraday movements of the index.     

Long-run Performance after Stock Splits: 1927 to 1996

We measure the postsplit performance of 12,747 stock splits from 1927 to 1996 using two methods to measure abnormal returns: size and book‐to‐market reference portfolios with bootstrapping, and calendar‐time abnormal returns combined with factor models. Between 1927 and 1996, neither method applied to splits 25 percent or larger finds performance significantly different from zero. Over selected subperiods, subsamples of 2–1 splits restricted by book‐to‐market availability requirements display positive abnormal returns using some methods. However, these samples show small or negligible abnormal returns using the calendar‐time method. Overall, the stock split evidence against market efficiency is neither pervasive nor compelling.     

Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market

The Markowitz portfolio optimization model, popularly known as the Mean-Variance model, assumes that stockreturns follow normal distribution. But when stock returns do not follow normal distribution, this model wouldbe inadequate as it would prescribe sub-optimal portfolios. Stock market literature often deliberates that stock returns are non-normal. In such context the Markowitz model would not be sufficient to estimate the portfolio risks. The purpose of this paper is to expand the original Markowitz portfolio theory (mean-variance) via adding the higher order moments like skewness (third moment about the mean) and kurtosis (fourth moment about the mean) in the return characteristics. The research paper investigates the impact of including higher moments using multi-objective programming model for portfolio stock selection and optimization. The empirical results indicate that the inclusion of higher moments had a considerable impact in estimating the returns behavior of portfolios. The portfolios optimized using all the four moments, generated higher returns for the given level of risk in comparison to the returns of the Markowitz model during the study period 2000–2011. The results of this study would be immensely useful to fund managers, portfolio managers and investors as it would help them in understanding the Indian stock market behavior better and also in selecting alternative portfolio selection models.     

Option trading after the opening bell and intraday stock return predictability

Prior literature finds that information is reflected in option markets before stock markets, but no study has explored whether option volume soon after market open has predictive power for intraday stock returns. Using novel intraday signed option-to-stock volume data, we find that a composite option trading score (OTS) in the first 30 min of market open predicts stock returns during the rest of the trading day. Such return predictability is greater for smaller stocks, stocks with higher idiosyncratic volatility, and stocks with higher bid–ask spreads relative to their options’ bid–ask spreads. Moreover, OTS is a significantly stronger predictor of intraday stock returns after overnight earnings announcements. The evidence suggests that option trading in the 30 min after the opening bell has predictive power for intraday stock returns.     

Robust inference in single firm/single event analyses

Single firm/single event (SFSE) studies are relevant in corporate finance. Since inference on abnormal returns in this context necessarily relies on the time series variance of these abnormal returns, the implied problem of heteroscedasticity is obvious, although hard to solve. We analyze robust inference in an SFSE setting using Monte Carlo and resampling experiments. Estimation is biased when the calibration and event period occur in different volatility regimes. We develop a unique specification test for these structural breaks. The most robust inference is obtained by using intraday data and a multiplicative component GARCH estimator.     

Probability distribution of returns in the Heston model with stochastic volatility*

Abstract

We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker‐Planck equation exactly and, after integrating out the variance, find an analytic formula for the time‐dependent probability distribution of stock price changes (returns). The formula is in excellent agreement with the Dow‐Jones index for time lags from 1 to 250 trading days. For large returns, the distribution is exponential in log‐returns with a time‐dependent exponent, whereas for small returns it is Gaussian. For time lags longer than the relaxation time of variance, the probability distribution can be expressed in a scaling form using a Bessel function. The Dow‐Jones data for 1982–2001 follow the scaling function for seven orders of magnitude.     

Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas

We propose to model the joint distribution of bid-ask spreads and log returns of a stock portfolio by using Autoregressive Conditional Double Poisson and GARCH processes for the marginals and vine copulas for the dependence structure. By estimating the joint multivariate distribution of both returns and bid-ask spreads from intraday data, we incorporate the measurement of commonalities in liquidity and comovements of stocks and bid-ask spreads into the forecasting of three types of liquidity-adjusted intraday Value-at-Risk (L-IVaR). In a preliminary analysis, we document strong extreme comovements in liquidity and strong tail dependence between bid-ask spreads and log returns across the firms in our sample thus motivating our use of a vine copula model. Furthermore, the backtesting results for the L-IVaR of a portfolio consisting of five stocks listed on the NASDAQ show that the proposed models perform well in forecasting liquidity-adjusted intraday portfolio profits and losses.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

A simple two-component model for the distribution of intraday returns

We model the conditional distribution of high-frequency financial returns by means of a two-component quantile regression model. Using three years of 30 minute returns, we show that the conditional distribution depends on past returns and on the time of the day. Two practical applications illustrate the usefulness of the model. First, we provide quantile-based measures of conditional volatility, asymmetry and kurtosis that do not depend on the existence of moments. We find seasonal patterns and time dependencies beyond volatility. Second, we estimate and forecast intraday Value at Risk. The two-component model is able to provide good-risk assessments and to outperform GARCH-based Value at Risk evaluations.     

Intraday online investor sentiment and return patterns in the U.S. stock market

We implement a novel approach to derive investor sentiment from messages posted on social media before we explore the relation between online investor sentiment and intraday stock returns. Using an extensive dataset of messages posted on the microblogging platform StockTwits, we construct a lexicon of words used by online investors when they share opinions and ideas about the bullishness or the bearishness of the stock market. We demonstrate that a transparent and replicable approach significantly outperforms standard dictionary-based methods used in the literature while remaining competitive with more complex machine learning algorithms. Aggregating individual message sentiment at half-hour intervals, we provide empirical evidence that online investor sentiment helps forecast intraday stock index returns. After controlling for past market returns, we find that the first half-hour change in investor sentiment predicts the last half-hour S&P 500 index ETF return. Examining users’ self-reported investment approach, holding period and experience level, we find that the intraday sentiment effect is driven by the shift in the sentiment of novice traders. Overall, our results provide direct empirical evidence of sentiment-driven noise trading at the intraday level.     

Turn-of-Month Evaluations of Liquid Profits and Stock Returns: A Common Explanation for the Monthly and January Effects

This paper presents and tests a hypothesis that the standardization of payments in the United States at the turn of each calendar month generally induces a surge in stock returns at the turn of each calendar month. The hypothesis also asserts that returns generally will be greater following the month of December and will vary inversely with the stringency of monetary policy. Empirical results using stock index returns for 1969–1986 support the hypothesis. This analysis provides an explanation for the previously documented monthly effect in stock returns and a partial explanation for the January effect.     

OVERREACTION AND REVERSE ANTICIPATION: TWO RELATED PUZZLES?

In this article we investigate stock price behavior before and after surprise events. We form four base portfolios and sixteen control portfolios, taking into consideration the event direction, the magnitude of event-day surprises, the potentially confounding effects due to calendar regularities in stock returns, and the ex-post outlier month of October 1987. Using capital market data from 1964 to 1989, we find a pre-event stock price behavior pattern that we call the reverse anticipation puzzle. We also confirm the existence of the overreaction pattern. The pre- and post-event stock price behavior patterns are found to be similar.     

Information transfer,microstmctures and intraday price return spikes

Previous research has identified overnight public information as the cause of higher opening returns and mean reversion in security markets. This paper tests this hypothesis by using an intervention and transfer function time series model to filter out the dynamic effects of an overnight information set on the opening, and subsequent, intraday AOI stock and SPI futures intraday price returns. A further research objective was to analyse the process by which information is transferred into prices and whether there is a differential impact across stock and futures markets. It was determined that the information contained in the overnight US stock market had: (i) a differential impact on the Australian stock and futures market, and (ii) after filtering out the impact of overnight information, a significant reversal tendency remained in both markets after opening. Further analysis supported the conclusion that price spikes at opening were not wholly related to overnight information. Other possible explanations, such as different trading mechanisms, did not provide a satisfactory explanation. Overall, it appears that the uncertainty participants face at the beginning of a trading session may induce a number of subtle market reactions (both rational and irrational), in markets with different microstmctures and trading clientele.     

Psychological barriers in European stock markets: Where are they?

We examine four European stock indices and the prices of eight major German stocks for indications of psychological barriers. The frequency, (expected) returns, intraday volatility and trading volume of these assets are studied contingent on whether the prices lie within a certain range around round numbers. Our results indicate that psychological barriers do not exist on a consistent basis. It seems that some barriers have disappeared after these anomalies have been published. This discovery is consistent with current literature findings about disappearing stock market anomalies.     

Weather and intraday patterns in stock returns and trading activity

We examine the relation between weather in New York City and intraday returns and trading patterns of NYSE stocks. While stock returns are found to be generally lower on cloudier days, cloud cover has a significant influence on stock returns only at the market open. There are significantly more seller-initiated trades when there is more cloud cover at the market open, which is consistent with the return results. Cloudy skies are associated with higher volatility and less market depth over the entire trading day. Finally, cloud cover is not significantly correlated with spread measures and turnover ratios. The findings overall suggest that weather has a significant influence on investors’ intraday trading behavior.     

Social media bots and stock markets

This study examines the link between information spread by social media bots and stock trading. Based on a large sample of tweets mentioning 55 companies in the FTSE 100 composites, we find significant relations between bot tweets and stock returns, volatility, and trading volume at both daily and intraday levels. These results are also confirmed by an event study of stock response following abnormal increases in the volume of tweets. The findings are robust to various specifications, including controlling for traditional news channel, alternative measures of volatility, information flows in pretrading hours, and different measures of sentiment.     

New evidence on the turn-of-the-year effect from closed-end fund IPOs

One of the most persistent securities anomalies is the january effect, whereby significant positive abnormal returns occur during the first few days of the calendar year, especially among small capitalization stocks. I detect a statistically significant January seasonal among a sample of closed-end stock funds that went public during the immediately preceding calendar year. However, contrary to prior research, the results indicate that the abnormal January returns are associated with year-end tax-loss-selling, but do not exhibit a small firm effect.     

Seasonality in the cross-section of stock returns

This paper presents a new pattern in the cross-section of expected stock returns. Stocks tend to have relatively high (or low) returns every year in the same calendar month. We recognize the annual cross-sectional autocorrelation pattern documented in Jegadeesh [1990. Evidence of predictable behavior of security returns. Journal of Finance 45, 881–898] at lags of 12, 24, and 36 months as part of a general pattern that lasts up to 20 annual lags, superimposed on the general momentum/reversal patterns. This pattern explains an economically and statistically significant magnitude of the cross-sectional variation in average stock returns. Volume and volatility exhibit similar seasonal patterns but they do not explain the seasonality in returns. The pattern is independent of size, industry, earnings announcements, dividends, and fiscal year. The results are consistent with the existence of a persistent seasonal effect in stock returns.     

The Long‐run Performance Following Dividend Initiations and Resumptions: Underreaction or Product of Chance?

We examine the long-term stock performance following dividend initiations and resumptions from 1927 to 1998. We show that postannouncement abnormal returns are significantly positive for equally weighted calendar time portfolios, but become insignificant when the portfolios are value weighted. Moreover, the equally weighted results are not robust across subsamples. We also document postannouncement reductions in the risk factor loadings of underlying stocks. Cross-sectionally, these reductions are negatively related to the contemporaneous price drifts, suggesting the price drifts may be a sample-specific result of chance. Our results underscore the importance of testing for changes in risk loadings in future long-term event studies.