Fractional integration and mean reversion in stock prices

The Efficient Market Hypothesis (EMH) is frequently tested by measuring the degree of mean reversion in stock prices, since highly predictable changes might indicate that investors are not fully rational. Existing studies often rely on statistical tests which impose too restrictive assumptions on the time series behavior of the series of interest, and have very low power. This paper uses a test for unit roots and other nonstationary (and stationary) hypotheses—recently developed by Robinson (1994)—which allows for fractional alternatives and outperforms rival statistics. Its application to U.S. real stock returns suggests that there is no permanent component in stock prices, since the series examined is close to being I(0). The key question then becomes whether there exists an autocorrelated structure, which would imply that the series is perfectly predictable, and hence that the market might not be efficient.     

Volatility of stock prices and market efficiency

Recently, historical price series along with the dividend series have been used to severely question the Efficient Markets Hypothesis. The literature suggests that the stock prices vary too much to be explained by subsequent changes in dividends. It is argued in this paper that these results require the assumption of stationarity of the price process and that this assumption is not compatible with the random walk model of Efficient Markets. A non-stationary dividend process, which is compatible with the random walk model of Efficient Markets, results in a reversal of earlier results. The new results are shown to be consistent with the empirical findings. Simulations are run to verify the results.     

Maritime businesses: volatile stock prices and market valuation inefficiencies

This paper examines 12 maritime equity price series for behavioral stability and efficient market pricing for the 1989–2002 period. Five self-affine fractal analysis techniques for estimating the Hurst exponent, Mandelbrot–Lévy characteristic exponent, and fractal dimension are employed to explore the price series fractal properties. Techniques employed are rescaled-range analysis, power-spectral density analysis, roughness–length analysis, the variogram or structure function method, and wavelet analysis. Formal hypothesis tests provide evidence of a change in market behavior between the 1989–1994 and 1995–2002 periods. Hypothesis tests also provide evidence against efficient valuation of the maritime businesses sampled, supporting the multifractal model of asset returns (MMAR), and disconfirming the weak form of the Efficient Market Hypothesis (EMH). Strong evidence is presented for antipersistence of some maritime equities in the sample, suggesting market participants habitually overreact to new information, and never learn not to. An important implication of this finding is that financial derivatives based on the sampled equities cannot be efficiently priced.     

Empirical analysis of long memory,leverage, and distribution effects for stock market risk estimates

In this study, eight generalized autoregressive conditional heteroskedasticity (GARCH) types of variance specifications and two return distribution settings, the normal and skewed generalized Student's t (SGT) of Theodossiou (1998), totaling nine GARCH-based models, are utilized to forecast the volatility of six stock indices, and then both the out-of-sample-period value-at-risk (VaR) and the expected shortfall (ES) are estimated following the rolling window approach. Moreover, the in-sample VaR is estimated for both the global financial crisis (GFC) period and the non-GFC period. Subsequently, through several accuracy measures, nine models are evaluated in order to explore the influence of long memory, leverage, and distribution effects on the performance of VaR and ES forecasts. As shown by the empirical results of the nine models, the long memory, leverage, and distribution effects subsist in the stock markets. Moreover, regarding the out-of-sample VaR forecasts, long memory is the most important effect, followed by the leverage effect for the low level, whereas the distribution effect is crucial for the high level. As for the three VaR approaches, weighted historical simulation achieves the best VaR forecasting performance, followed by filtered historical simulation, whereas the parametric approach has the worst VaR forecasting performance for all the levels. Furthermore, VaR models underestimate the true risk, whereas ES models overestimate the true risk, indicating that the ES risk measure is more conservative than the VaR risk measure. Additionally, based on back-testing, the VaR provides a better risk forecast than the ES since the ES highly overestimates the true risk. Notably, long memory is important for the ES estimate, whereas both the long memory and the leverage effect are crucial for the VaR estimate. Finally, via in-sample VaR forecasts in regard to the low level, it is found that long memory is important for the non-GFC period, whereas the distribution effect is crucial for the GFC period. On the other hand, with regard to the high level, the distribution effect is crucial for both the non-GFC and the GFC period. These results seem to be consistent with those found in the out-of-sample VaR forecasts. In accordance with these results, several important policy implications are proposed in this study.     

An investigation of long memory in various measures of stock market volatility, using wavelets and aggregate series

Using methods based on wavelets and aggregate series, long memory in the absolute daily returns, squared daily returns, and log squared daily returns of the S&P 500 Index are investigated. First, we estimate the long memory parameter in each series using a method based on the discrete wavelet transform. For each series, the variance method and the absolute value method based on aggregate series are then employed to investigate long memory. Our findings suggest that these methods provide evidence of long memory in the volatility of the S&P 500 Index. Our esteemed colleague, Robert DiSario, passed away on December 31, 2005.     

Long memory in the Ukrainian stock market and financial crises

This paper examines persistence in the Ukrainian stock market during the recent financial crisis. Using two different long memory approaches (R/S analysis and fractional integration) we show that this market is inefficient and the degree of persistence is not the same at different stages of the financial crisis. Therefore trading strategies might have to be modified. We also show that data smoothing is not advisable in the context of R/S analysis.     

Press freedom and jumps in stock prices

Press freedom varies substantially across countries. In a free environment, any news immediately becomes public knowledge through mediums including various electronic media and published materials. However, in an unfree environment, (economic) agents would have more discretionary powers to disclose good news immediately, while hiding bad news or releasing bad news slowly. We argue that this discretion affects stock prices and that stock markets in countries with a free press should be better processors of economic information. Using an equilibrium asset-pricing model in an economy under jump diffusion, we decompose the moments of the returns of international stock markets into a diffusive risk and a jump risk part. Using stock market data for a balanced panel of 50 countries, our results suggest that in countries with a free press, the better processing of bad news leads to more frequent negative jumps in stock prices. As a result, stock markets in those countries are characterized by higher volatility, driven by higher jump risk and more negative return asymmetry. The results are robust to the inclusion of various controls for governance and other country- or market-specific characteristics. We interpret these as good stock market characteristics because a free press improves welfare and increases economic growth.     

Explaining movements in UK stock prices

We examine movements in aggregate UK stock prices by decomposing the variance of unexpected real stock returns into components due to revisions in expectations of future dividends, discount rates, and the covariance between the two. The contribution of news about future discount rates is about four times that of news about future dividends, with no significant covariance between them. Our analysis of excess returns uncovers a positive covariance between news about dividends and news about real interest rates. Since these two elements have opposite effects on current stock prices, their combined effect is negligible. Persistence in expected returns, as well as predictability, are found to be important in explaining stock price movements.     

Order aggressiveness, pre-trade transparency, and long memory in an order-driven market

Recent empirical research has documented that the state of the limit order book influences stock investors' strategies. Investors place more aggressive orders when the same side of the order book is thicker, and less aggressive orders when it is thinner. We conjecture and demonstrate that this behavior is related to long memories of trading volume, volatility, and order signs in stock markets. We investigate our conjecture in two types of artificial stock markets: a transparent market, in which agents observe all limit orders on both sides of the book and order volumes at those prices before they trade; and a less transparent market, in which agents observe only the best five bid and ask quotes with the depth available at these limit prices. The first market structure resembles certain actual stock exchanges in the level of pre-trade transparency, such as the Australian Stock Exchange, NYSE OpenBook, and the London Stock Exchange, whereas the second market structure is consistent with stock exchanges such as Euronext Paris, the Toronto Stock Exchange, the Tokyo Stock Exchange, and Hong Kong Exchanges and Clearing. We demonstrate that our long memory results are robust with different levels of pre-trade transparency, implying that the strategy constructed by the state of the order book is key for explaining long memories in many actual stock exchanges.     

The relationship between oil prices,the stock market and the exchange rate: Evidence from Mexico

This paper analyzes the variables of oil price, exchange rate and stock market index to explain how they interact with each other in the Mexican economy. The examined period includes monthly data from January 1992 to June 2017. A Vector Autoregressive Model (VAR) is implemented that includes oil prices, the nominal exchange rate, the Mexican stock market index, and the consumer price index. Results indicate that the exchange rate has a negative and statistically significant effect on the stock market index; this indicates that an appreciation of the exchange rate is related to an increase in the stock market index. It is also found that the consumer price index has a positive effect on the exchange rate and a negative effect on the stock market index. The results also indicate that oil prices are statistically significant against the exchange rate, concluding that an increase in oil prices creates an appreciation of the exchange rate. In addition, the impulse-response functions show that the effects found tend to disappear over time.     

Predicting stock market crises using daily stock market valuation and investor sentiment indicators

The purpose of this paper is to develop a daily early warning system for stock market crises using daily stock market valuation and investor sentiment indicators. To achieve this goal, we use principal components analysis to propose a comprehensive index of daily market indicators that reflects stock market valuation and investor sentiment. Based on the comprehensive index, we employ a logit model with Ensemble Empirical Mode Decomposition to develop a daily early warning system for stock market crises. Finally, we apply the proposed system to the early warning for stock market crises in China. The in-sample forecasting results show that investor sentiment and the forecast horizon by Ensemble Empirical Mode Decomposition improve the forecasting performance of conventional early warning systems. The out-of-sample forecasting results indicate that the proposed warning system still has a good performance.     

Booms,busts and behavioural heterogeneity in stock prices

We estimate a behavioural heterogeneous agents model with boundedly rational traders who know the fundamental stock price, but disagree about the persistence of deviations from the fundamental. Some agents (fundamentalists) believe in mean-reversion of stock prices, while others (chartists) expect a continuation of the trend. Agents gradually switch between the two rules, based upon their relative performance, leading to self-reinforcing regimes of mean-reversion and trend-following. For the fundamental benchmark price we use two well-known models, the Gordon model with a constant risk premium and the Campbell-Cochrane consumption-habit model with a time-varying risk premium. We estimate a two-type switching model using U.S. stock prices until 2016Q4. The estimations show an improvement over representative agent models that is both statistically and economically significant. Our model suggests that behavioural regime switching strongly amplifies booms and busts, in particular, the dot-com bubble and the financial crisis in 2008.     

Governance and stock market performance

This study uses international asset pricing models to investigate the link between the quality of government institutions and the performance of global stock markets. The results demonstrate a significant positive association between stock market performance measures and the quality of the institutional environment. Performance measures examined for the cross-section of countries were the average monthly stock index excess returns and the Sharpe ratio. All measures of performance were adjusted for global and local risk factors known to explain their international variation. The quality of governance is also found to be negatively associated with stock market total risk and idiosyncratic risk, consistent with the notion that stable institutions are linked to reduced variations in equity returns. These findings suggest countries with better-developed governance systems have stock markets with higher returns on equity and lower levels of risk. The results lend support for the view that a precondition for financial market development is the improvement of the institutions which govern the process of exchange.     

Budget deficits and stock prices: International evidence

The purpose of this research is to provide empirical evidence regarding deficits and their effects on stock prices. We investigate whether changes in deficits cause changes in stock prices and if so, in what direction. We use Granger causality tests and impulse response analysis of vector autoregressive models to assess the relationship between budget deficits and stock prices in several industrialized nations. The evidence from impulse response analysis and Granger causality tests shows that only in the U.S. deficit reductions have an inverse effect on equity returns.     

Market integration between conventional and Islamic stock prices

The paper assesses the market integration between conventional and Islamic stock prices from the long- and short-run perspectives for France, Indonesia, the UK and the US from September 8, 2008 to September 6, 2013 using various econometric approaches. The results show long-run relationships for all countries, except for the UK where there is no cointegration between conventional and Islamic stock prices. These findings suggest that the Islamic finance industry in the considered economies (except the UK) does not seem to be compliant to Islamic law's maxims, which hinders portfolio managers and market participants to benefit from the opportunities of international diversification and hedging effectiveness. From the correlation perspective, there is evidence of weak linkages between the Indonesian market and the developed markets for both conventional and Islamic stock prices, thus suggesting that investors can diversify their portfolios at the international level to minimize risk. However, there is high connection between the developed markets for both conventional and Islamic indexes. In addition, for each economy, the Islamic index is found to be strongly linked with its conventional counterpart. The structural change analysis reveals common break dates for several cross correlations, thus reflecting the similar time-paths of the interactions between markets. The presence of breaks in the inter-market linkages has important implications for international investors as regards portfolio diversification benefits and for financial policy makers regarding contagion risks and market policies.     

Jumps in equilibrium prices and market microstructure noise

Asset prices observed in financial markets combine equilibrium prices and market microstructure noise. In this paper, we study how to tell apart large shifts in equilibrium prices from noise using high frequency data. We propose a new nonparametric test which allows us to asymptotically remove the noise from observable price data and to discover jumps in fundamental asset values. We provide its asymptotic distribution to decide when such jumps occur. In finite samples, our test offers reasonable power for distinguishing between noise and jumps. Empirical evidence indicates that it is necessary to incorporate the presence of jumps in equilibrium prices.     

The values and incentive effects of options on the maximum or the minimum of the stock prices and market index

In this study, we employ the certainty equivalent principle to investigate cost efficiency and incentives of the options on the maximum or the minimum of the stock prices and market index levels. In addition, the options with averaging features are also considered. Numerical results show that options on the maximum are more cost efficient and incentive-efficient than traditional ones. As for options on the minimum, they are more cost efficient than traditional ones only when the weight in the options is not very large. However, options on the minimum also provide stronger incentives to increase stock prices than traditional ones.     

Information flows and stock market volatility

This study examines how news is distributed across stocks. A model is developed that categorizes a stock's latent news into normal and nonnormal news, and allows both types of news to be filtered through to other stocks. This is achieved by formulating a model that jointly incorporates a multivariate lognormal‐Poisson jump process (for nonnormal news) and a multivariate GARCH process (for normal news), in addition to a news (or shock) transmission mechanism that allows the shocks from both processes to impact intertemporally on all stocks in the system. The relationship between news and the expected volatility surface is explored and a unique news impact surface is derived that depends on time, news magnitude, and news type. We find that the effect of nonnormal news on volatility expectations typically builds up before dissipating, with the news transmission mechanism effectively crowding‐out normal news and crowding‐in nonnormal news. Moreover, in contrast to the standard approach for measuring leverage effects using asymmetric generalized autoregressive conditional heteroskedasticity models, we find that leverage effects stem predominantly from nonnormal news. Finally, we find that the capacity to identify positively or negatively correlated stock returns is ambiguous in the short term, and depends heavily on the behavior of the nonnormal news component.     

Tornado activity,house prices,and stock returns

In this paper we investigate the effects of tornado activity on house prices and stock returns in the US. First, using geo-referenced and metropolitan statistical area (MSA)-level data, we find tornado activity to be responsible for a significant drop in house prices. Spillover tornado effects between adjacent MSAs are also detected. Furthermore, our granular analysis provides evidence of tornadoes having a negative impact on stock returns. However, only two sectors seem to contribute to such a negative effect (i.e., consumer discretionary and telecommunications). In a macro-analysis, which relies on aggregate data for the South, West, Midwest and Northeast US regions, we then show that tornado activity generates a significant drop in house prices only in the South and Midwest. In these regions, tornadoes are also responsible for a drop in income. Tornado activity is finally found to positively (negatively) affect stock returns in the Midwest (South). If different sectors are examined, a more heterogeneous picture emerges.     

Value at risk and return in Chinese and the US stock markets: Double long memory and fractional cointegration

Given that the United States is an engine of global stock market while China is the largest emerging market with a cornucopia of anomalies in particular, it is vital to investigate the risk-return relationship in the two markets. This paper brings new insights not only into risk-return tradeoff, but also to the leverage effect, with the application of the fractionally co-integrated vector auto-regression (FCVAR) model capturing the fractional cointegrated relationship and long memory property. Results show that China stock markets own the property of double long memory but the US markets don’t. Most of all, in the US market, a positive risk-return tradeoff exists for the whole sample while after the crisis, even we find the negative relation, it’s not a volatility feedback effect but low risk and high returns. However, there is only a volatility feedback effect in China stock markets. Besides, there is a leverage effect in the US market, while Chinese market exhibits a reverse one, another anomaly, indicating significant difference in the two markets again.