Cross-sectional Standard Deviation Research Articles

Risk and return in the Chinese stock market: Does equity return dispersion proxy risk?

We examine whether equity return dispersion, measured by the cross-sectional standard deviation of stock returns, is systematically priced in the cross-section of stock returns in China. We find that return dispersion carries a positive price of risk even after controlling for market, size, book-to-market, and idiosyncratic volatility effects. We observe that stocks with greater sensitivities to equity return dispersion yield higher average returns. The finding of a significant return dispersion effect is robust to alternative portfolio sorts based on the well-established risk factors as well as industry portfolios. We argue that equity return dispersion captures the fundamental uncertainty associated with economic transitions and the flexibility of adaptability to fundamental economic restructuring that cannot be captured by market and firm level factors. To that end, return dispersion serves as a more meaningful proxy for risk in this emerging market that has experienced a significant economic transition during much of the sample period.

Volume-herding interaction in the American market

This paper examines the existence of herding in the US market. We study the turnover effect on herding movement by modifying the Cross- Sectional Standard Deviation (CSSD) model and the Cross-Sectional Absolute Deviation (CSAD) model. Results are inconclusive about the presence of herding in the US financial market. However, we find that trading volume can trigger herding. By applying VAR and Granger causality tests, we find a strong link between herding and trading volume in both directions. More particularly, we find that trading volume can enhance herding behaviour and vice versa, i.e. herding intensifies trading. Moreover, we examine the herding behaviour during the subprime crisis, and find that herding is inhibited during this period.

The Impact of Macroeconomic Factors on the Herding Behaviour of Investors

This study uses the linear model based on the notion of cross-sectional standard deviation (CSSD) by Christie and Huang (1995) and nonlinear model based on cross-sectional absolute deviation (CSAD) proposed by Chang et al. (2000) to provide evidence for the existence of herding behaviour by investors in Taiwan during the period January 4, 2000 to December 28, 2012. We examine whether returns, volume, volatility, SP thus, this paper further examines how exchange rate and interest rate affect herding effect. We investigate asymmetric herding behaviour under different market conditions. Finally, this paper uses quantile regression to estimate the herding effect. First, we find evidence of herding behaviour based on the CSAD model. Second, the cross-sectional return dispersion in Taiwan exhibits a positive (negative) relationship with the US market and financial crisis (interest rate). Third, we find asymmetric herding behaviour under different conditions for market returns, trading volume, VX and interest rate. Fourth, Taiwan’s investors consistently exhibit herding behaviour in different quantiles during different market conditions.

Monetary Policy with Diverse Private Expectations

We study the impact of diverse beliefs on conduct of monetary policy. Individual belief is modeled by a state variable that defines an individual’s perceived laws of motion. We use a New Keynesian Model that is solved with a quadratic approximation hence individual decisions are quadratic functions. Aggregation renders the belief distribution an aggregate state variable. Although the model has standard technology and policy shocks, diverse expectations change materially standard results about a smooth trade-off between inflation volatility and output volatility. Our main results are summed up as follows: (i) The policy space contains a curve of singularity which is a collection of policy parameters that divides the space into two sub-regions. Some trade-off between output and inflation volatilities exists within each region and some across regions. (ii) The singularity causes volatility of variables to be non monotone in policy parameters. Policymakers cannot assume a more aggressive policy will change outcomes in a predictable manner. (iii) When beliefs are diverse a central bank must also consider the volatility of individual consumption and the related volatility of financial markets. We show aggressive anti-inflation policy increases consumption volatility and aggressive output stabilization policy entails rising inflation volatility. Efficient central bank policy must therefore be moderate. (iv) High optimism about the future typically lowers aggregate output and increases inflation. This “stagflation” effect is stronger the stickier prices are. Policy response is muted since the effects of higher inflation and lower output on interest rates partially cancel each other. Effective policy requires targeting exuberance directly or its effects in asset markets. Central banks already do so with short term interventions. (v) The observed high serial correlation of 0.80 in policy shocks contributes greatly to market volatility and we show that a reduction in persistence of central bank’s deviations from a fixed rule will contribute to stability. (vi) Belief dispersion is measured by cross sectional standard deviation of individual beliefs. An increased belief diversity is found to make policy coordination harder and results in lower aggregate output and lower rate of inflation. Bank policy can lower belief dispersion by being more transparent.

Do investors herd in Indian market

This paper examines the presence of herd behavior in Indian stock market in extreme market conditions using data from the National Stock Exchange. The study used the measures suggested by Christie and Huang (Financial Anal J 51:31–37, 1995) and Chang et al. (J Bank Finance 24:1651–1679, 2000) based on cross-sectional standard deviation and cross-sectional absolute deviation, respectively. Empirical results based on daily, weekly, and monthly data indicate that during periods of extreme price movements, equity return dispersions tend to increase rather than decrease, hence providing evidence against the presence of herding in the Indian stock market for the years 2000–2013. Even no evidence of herding is found during the extremely high and extremely low trading volume days. Owing to the regulatory reforms of the Indian equity market and the intense presence of the foreign institutional investors, investors’ behavior seems more rational, that validates the application of rational pricing models in the Indian stock markets.

Return Dispersion, Size, and the Cross-Section of Stock Returns - Evidence from the German Stock Market

This paper investigates whether return dispersion (RD), proxied by the cross-sectional standard deviation of stock returns, captures variation in returns across German stocks between 1989 and 2010. I address existing evidence based on U.S. equity data that RD may serve as a proxy economic state variable. In the out-of-sample test I confirm the countercyclical character of RD and show that it loads significantly negatively on future equal-weighted average market return. Sorting stocks by their absolute loadings on RD, I uncover the negative pattern in simple average portfolio returns. Further analysis indicates that the negative relationship between absolute loadings on RD and future returns is present only in micro stock subgroup. This finding casts doubt on the RD as proxy for state variable. Instead, it suggests its relation to mispricing and idiosyncratic risk components. As a secondary results I confirm the existence of reversed size effect in German stock market over the considered period.

An Examination of Herd Behavior in The Indonesian Stock Market

We examine herd behavior in Indonesian Stock Exchange, using daily and weekly stocks return from 2007 until 2010. We employ the cross sectional standard deviation of returns (CSSD methodology developed by Christie and Huang (1995) and cross sectional absolute dispersion (CSAD methodology developed by Chang et al. (2000) to detect the presence of herd behavior. Using daily and weekly CSSD, we document the nonexistence of herding behavior in Indonesian stock market. However, using CSAD of either data frequency the result demonstrates the presence of herding behavior, particularly on big capitalization and liquid stocks. The result differs from Chang et al. (2000) who find no different impact of herding behavior across size-based portfolios

A New Explanation for Call Option Overpricing: Theory and Empirical Evidence

A recent empirical study (Constantinides et al, 2011) argues that S&P 500 Index call options are frequently overpriced in the sense that any rational agent can improve her expected utility by writing these calls. Little work has addressed why such apparent mispricing is so common. For the first time in literature, I develop a stylized economic model to show that such overpricing of call options is consistent with equilibrium in an economy where agents have portfolio constraints and heterogeneity in beliefs on both expected return and volatility. Consistently with the well-established “leverage effect,” it is assumed that bearish agents expect higher volatility than bullish agents do. Within my model, an underlying stock buyer has one motive (expectation of higher return) but a call buyer has two motives (expectation of higher return and expectation of higher volatility) so that call options are overpriced relative to the underlying stock when portfolio constraints of call suppliers are binding. Consequently, call option overpricing occurs when beliefs dispersion is large and the capacity of liquidity providers is small. Empirically, I propose a model-free methodology to investigate the determinants of option overpricing and verify my explanation by documenting that option overpricing is more common when cross sectional standard deviations of beliefs are large and options transaction volume is small. The findings are robust to various implementations of the empirical study.

Herding and Positive Feedback Trading in American Stock Market: A Two Co-directional Behavior of Investors

Using aggregate data from DJIA since 1987, this paper attempts to address two potential co-directionalbehaviors of investors: Herding and positive feedback trading. These behavioral patterns bear interestingimplications for market price as they may lead to excess volatility and mispricing. To empirically test for herdingbehavior, we employ two econometric techniques: the Cross Sectional Standard Deviation (CSSD) and the crosssectional absolute standard deviation (CSAD), while we employ the model formally introduced by Sentana andWadhwani (1992) to empirically test for positive feedback trading. Our results support the joint significantpresence of herding and positive feedback trading behaviors during periods of relatively large market pricemovements.

Do investors herd in emerging stock markets?: Evidence from the Taiwanese market

This paper has three main contributions to the literature on investor herds. First, it extends investor herding studies to an emerging yet relatively sophisticated Taiwanese stock market at the sector level by using firm level data. Second, it employs different methodologies designed to test the existence of investor herds to better understand the sources of herd behavior. Third, it discusses the implications of different herding measures for investors exposed to systematic and unsystematic risks. We find that the linear model based on the cross-sectional standard deviation (CSSD) testing methodology yields no significant evidence of herding. However, the non-linear model proposed by Chang et al. (2000) and the state space based models of Hwang and Salmon (2004) lead to consistent results indicating strong evidence of herd formation in all sectors. We also find that the herding effect is more prominent during periods of market losses. Our results suggest limited diversification opportunities for investors in this market, especially during periods of market losses when diversification is most needed. Further research is necessary to see whether similar findings hold for other emerging markets.

HERDING MEASURES IN EQUITY MARKETS: A CASE STUDY OF BURSA MALAYSIA

This study examines the issue of herding in the Malaysian equity market over the period 1993 – 2004. Using the method proposed by Christie and Huang (1995), we did not detect any evidence of herding for the whole market, the large firms or the small firms during the pre-crisis, crisis and the post-crisis periods. The modified method of Christie and Huang (1995) produced similar findings. However, using the method proposed by Chang et al. (2000), herding was found in the overall market in the whole period. In the pre-crisis period, herding in the market during the market decline could be attributed to both the large and small firms. Rather surprisingly, there was no herding in the crisis period. In the post-crisis period, herding was detected in the market during market rise and this could be attributed to the small firms. Large firms, on the other hand, witnessed herding during market decline. The modified method of Chang et al. (2000) detected more evidence of herding with the use of cross-sectional inter-quartile range but lessevidence of herding when cross-sectional standard deviation is used.

The Cross-Section of Firms Over the Business Cycle: New Facts and a DSGE Exploration

Using a German firm-level data set, this paper is the first to jointly study the cyclical properties of the cross-sections of firm-level real value added and Solow residual innovations, as well as capital and employment adjustment. We find two new business cycle facts: 1) The cross-sectional standard deviation of firm-level innovations in the Solow residual, value added and employment is robustly and significantly countercyclical. 2) The cross-sectional standard deviation of firm-level investment is procyclical. We show that a heterogeneous-firm RBC model with quantitatively realistic countercyclically disperse innovations in the firm-level Solow residual and non-convex adjustment costs calibrated to the non-Gaussian features of the steady state investment rate distribution, produces investment dispersion that positively comoves with the cycle, with a correlation coefficient of 0.58, compared to 0.45 in the data. We argue more generally that the cross-sectional business cycle dynamics impose tight empirical restrictions on structural parameters and stochastic properties of driving forces in heterogeneous-firm models, and are therefore paramount in the calibration of these models.

Forecasting Fund Manager Alphas: The Impossible Just Takes Longer

Expected alpha from active fund managers can be forecasted—as long as one is mindful of the rules of the zero-sum game of investing. Explicit forecasts are preferred over implicit forecasts because sponsors can use explicit forecasts to build optimized portfolios of managers with improved manager weighting. To make explicit alpha forecasts, the investor combines two equations derived from the fundamental law of active management. The elemental variables for the equations are the sponsor’s estimate of the manager’s “goodness” at beating the manager’s benchmark, the sponsor’s assessment of the sponsor’s skill in estimating manager ability, the cross-sectional standard deviation of manager skill, portfolio breadth, implementation efficiency, expected active risk of the portfolio, and fees.

Alpha budgeting — Cross-sectional dispersion decomposed

(All work in this paper is based on research conducted by the two authors working for Morgan Stanley and the findings have appeared in the Morgan Stanley Quantitative and Derivative Strategies publication as of March 2006). The last three years have witnessed markedly lower volatility in global equity markets, combined with higher correlation and lower dispersion. This has meant greater challenges for asset allocation and stock selection — alpha opportunities appear limited. How should the investment process be structured to maximise exploitation of the available alpha? We introduce cross-sectional standard deviation (or dispersion) as a metric for alpha opportunities, and show how it can shed light on the management of research resources, and on the optimal combination of investment strategies. The metric allows for objective alpha budgeting in the investment process. This involves both the identification of the key top-down drivers of dispersion in a given market regime, and the appropriate ‘alpha granularity’, which is linked to the optimal concentration of stocks in the portfolio. Alpha budgeting from top-down allocations — country, sector, size, style and beyond: using a novel decomposition framework of cross-sectional dispersion, we show the relative magnitude of top-down allocation decisions for several organisational structures. In Europe, sector investing continues to provide greater opportunities than country investing. Alpha opportunities and volatility — hedging opportunities: we establish a linkage between cross-sectional standard deviation (dispersion) and time-series correlation and volatility. Low return dispersion can be a business model risk for active stock pickers; we show how targeted exposure to volatility can be used as a hedge.

Negotiation and the IPO Offer Price: A Comparison of Integer versus Non-integer IPOs

We investigate the pricing of 4,523 initial public offerings of common stock with offer dates between 1981 and 2000. Our study documents that approximately three-fourths of IPOs have integer offer prices. Average initial returns for IPOs with integer offer prices are significantly higher (25.5 percent) than those priced on the fraction of the dollar (8.1 percent). Higher initial returns for integer offerings are observed for 18 of the 20 years of our study and over various ranges of offer prices. Initial returns for integer and fractional IPOs are similar for the subsample of offerings priced below the original filing range. However, significant differences are found for IPOs priced within and above the filing range. For instance, the average initial return for integer offerings priced above the filing range is 65.5 percent compared to 19.9 percent for those priced on the fraction of the dollar. Similar to the arguments made by Harris (1991), we hypothesize that integer versus fractional dollar IPOs are the result of negotiations between the issuing firm and underwriter. Under the negotiation hypothesis, the frequency of integer pricing should be a positive function of the offer price and uncertainty. With greater uncertainty, the extent of underpricing for integer offerings should be higher than for fractional offerings as the investment bank seeks to manage its underwriting risk. We present evidence supportive of the negotiation hypothesis. Specifically, we observe that the frequency of integer prices for the sample of IPOs priced at $15 and above is about twenty percentage points higher than for those IPOs priced below $10 per share. We also document that both the cross-sectional standard deviation of initial returns and the ex-post standard deviation of daily stock returns is highest for offerings priced on the dollar. This higher level of uncertainty for integer offerings is consistent with their high degree of underpricing.

Return Dispersion and Active Management

The cross-sectional variation of U.S. stock returns has been unusually high in the past few years. The wide dispersion in security returns has led to correspondingly wide dispersion in fund returns. For example, the cross-sectional standard deviation of returns on actively managed domestic equity mutual funds was 24 percent in 1999, compared with only 5 percent in 1996. We argue that the wide dispersion in fund performance is a natural result of increased security return dispersion and has little to do with changes in the informational efficiency of the market or the range of managerial talent. The dramatic increase in return dispersion warrants a reexamination of traditional methodologies for measuring fund performance that implicitly assume constant dispersion. We show how performance benchmarking can be extended to incorporate the information embedded in return dispersion, as well as the benchmark mean return, by correcting fund alphas with a period- and asset-class-specific measure of security return dispersion.

Reliable Change Formula Query: Temkin et al. reply

Hinton-Bayre (2000) raises a point that may occur to many readers who are familiar with the Reliable Change Index (RCI). In our previous paper comparing four models for detecting significant change in neuropsychological performance (Temkin et al., 1999), we used a formula for calculating Sdiff, the measure of variability for the test–retest difference, that differs from the one Hinton-Bayre has seen employed in other studies of the RCI. In fact, there are two ways of calculating Sdiff—a direct method and an approximate method. As stated by Jacobson and Truax (1991, p. 14), the direct method is to compute “the standard error of the difference between the two test scores” or equivalently [begin square root](s12 + s22 − 2s1s2rxx′)[end square root] where si is the standard deviation at time i and rxx′ is the test–retest correlation or reliability coefficient. Jacobson and Truax also provide a formula for the approximation of Sdiff when one does not have access to retest data on the population of interest, but does have a test–retest reliability coefficient and an estimate of the cross-sectional standard deviation, i.e., the standard deviation at a single point in time. This approximation assumes that the standard deviations at Time 1 and Time 2 are equal, which may be close to true in many cases. Since we had the longitudinal data to directly calculate the standard error of the difference between scores at Time 1 and Time 2, we used the direct method. Which method is preferable? When the needed data are available, it is the one we used.

Growth curves of Dutch children with Down's syndrome

Two thousand and forty-five observations on height and weight were collected from 295 healthy Dutch children with Down's syndrome. In a cross-sectional analysis, means and standard deviations were calculated per age-class, and subsequently smoothed, resulting in age references between 0 and 20 years. Each child contributed only once in every age class. In a subgroup in whom more than four measurements were available before puberty, quadratic regression functions were determined on the basis of the full data set, as well as for individual children separately (54 boys and 25 girls). The average coefficients of the individual regression functions were almost identical to the coefficients of the regression line through all data, indicating that the reference curve for the mean height based on cross-sectional analysis adequately represents longitudinal growth during childhood. Dutch children with Down's syndrome are taller than their US peers (P50 equals P75) but more than 2 SD shorter than normal Dutch children. Above the age of 10 years, the mean weight for height is above the P90 of normal children.

Following the Pied Piper: Do Individual Returns Herd around the Market?

Do equity returns indicate the presence of herd behavior on the part of investors during periods of market stress? To test this proposition, the cross-sectional standard deviation of returns, or dispersion, is used to capture herd behavior. When individual returns herd around the market consensus, dispersions are predicted to be relatively low. In contrast, rational asset pricing models predict an increase in dispersion because individual returns are repelled away from the market return when stocks differ in their sensitivity to market movements. The results for both daily and monthly returns are inconsistent with the presence of herding during periods of large price movements. For example, during extreme down markets, when herding is expected to be most prevalent, the magnitude of the increase in the dispersion of actual returns is mirrored by the increase in the dispersion of predicted returns that are estimated from a rational asset pricing model.

Regional growth and migration: A Japan-United States comparison

Do poor economies grow faster than rich ones? This important economic question (which we call β-convergence) is analyzed in this paper using two regional data sets: 47 prefectures in Japan and 48 states of the United States. We find clear evidence of convergence in both countries: poor prefectures and states grow faster. We also find that there is intraregional as well as interregional convergence. We analyze the cross-sectional standard deviation across perfectures and states. We find that in both countries there has been a long term decline (a phenomenon that we call θ-convergence). Finally we study the determinants of the rates of regional in-migration and, again, find striking similarities. In both countries, the reaction of net in-migration rates to the log of initial income is slightly above 0.025, which indicates a slow (although very significant) speed of population adjustment to income differentials. We find little evidence in favor of the argument that population movements are the reason why we find convergence across economies.