Universal price impact functions of individual trades in an order-driven market

The trade size ω has a direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization C is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in the scaling is unclear and the anomalous negative correlation between price change r and trade size ω for small trades is unexplained. Here we show that these issues can be addressed by taking into account the aggressiveness of orders that result in trades together with a proper normalization technique. Using order book data from the Chinese market, we show that trades from filled and partially filled limit orders have very different price impacts. The price impact of trades from partially filled orders is constant when the volume is not too large, while that of filled orders shows power-law behavior r?～?ω^α with α?≈?2/3. When returns and volumes are normalized by stock-dependent averages, capitalization-independent scaling laws emerge for both types of trades. However, no scaling relation in terms of stock capitalization can be constructed. In addition, the relation α?=?α_ω/α _r is verified for some individual stocks and for the whole data set containing all stocks using partially filled trades, where α_ω and α _r are the tail exponents of trade sizes and returns. These observations also enable us to explain the anomalous negative correlation between r and ω for small-size trades.     

Stochastic volatility,power laws and long memory

Benoit B Mandelbrot comments on the paper by Blake LeBaron, on page 621 of this issue, by tracing the merits and pitfalls of power-law scaling models from antiquity to the present.     

Scaling and universality in economics: empirical results and theoretical interpretation

H Eugene Stanley and Vasiliki Plerou comment on the paper by Blake LeBaron, on page 621 of this issue, by examining the degree to which the twin concepts of scaling and universality apply to economic systems as compared with other physical systems comprising a large number of interconnected and interacting components.     

Herding in the German Mutual Fund Industry

This paper analyses the trading activity of German mutual funds in the 1998–2002 period to investigate whether German mutual fund managers are engaged in herding behaviour. Another objective of the study is to determine the impact of this herd‐like trading on stock prices. Our results provide evidence of herding and positive feedback trading by German mutual fund managers. We show that a significant portion of herding detected in the German market is associated with spurious herding as a consequence of changes in benchmark index composition. Investigating the impact of mutual fund herding on stock prices, we find that herding seems to neither destabilise nor stabilise stock prices.     

Statistical tests of distributional scaling properties for financial return series

Existing empirical evidence of distributional scaling in financial returns has helped motivate the use of multifractal processes for modelling return processes. However, this evidence has relied on informal tests that may be unable to reliably distinguish multifractal processes from other related classes. The current paper develops a formal statistical testing procedure for determining which class of fractal process is most consistent with the distributional scaling properties in a given sample of data. Our testing methodology consists of a set of test statistics, together with a model-based bootstrap resampling scheme to obtain sample p-values. We demonstrate in Monte Carlo exercises that the proposed testing methodology performs well in a wide range of testing environments relevant for financial applications. Finally, the methodology is applied to study the scaling properties of a data-set of intraday equity index and exchange rate returns. The empirical results suggest that the scaling properties of these return series may be inconsistent with purely multifractal processes.     

The endo–exo problem in high frequency financial price fluctuations and rejecting criticality

The endo–exo problem lies at the heart of statistical identification in many fields of science, and is often plagued by spurious strong-and-long memory due to improper treatment of trends, shocks and shifts in the data. A class of models that has shown to be useful in discerning exogenous and endogenous activity is the Hawkes process. This class of point processes has enjoyed great recent popularity and rapid development within the quantitative finance literature, with particular focus on the study of market microstructure and high frequency price fluctuations. We show that there are important lessons from older fields like time series and econometrics that should also be applied in financial point process modelling. In particular, we emphasize the importance of appropriately treating trends and shocks for the identification of the strength and length of memory in the system. We exploit the powerful Expectation Maximization algorithm and objective statistical criteria (BIC) to select the flexibility of the deterministic background intensity. With these methods, we strongly reject the hypothesis that the considered financial markets are critical at univariate and bivariate microstructural levels.     

S&P 100 Index Option Volatility

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility.     

Empirically based modeling in financial economics and beyond, and spurious stylized facts

The discovery of the dynamics of a time series requires construction of the transition density. We explain why 1-point densities and scaling exponents cannot determine the class of stochastic dynamics. Time series require some sort of underlying statistical regularity to provide a basis for analysis, and we construct an exhaustive list of such tests. The condition for stationary increments, not scaling, determines the existence of long time pair autocorrelations. We conjecture that for a selfsimilar process neither the pair correlations 〈x(t)x(s)〉 nor the 2-point density scales in both times t and s except in a pathological case, and give examples using three well-known Gaussian processes. An incorrect assumption of stationary increments can generate spurious stylized facts, including fat tails. When a sliding window is applied to nonstationary, uncorrelated increments then a Hurst exponent H_s = 1 / 2 is generated by that procedure even if the underlying model scales with a Hurst exponent H ≠ 1/2. We explain how this occurs dynamically. The nonstationarity arises from systematic unevenness in the traders' behavior in real time. Spurious stylized facts arise mathematically from using a log increment with a ‘sliding window’ to read the series. In addition, we show that nonstationary processes are generally not globally transformable to stationary ones. We also present a more detailed explanation of our recent FX data analysis and modeling.     

Is herding spurious or intentional? Evidence from analyst recommendation revisions and sentiment

Using institutional holdings data for 1993–2015, we investigate whether institutional herding is spurious or intentional by analysing the impact on herding of analyst recommendation revisions and sentiment. In addition to examining their effect separately, we consider the impact of their interaction. Utilising the Sias method, we develop competing hypotheses concerning spurious and intentional herding, an issue of direct interest to fund investors, given the principal-agent relationship inherent in fund management. Results strongly suggest herding is spurious. Analysis of the relationship between herding and subsequent returns, and findings from robustness tests add further support.     

tay's as good as cay: Reply

In a recent comment on our published work [Lettau, M., Ludvigson, S., 2001. Consumption, aggregate wealth, and expected stock returns. Journal of Finance 56, 815–850], Michael Brennan and Yihong Xia [2005. tay's as good as cay. Finance Research Letters 2, 1–14] advance the following argument: A “mechanistic” variable tay, where t is a linear time trend, forecasts stock returns. Since “t has no foresight,” the argument goes, the predictive power of this variable must be attributable to what they call “look-ahead bias.” The authors assert that cay is subject to the same look-ahead bias (generated because we use the full sample to estimate the cointegrating parameters in cay), implying that its forecasting power must be spurious. In this response, we explain why this critique is misplaced.     

Dividend persistence and dividend behaviour

This article demonstrates how a spurious regression problem caused by dividend persistence is compounded by a spurious correlation problem when the dependent and independent variables in dividend behaviour regressions are ratios composed of common component variables. This article utilises a simulation procedure to take account of these problems, with the findings implying that extreme care should be taken when using ratios as predictor or explanatory variables in time series regression. This article introduces a reformulated Lintner first difference dividend behaviour model that is not subject to spurious regression in which past prices predict subsequent changes in dividends.     

Spurious Regressions in Financial Economics?

Even though stock returns are not highly autocorrelated, there is a spurious regression bias in predictive regressions for stock returns related to the classic studies of Yule (1926) and Granger and Newbold (1974) . Data mining for predictor variables interacts with spurious regression bias. The two effects reinforce each other, because more highly persistent series are more likely to be found significant in the search for predictor variables. Our simulations suggest that many of the regressions in the literature, based on individual predictor variables, may be spurious.     

A SIMULATION ANALYSIS OF HERDING AND UNIFRACTAL SCALING BEHAVIOUR

We model the financial market using a class of agent‐based models in which agents’ expectations are driven by heuristic forecasting rules (in contrast to the rational expectations models used in traditional theories of financial markets). We show that, within this framework, we can reproduce unifractal scaling with respect to three well‐known power laws relating (i) moments of the absolute price change to the time‐scale over which they are measured, (ii) magnitude of returns with respect to their probability and (iii) the autocorrelation of absolute returns with respect to lag. In contrast to previous studies, we systematically analyse all three power laws simultaneously using the same underlying model by making observations at different time‐scales and higher moments. We show that the first two scaling laws are remarkably robust to the time‐scale over which observations are made, irrespective of the model configuration. However, in contrast to previous studies, we show that herding may explain why long memory is observed at all frequencies. Copyright © 2013 John Wiley & Sons, Ltd.     

True or spurious long memory in European non-EMU currencies

We examine the Croatian Kuna, the Czech Koruna, the Hungarian Forint, the Polish Złoty, the Romanian Leu, and the Swedish Krona whether their Euro exchange rates volatility exhibits true or spurious long memory. Recent research reveals long memory in foreign exchange rate volatility and we confirm this finding for these currency pairs by examining the long memory behavior of squared residuals by means of the V/S test. However, by using the ICSS approach we also find structural breaks in the unconditional variance. Literature suggests that structural breaks might lead to spurious long memory behavior. In a refined test strategy, we distinguish true from spurious long memory for the six exchange rates. Our findings suggest that Czech Koruna and Hungarian Forint only feature spurious long memory, while the rest of the series have both structural breaks and true long memory. Lastly, we demonstrate how to extend existing models to jointly model both properties yielding superior fit and better Value-at-Risk forecasts. The results of our work help to avoid misspecification and provide a better understanding of the properties of the foreign exchange rate volatility.     

Random walk and breaking trend in financial series: An econometric critique of unit root tests

The present note sheds light on several pitfalls associated with unit root tests that are overlooked by a growing volume of literature in financial economics. Specifically, several studies have confused unit root tests with the Random Walk hypothesis. Unit root tests are not designed for such a task since they aim at investigating whether a time series is difference-stationary or trend-stationary and are not, therefore, predictability tests. Secondly, we emphasize some serious shortcomings associated with the widely used unit root test developed by Zivot and Andrews [Zivot, E. & Andrews, D.W.K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business and Economic Statistics, 10, 251–270.]. In particular, we stress that results from the Zivot–Andrews test are sensitive to the methods employed to calculate the critical values and to select the maxim lag k. Furthermore, Zivot–Andrews test imposes a one time structural break in a time series; however recent studies showed that not counting for other true structural breaks may bias the results and may cause a spurious rejection of the unit root null hypothesis. Finally, we support our arguments by an empirical example based on the findings of Narayan and Smyth [Narayan, K.P. & Smyth, R. (2004). Is South Korea’s stock market efficient? Applied Economics Letters, 11, 707–710.] with regards to the efficiency of South Korean stock market. We show that contrary to what the authors claim, the KSE (KOSPI) price index is predictable, and hence the South Korean stock market is not informationally efficient.     

From Minority Games to real markets

We address the question of market efficiency using the Minority Game (MG) model. First we show that removing unrealistic features of the MG leads to models which reproduce a scaling behaviour close to what is observed in real markets. In particular we find that (i) fat tails and clustered volatility arise at the phase transition point and that (ii) the crossover to random walk behaviour of prices is a finite-size effect. This, on one hand, suggests that markets operate close to criticality, where the market is marginally efficient. On the other it allows one to measure the distance from criticality of real markets, using cross-over times. The artificial market described by the MG is then studied as an ecosystem with different species of traders. This clarifies the nature of the interaction and the particular role played by the various populations.     

Ranking accounting journals using dissertation citation analysis: A research note

Prior literature on accounting journal rankings has provided different journal lists depending on the type of examination (citations- vs. survey-based) and the choice of journals covered. A recent study by Bonner, Hesford, Van der Stede, and Young (2006) [Bonner, S., Hesford, A., Van der Stede, W. A., & Young, M. S. (2006). The most influential journals in academic accounting. Accounting, Organizations and Society, 31(7), 663–685] documents disproportionately more citations in the financial accounting area, suggesting a financial accounting bias in the accounting literature. We use citations from accounting dissertations completed during 1999–2003 to provide a ranking of accounting journals. The database allows us to assess the research interests of new accounting scholars and the literature sources they draw from. Another innovation is our ranking of accounting journals based on specialty areas (auditing, financial, managerial, tax, systems, and other) and research methods (archival, experimental, modeling, survey, and other). To mitigate the financial accounting bias documented by Bonner et al. (2006), we derive a ranking metric by scaling (normalizing) the journal citations by the number of dissertations within each specialty area and research method. Overall, the top journals are, JAR, AOS, TAR, and JAE. We also provide evidence that top journal rankings do vary by specialty area as well as by research methods.     

The Feldstein-Horioka Puzzle and Spurious Ratio Correlation

This study shows that the Feldstein-Horioka puzzle resembles a spurious ratio correlation due to a common deflator (Pearson 1896/7). Empirically, the Feldstein-Horioka specification and its counterpart with an arbitrary deflator – final domestic demand – give similar results. Monte Carlo results also indicates that the slope β and R² of the ratio regression are upward biased. Theoretically, assuming each of the original undeflated variables are linear homogeneous functions of the deflator and random disturbances, formulas for β and R² are derived. As saving and investment rates are numerically small relative to the disturbances, both β and R² are predominantly determined by the disturbances and they tend towards unity when the disturbances are close in magnitude. The Feldstein-Horioka results are therefore noisy, though not entirely spurious, and do not necessarily reflect a strong correlation between investment and savings.     

Testing for Income Smoothing Using the Backing Out Method: A Review of Specification Issues

This study investigates potentially spurious correlation in prior studies of income smoothing which use a research method that we call backing out. If E is reported income, Y a discretionary earnings component hypothesized to smooth income, and T the smoothing target, the backing out method consists of regressing Y on E – Y – T. A negative regression coefficient is interpreted as evidence that Y is being managed to smooth earnings. We argue that the negative regression coefficient may simply reflect the positive correlation between E and T, which may or may not be the result of manipulating Y. If E is not manipulated by Y, the negative regression coefficient reflects measurement errors in E – Y as an estimate of unmanaged earnings.We replicate the backing out method of prior studies and use each of the accrual and cash flow components of earnings in the Statement of Cash Flows for Y. We find that the regression coefficient, hypothesized to be negative because of smoothing with Y, is always negative and its magnitude depends on the variances of Y and E – T (smoothing error) independent of the nature of Y (discretionary or nondiscretionary). We conclude that the negative coefficient on E – Y – T is equally consistent with three possibilities: (1) managers smooth earnings with Y, (2) managers smooth earnings with something other than Y, and (3) managers do not smooth earnings at all.     

An application of a random level shifts model to the volatility of Peruvian stock and exchange rate returns

The literature has shown that the volatility of stock and forex rate market returns shows the characteristic of long memory. Another fact that is shown in the literature is that this feature may be spurious and volatility actually consists of a short memory process contaminated with random level shifts (RLS). In this paper, we follow recent econometric approaches estimating an RLS model to the logarithm of the absolute value of stock and forex returns. The model consists of the sum of a short-term memory component and a component of level shifts. The second component is specified as the cumulative sum of a process that is zero with probability ‘1-alpha’ and is a random variable with probability ‘alpha’. The results show that there are level shifts that are rare, but once they are taken into account, the characteristic or property of long memory disappears. Also, the presence of General Autoregressive Conditional Heteroscedasticity (GARCH) effects is eliminated when included or deducted level shifts. An exercise of out-of-sample forecasting shows that the RLS model has better performance than traditional models for modelling long memory such as the models ARFIMA (p,d,q).