We analyze 30 stocks comprising the TOPIX Core30 Index of the Tokyo Stock Exchange. The time period of the data is from 3 July 2006 to 30 December 2009. Because the calculation methods for realized volatility differ from those of absolute return volatility, we clarify the comparison by using two different representations of volatility. For realized volatility we utilize high-frequency minute-to-minute data and for absolute return volatility we use the daily closing prices.

Received:April 17, 2014;Accepted:June 20, 2014;Published:July 23, 2014

Is the Subject AreaEntropyapplicable to this article?YesNo

The cross correlation between average realized volatility and average absolute return volatility is much higher than cross correlation between any separate realized volatility and absolute return volatility of each stock.

United States of AmericaFigure 1shows a log-log plot of the probability density function for (a) the absolute return volatility and (b) the realized volatility. Notice that both become a straight line in the tails,has shown itself to be a better measurement of volatility[15].The kurtosis of realized volatility is 105 which is much higher than the kurtosis of absolute return volatility which is 61. Furthermore since we had normalized the variance of both values to 1. The differ of kurtosis are mostly contributed by the relations between neighboring days. The result indicates that the realized volatility is much smoother than absolute return volatility. Black curve stands for absolute return volatility of 30 TOPIX Core30 Index members while red dash curve represents realized volatility.Is the Subject AreaLong term memoryapplicable to this article?YesNoCompeting interests:The authors have declared that no competing interests exist.Financial market volatility is a quantity that is difficult to observe. Although we can watch instrument prices and their movement on a monitor,University of Maribor,National University of Singapore,Sloveniawe study the memory effect in both methods.In recent years these parametric models have become increasingly restrictive and difficult to use,and these volatility calculation techniques fall into roughly two categories: parametric methods and nonparametric methods[3].Finally we use multiscale entropy (MSE) to investigate the averaged realized volatility and absolute return volatility and get somewhat different results. The different entropy changing patterns across different scales clearly indicate that the configurations and behaviors observed when using the realized volatility method differ from those observed when using the absolute return volatility method.Conceived and designed the experiments: ZZ ZQ TT. Performed the experiments: ZZ ZQ. Analyzed the data: ZZ ZQ. Contributed reagents/materials/analysis tools: ZZ TT. Contributed to the writing of the manuscript: ZZ ZQ TT HS BL.Is the Subject AreaMeasurementapplicable to this article?YesNoIn recent decades,SV models are based on an autoregressive formulation of a continuous function describing the latent volatility process[6]. In contrast to discrete-time models,financial markets have grown rapidly and financial instruments have become increasingly complex. The result is a market that is highly volatile and that produces a level of risk that strongly affects all investment decisions[1]. The ever-growing need for theoretical and empirical risk indicators has driven a rapid expansion of research on price volatility in financial markets. Since volatility is strongly linked to uncertainty,and supports the clustering feathers pattern shown inFig. 2.Is the Subject AreaFinancial marketsapplicable to this article?YesNoEditor:Matjaz Perc,and there has been an movement toward the use of flexible and computationally simple nonparametric measurements,Singapore,Republic of SingaporeFor more information about PLOS Subject Areas,Chinese Academy of Sciences,indicating that its fluctuations are stronger. This is because the absolute return volatility captures only the change in daily closing price,Shenyang,clickhere.Is the Subject AreaShort term memoryapplicable to this article?YesNoAffiliationCenter for Polymer Studies and Department of Physics,has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.The conditional probability density for the largest and smallest 1/6th portion of the absolute return volatility (black line) and realized volatility (blue dots).is much sharper than of absolute return volatility changesAffiliationsShenyang Institute of Automation,as a risk indicator,

Copyright:© 2014 Zheng et al. This is an open-access article distributed under the terms of theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Is the Subject AreaProbability densityapplicable to this article?YesNo

In this paper we compare the two most popular nonparametric volatilitiesabsolute return volatility and realized volatilityand focus on their accuracy as risk indicators, their short-term effect, and their long-term memory. Because realized volatility reflects intra-day variance and absolute return volatility reflects day-to-day change, we will also determine ways in which they differ. Our comparison will provide a clear understanding of the advantages and disadvantages of these two measurements, and this will make possible the development of better guidelines for both researchers and market participants.

Citation:Zheng Z, Qiao Z, Takaishi T, Stanley HE, Li B (2014) Realized Volatility and Absolute Return Volatility: A Comparison Indicating Market Risk. PLoS ONE 9(7): e102940.

it is a key input in many investment decisions and in overall portfolio management. Because investors and portfolio managers must determine what levels of risk they can bear and because volatility is the primary risk indicator[2],and have a small high-low spread. On the other hand,and they model the corresponding diffusion processes in the form of stochastic differential equations[7].The simplest measurement of instrument price volatility is tracking the absolute return values and observing the range of day-to-day price changes. This traditional method of volatility modeling from daily returns measures the log-difference of closing prices. Treating absolute returns as a proxy for volatility is the basis of much of the modeling efforts presented in the literature[8][10]. It has been used primarily in econometrics and econophysics research[11][14]and,indicating that the fluctuations of the realized volatility are much smaller and thus easier to predict over the short term. This supports what is shown inFig. 3,e.g.,two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior.

Is the Subject AreaAutocorrelationapplicable to this article?YesNo

We next examine the ways in which the two methods of calculating volatility differ and draw a distribution of the daily changes in both.Figure 2shows that the probability density of the daily change of realized volatility (red dashes) is sharper than that of absolute return volatility (black line) and that both distributions exhibit positive excess kurtosis, i.e., they are leptokurtic. The kurtosis of the daily changes for realized volatility is larger, indicting that it is more stable than absolute volatility and that there is a smaller probability it will exhibit large fluctuations. In other words, realized volatility can usefully model the clustering properties of volatility in which random periods of low activity are followed by periods of high activity, a behavior often observed in financial markets.

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The second method, measuring realized volatility, summarizes all the variances sampled at regular intra-daily intervals under some assumptions of the quadratic variation of the underlying diffusion process[16][18]. Realized volatility measurements, which track the variance of price changes on an intra-day basis, have become possible in recent years because of the increasing availability of high frequency data. Although this volatility measurement derived from high frequency data is more accurate and in principle a better aid in forecasting volatility, it exhibits numerous micro-structural problems. Price discreteness, bid-ask bounce[19], screen fighting[20], non-trading hours, and the irregular spacing of quotes and transactions can all bias volatility estimates. By appropriately adjusting bias and investigating returns standardized by realized volatility, it is found that the return dynamics are consistent with a Gaussian stochastic process incorporating time-varying volatility[21][24].

AffiliationsDepartment of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore, Republic of Singapore, NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore, Republic of Singapore

Is the Subject AreaFinanceapplicable to this article?YesNo

The distribution peak (near 0) of realized volatility changes between neighboring days

In this paper we use several methods to study the clustering and memory effects in two commonly used nonparametric methods of calculating volatility, absolute return volatility and realized volatility. We apply them to both intraday data and daily data and find that both methods are good indicators of market risk because they clearly show the fat-tail and clustering behavior of market price fluctuations. We analyze the short-term and long-term memory effects generated by both methods and find that both offer good predictions of future market behavior. Realized volatility is a better method for describing short-term effects than absolute return volatility and thus it provides a better estimate of near-future possible risk. When we measure the long-term memory capabilities, the two methods are almost the same. Both are sensitive to financial crises, as is shown in their detection of the 2008 global financial crisis. Our analytic comparison of the two approaches will provide researchers and market traders with a more complete understanding of their choices when using volatility as a risk indicator.

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Boston University,Department of Physics and Centre for Computational Science and Engineering,Boston,Massachusetts,indicating that both volatilities follow a power-law distribution. The fat tails indicate that the probability that the absolute return volatility or realized volatility will be significantly large is higher than would be indicated by a Gaussian (normal) distribution. The tails of the realized volatility are somewhat fatter than the tails of the absolute return volatility,while the realized volatility captures data on the basis of quotes sampled at discrete intervals throughout the day. Note that using these two volatility calculation methods means that a zero return will not provide useful information for a given trading day. It also means that although a high return may signal a high absolute return volatility during the day,absolute return volatility is easier to calculate and,Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models,most continuous-time models are used in the development of asset and derivative pricing theories. They assume that the sample paths are continuous,we cannot directly watch volatility. Volatility must be approximated using calculations that draw on such observable values as daily price changes or intraday price changes,i.e.,realized volatility can capture this phenomenon exactly and thus will offer more insights into price-change behavior.Parametric approaches to volatility modeling are based on explicit functional form assumptions regarding the volatility and include both discrete-time models and continuous-time models. The most widely used discrete-time models are the ARCH model[4]and stochastic volatility (SV) model. Much has been written about the ARCH model and it has been modified into dozens of different variations,reliable forecasts of market volatility are pivotal. Thus comparing the predictive capabilities of existing methods of quantifying market volatility can potentially produce extremely valuable information for both market researchers and active traders.Note that both methods of calculating volatility allow us to calculate and analyze fat-tail and clustering properties. In order to understand the underlying dynamics of these two features,the generalized autoregressive conditional heteroskedasticity model (GARCH)[5]. In parallel with the ARCH class of models,P.R. China,two of which are widely used: absolute return volatility and realized volatility.We thank B. Podobnik for his constructive suggestions.Figure 4shows the probability density function of the mean conditional absolute return volatility and the realized volatility given the smallest 1/6th and the largest 1/6th of the whole value. The plot shows that the two lines indicating the smallest and the largest 1/6th portions have a repeated area,in recent years,that realized volatility better demonstrates the short-term effect,which is highlighted in gray. The repeated area (gray area) of the absolute return volatility is much larger than the repeated area (deep gray area) of the realized volatility,it may also simply indicate that the opening price is significantly different from the closing price the previous day but very close to the closing price of the same trading day.

AffiliationsDepartment of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore, Republic of Singapore, NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore, Republic of Singapore

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AffiliationHiroshima University of Economics, Hiroshima, Japan

Contributed equally to this work with: Zeyu Zheng, Zhi Qiao

Funding:ZZ, ZQ, BL thank Econophysics and Complex Networks fund number R–133 from National University of Singapore ( TT thanks Japan Society for the Promotion of Science Grant ( Number 25330047. HES thanks Defense Threat Reduction Agency ( (Grant HDTRA-1-10-1- 0014, Grant HDTRA-1-09-1-0035) and National Science Foundation ( (Grant CMMI 1125290). ZZ thanks Chinese Academy of Sciences ) Grant Number Y4FA030A01. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data Availability:The authors confirm that all data underlying the findings are fully available without restriction. The data source is from Tokyo Stock Exchange, Inc. see

Contributed equally to this work with: Zeyu Zheng, Zhi Qiao