Intervalling Effect Research Articles

Modelling Intervalling Effect of High Frequency Trading on Portfolio Volatility

This paper theoretically examines whether reducing the minimum trading interval could affect portfolio volatility. Modelling the underlying de-trended asset price with Ornstein Uhlenbeck process, the paper investigates the volatility of portfolios that employ buy and hold strategy and momentum strategy. The paper presents theoretical evidence that the fast trading could increase portfolio price fluctuation and hence potentially suggests another cost of high frequency trading, besides the well-known damages including herding, aggressive trading strategies dark pools, immediate-or-cancel type orders.

Is a larger equity market more information efficient? Evidence from intervalling effect

This paper investigates the impact of equity return autocorrelation on financial market efficiency via intervalling effect. A simple model is proposed to show that the degree of intervalling effect is related to the security return autocorrelation. A more general version of Levy and Levhari hypothesis is proposed to find that the degree of the autocorrelations of the security and the market returns determines the existence and the direction of the intervalling effect and the size of the intervalling effect are dependent on the degree of the security autocorrelations. Empirical evidence of the latter is presented.

Intervalling Effect On Estimating The Beta Parameter For The Largest Companies On The WSE

Abstract In the modern portfolio theory investment risk plays a crucial role. It is the subject of numerous studies and publications, in particular in relation to the management of investment portfolios. Commonly used measure of investment management in equities is a beta parameter, which is used to estimate individual stock risk and portfolio risk. In particular, numerous studies the subject of which are the beta parameter properties such as stability in the context of the stock market cycle phases, intervalling effect, length estimation sample etc. The main objective of this paper is to investigate the intervalling effect on the beta parameter. The empirical analysis is carried out for the 33 largest companies of the Warsaw Stock Exchange (WSE) on a sample from the years 2005 to 2012 on the basis of daily, weekly and monthly rates of return. Statistical verification of the hypothesis of the importance of the frequency measuring the return of shares will be based on the single-index Sharpe’s model.

Does intervalling effect affect ETFs?

PurposeThis paper aims to investigate the intervalling effect bias in ETFs' systematic risk expressed by beta. The authors' findings reveal the existence of a significant intervalling effect on ETFs' beta obtained by the ordinary least squares method (OLS). Also investigated is the impact of ETFs' capitalization on beta. Results provide evidence that small cap ETFs have greater betas than large cap ETFs. Results also reveal that the OLS beta of all ETFs increases when the return interval is lengthened regardless of capitalization. The impact of ETFs' trading activity on systematic risk is assessed too. Findings give evidence that the OLS betas of the ETFs that trade infrequently are biased downwards while the beta of the frequently traded ETFs is biased upwards. Finally, the paper reveals a strong intervalling effect on ETFs' tracking error.Design/methodology/approachThe authors employ a sample of 40 broad‐based ETFs listed on Nasdaq Stock Exchange to test whether beta estimates change when the return interval measurement changes. Their data cover a maximum period of ten years starting from September 16, 1998 using daily, weekly and monthly return data. The authors estimate beta applying three alternative methods: the market model applied with the OLS method, the Scholes and Williams model (SW beta) and the Dimson model (Dim beta).FindingsResults indicate that the average beta of ETFs derived by the OLS method increases when the return interval increases. The differences among the daily, weekly and monthly OLS betas are statistically significant at the 1 per cent level. This finding implies a strong intervalling effect bias in ETFs' OLS beta. On the other hand, the authors did not find any statistically significant differences in daily, weekly and monthly Scholes and Williams and Dimson betas. Moreover, results show that the daily and weekly OLS and Scholes and Williams betas and weekly OLS and Dimson betas are significantly different from each other.Originality/valueIn this paper using a sample of 40 broad‐based ETFs listed on Nasdaq Stock Exchange, the authors have examined various issues concerning: the intervalling effect bias in ETFs' systematic risk, the relation between beta and capitalization of ETFs, the relation between beta and trading frequency of ETFs and, finally, the intervalling effect bias in ETFs' tracking error. While the literature on intervalling effect on securities' beta and the relation between systematic risk and market value and trading activity is voluminous, this is the first attempt to examine these issues with respect to ETFs.

The sensitivity of beta to the time horizon when log prices follow an Ornstein–Uhlenbeck process

This paper provides a new theoretical approach to investigate the sensitivity of the familiar beta of the capital asset pricing model to the length of the return measurement interval; a phenomenon known as the intervalling effect. By setting the problem in a continuous time setting, and using exact results, we are able to generalize existing results in the literature. We derive an expression for beta as a function of the time horizon h, conditional on current time t. We show that beta is monotonic in h and derive conditions for it to be increasing or decreasing.

A conditional CAPM: implications for systematic risk estimation

PurposeThe purpose of this paper is to examine, whether or not, the residuals of the market model (MM) are conditionally heteroscedastic; to examine, whether or not, there exists an intervalling effect in conditional heteroscedasticity in the residuals of the MM; to propose a simple data‐driven conditional capital asset pricing model (CAPM); and to examine the effect of conditional heteroscedasticity on the estimation of systematic risk.Design/methodology/approachSystematic risk coefficients (betas) are estimated at first using data of various frequencies from the Athens stock exchange without taking into account conditional heteroscedasticity. The same procedure is repeated, but this time taking into consideration conditional heteroscedasticity, which is found to exist. The results of the two approaches are compared.FindingsEmpirical evidence is provided for the existence of: conditional heteroscedasticity in MM residuals; a pronounced intervalling effect on autoregressive conditional heteroscedasticity (ARCH) in MM residuals; and generalized autoregressive conditional heteroscedasticity in mean type of conditional heteroscedasticity for the majority of cases where ARCH was present in MM residuals. These findings are conducive to a conditional CAPM, which takes into account the effect of conditional variance on expected returns, rather than the standard CAPM.Practical implicationsBetter estimates of financial risk.Originality/valueThe intervalling effect in ARCH in the residuals of the MM is examined for the first time.

A conditional CAPM: implications for the estimation of systematic risk

The purpose of this paper is to examine: (i) whether or not, the residuals of the Market Model are conditionally heteroscedastic; (ii) whether or not, there exists an intervalling effect in conditional heteroscedasticity in the residuals of the Market Model; (iii) the effect of conditional heteroscedasticity on the estimation of systematic risk.; as well as to propose a simple data driven conditional CAPM. To this end daily closing price of stocks traded at the Athens Stock Exchange are used. Empirical evidence is provided for the existence of: (a) conditional heteroscedasticity in MM residuals; (b) a pronounced intervalling effect on ARCH in MM residuals; (c) GARCH in mean type of conditional heteroscedasticity for the majority of cases where ARCH was present in MM residuals. These findings in terms of theory are conducive to a conditional CAPM, which takes into account the effect of conditional variance on expected returns, rather than the standard CAPM. Furthermore, in terms of practical implications these findings may lead to better estimates of systematic risk.

Liquidity commonality and the intervalling effect

AbstractPast studies of liquidity commonality have reported conflicting findings regarding the relationship between market liquidity and firm size. The present paper provides empirical evidence that underlying estimation problems might be responsible for these results. We develop a model of information and spreads that provides some insights into the firm size–liquidity relationship. Our empirical evidence confirms the main testable implications of the model and presents evidence that the presence and strength of common covariability in liquidity depends upon the interval over which liquidity movements are measured. These intervalling effects are caused by delays in information being incorporated into bid and ask spreads.

Exchange rate exposure among European firms: evidence from France, Germany and the UK

AbstractWe investigate the pre‐Euro exposure to exchange rate changes of large firms in the UK, France and Germany. We find that the exchange rate sensitivity is considerably stronger than previously thought. In all three countries, firms typically gain value when their local currency depreciates against the US dollar, yet most UK firms lose value when sterling depreciates against the European currency unit. We also document the existence of an intriguing intervalling effect in the measurement of exchange rate exposure, which suggests that share prices might exhibit a delayed response to information, and prevents us from making robust generalizations concerning other exchange rate sensitivities.

Option Trading and the Intervalling Effect Bias in Beta

Prior studies show that the beta coefficient of a security changes systematically as the length of measurement interval is varied. This phenomenon, which is called the intervalling effect bias in beta, has been attributed to the friction in the trading system that causes the delays in the price-adjustment process. This study shows that option listing is associated with a decline in the beta intervalling effect bias. The decline is most pronounced for small firms. We also find that our sample firms grow significantly after option listing. Since prior research indicates that market value is a major determinant of the magnitude of the intervalling effect, we re-examine our results using a subsample that controls for market value. The results indicate that the decline in the beta bias from the pre-listing to post-listing period is still prevalent after we control for the change in firm size. Overall, the evidence is consistent with the notion that option trading reduces the delays in the price-adjustment process, which in turn reduces the intervalling effect bias in beta.

Sensitivity of Systematic Risk Estimates to the Return Measurement Interval Under Serial Correlation

This paper analytically and empirically investigates the sensitivity of the return measurement interval to the market beta estimate and suggests a market beta estimation method incorporating the investment horizon through a vector autoregressive (VAR) model when there is serial correlation in returns. The analytical relation between the beta estimate and the return measurement interval is obtained. Based on the analytical relation, a decision function for the intervalling effect is provided. It is found that the intervalling effect is mostly caused by January returns.

Price Limits and Beta

Price limits, which restrict daily price changes of a stock within a pre-specified range, make the stochastic properties of observed returns deviate from those of true returns, and hence lead to a biased estimates of the market model parameters. To investigate the impacts of price limits on the market model parameters, especially on beta, the restricted regression analysis is performed as well as the two-pass regression analysis used in examining the intervalling effect bias on beta. Empirical results suggest that, when prices are observed within a pre-specified bound, the estimates of beta using ordinary least squares substantially understate the true beta and suffer more from the intervalling effect bias. However, the delay effect of price limits on the adjustment of a security's price does not last too long, that is, remaining information is reflected on the subsequent day's stock prices very rapidly.

Intervalling effect on intertemporal stability among Asian emerging markets and developed markets

Using a direct test on the equality of variance-covariance matrices and on that of correlation matrices, the intervalling effect on the intertemporal stability in stock return relationships among six Asian emerging markets and four developed markets is examined. Our empirical results show that: (1) it pays to diversity into the Asian emerging markets as the correlations between Asian emerging markets and developed markets are smaller than those among developed markets only; (2) correlation matrices of stock returns are much more stable than the corresponding variance-covariance matrices-this result is robust across different lengths of holding intervals; (3) the shorter the time period considered, the more stable are the patterns of stock market co-movement, which is true for all holding intervals; and (4) with an increase in the length of the holding intervals, there is weak evidence that the stock market relationships among Asian emerging markets and developed markets become relatively more stable for each time period considered.

L’effet d’intervalle sur le marché à terme de la Bourse de Bruxelles

RésuméCet article traite de l’effet d’intervalle sur le marché à terme de la Bourse de Bruxelles. L’analyse empirique est menée sur les actions belges cotées sur ce marché pour une période allant de l’introduction du Computer Assisted Trading System (C.A.T.S.), début 1989, au 31 décembre 1992. La présence d’un effet d’intervalle est mise en évidence, l’estimation du risque systématique des 19 actions composant l’échantillon dépend de la longueur de l’intervalle de temps choisi pour calculer les rendements. L’estimation des betas à l’aide d’un modèle GARCH ne donne pas de meilleurs résultats que la régression linéaire simple et les valeurs des betas dépendent toujours de la longueur de l’intervalle de temps. L’effet d’intervalle semble donc ne pas être dû à la présence d’hétéroscédasticité conditionnelle. Il ressort également que, sur base de données journalières, les modèles proposés par Scholes et Williams et par Dimson qui ajustent le beta pour tenir compte de la faible fréquence des échanges, donnent aux coefficients une valeur plus proche de leurs valeurs asymptotiques que le fait la régression linéaire simple.

The intervalling effect bias in beta: A note

Based on a comprehensive sample of domestic securities traded on the Brussels Stock Exchange, this paper points out the intervalling effect in the estimated betas and examines the speed of convergence of these. The results reveal that the estimated betas seem to converge to their asymptotic values and that their value depends on what day the differencing interval starts. It also appears that the magnitude of the intervalling effect is inversely related to the market value of the firms.

Adjusting for the intervalling effect bias in beta: A Test using Paris Bourse Data

This paper uses a sample of daily returns data from the Paris Bourse to test the predictions of and adjustment procedures implied by the Cohen-Hawawini-Maier-Schwartz-Whitcomb (1983a,b) model of the intervalling effect bias in OLS beta estimates. CHMSW show that the bias diminishes asymptotically to zero as the differencing interval increases and that the sign of the bias depends on a stock's relative value of shares outstanding. We employ the three-pass regression procedure of CHMSW (1983b), but we test a broader set of second pass functional forms and use the Box-Cox (1964) transformation model to verify our chosen form. The CHMSW adjustment procedures are compared with that of Scholes-Williams (1977), and the latter is shown to contain a significant intervalling effect bias.

Estimating and Adjusting for the Intervalling-Effect Bias in Beta

The concept of beta as the measure of systematic risk has been widely accepted in the academic and financial community. Increasingly, betas are being used to estimate the cost of capital for corporations. Despite this, however, biases are generally present in ordinary least squares (OLS) estimates of beta. In particular, empirical estimates of beta are affected by friction in the trading process which delays the adjustment of a security's price to informational change and hence leads to an “intervalling-effect” bias. In this paper, we present and empirically test two procedures for correcting this bias. The first is to estimate the asymptotic value that OLS beta approaches as the differencing interval is lengthened without bound. The second procedure is to infer the value of beta by adjusting OLS beta for cross-sectional differences in the intervalling effect as a function of the depth of the market for a security (as measured by its value of shares outstanding). Our results suggest that a substantial correction is needed to get “true” beta estimates from short differencing interval data.