EPPS EFFECT STILL EXISTENT: DIFFERING UNCONDITIONAL CORRELATION BEHAVIORS FOR INTER-SECTOR STOCK PAIRS
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DOI : 10.26728/ideas.337
Year-Number: 2020-24
Language : null
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Abstract
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Abstract
For diversification purposes, investors may well distribute their investment budgets to different assets. Degree of co-movement between these assets is one of the critical determinants of portfolio performances. An investment strategy that favors putting the assets -of which the prices are driven by the same underlying factors- into to the same basket will be vulnerable to negative shocks. As the number of assets in an investment bundle grows, variance risk gradually fades whereas the covariance risk still lasts. In that regard, correlation numbers become significant. Measured correlation figures on the other hand differ as the adopted methodology for correlation calculation varies. As the time series of interest are constructed with narrower intervals for a given period, correlation numbers decrease almost all the time. This is called as Epps Effect in the literature and non-synchronicity and lead-lag relationships were shown to be main causes behind the scene. This study displays how correlation numbers continue rising as the measurement intervals gets larger for stock pairs of the same sector even though this is not the case when pairs are formed with the stocks of different sectors. Although trading practices and market dynamics changed tremendously, and algorithms took over considerable share in trading volumes, this study sheds light on the on-going existence of Epps Effect in an emerging market exchange in spite of the recent technological improvements in various layers of investment cycle.
Keywords
- In 1979, Thomas Epps analyzed four different stock prices in the same industry to detect the very
- In 1979, Thomas Epps analyzed four different stock prices in the same industry to detect the veryshort run co-movement among them. Prices of AMC, Chrysler, Ford and GM that are taken fromNew York Stock Exchange were recorded with ten minutes intervals for the first half of 1971 andEpps calculated inter-stock correlations (of log price changes) for time series constructed with ten,twenty and thirty minutes, one, two and three hours and one, two and three days of intervals. Hisfindings for the correlations of changes in the log prices were tabulated starting from the very short-term interval to three days and figures for the ten-minutes intervals were the lowest among. Eppsreached a revelatory conclusion that the correlations become quite low as the measurement interval gets shorter, whereas larger time steps yield larger correlation figures.
- Fisher (1966) seems to be the first who analyzes non-synchronicity; non-contemporaneous pricequotes during index calculations and its possible outcomes. Lo and MacKinlay (1990) touches uponfrequency differences in trades of different stocks and builds a stochastic model for non-synchronous asset prices. They take two imaginary stocks i and j, i being less frequently tradedamong investors. If some ground-breaking news reaches to market around closing hours and theprice of j shows an immediate response due to being more liquid while asset i’s price reacts to thisinformation with a lag, there will be a typical lag affect and that will impel a cross-autocorrelationbetween the prices of i and j. Hence, a portfolio which includes both assets will have an auto- correlation. This non-trading problem will bias the econometric results if not considered.
- Bonanno et al. (2001) selects one-hundred stocks from US equity markets for the period January1995- December 1998 and constructs a Minimum Spanning Tree (MST) and Hierarchical Tree(HT) by clustering the financial data on the basis of correlation coefficients. Having a correlationmatrix in hand, they calculate a metric distance out of correlation coefficients and in a senseconverts the numbers to visual presentations to utilize geometry and taxonomy. They first derivethe results with a time span of 6 hours and thirty minutes (one day) and later shortens the interval tonineteen minutes and thirty seconds (one day/20). As the time horizon gets tiny, MST and HTfigures become less complicated and mean correlation coefficients between the stock pairsdecrease, more salient diminution being observed among the mostly correlated pairs; that is, intra- sector correlation figures decrease faster than those of inter-sector.
- Reno (2003) likewise points out non-synchronous trading and lead-lag relationship to be thepossible causes behind the statistical findings of Epps (1979). Reno (2003) aims to breakdown theindividual impacts of these two alleged factors and seeks for other potential explanatory reasons. Headopts the Fourier method to complete his study; a method which enables him to use the data as it iswithout altering the time structure of tick-by-tick data. He made the most of Monte Carlosimulations and hypothesized that provided there is no lead-lag phenomenon and all the trades oftwo assets are simultaneous, there should not be any frequency related impacts in correlationmeasurements. He concluded those two factors are the main reasons of declining correlations withhigher frequency and presented an evidence from his analysis on DEM-USD and JPY-USDexchange rates data. With simultaneous quotes, Epps effect was eliminated to some extent althoughnot eradicated completely. He calculated 8 seconds of lead-lag relationship in the data pair andreanalyzed his findings by shifting one of the data series 8 seconds to secure synchronicity. Thisoperation substantially decreased the Epps effects and made him to assert non-synchronous tradingand lead-lag relationship are the principal causes of Epps effect. His analysis on two stocks -Mobil and Exxon- also gave similar results- lag period this time being 70 seconds.
- Asynchronicity in trades is one of the mostly uttered causes of correlation decreases for shorter timewindows. As the trading activity is accelerated, number of contemporaneous price pairs will beincreasing and that would inhibit the correlation magnitudes falling further down as the timeintervals get narrower. This was shown theoretically via Monte Carlo simulations in Reno (2003).Toth and Kertesz (2009) this time however discusses that empirical findings for higher tradingactivity suggest not to be so straightforward about the alleged achievements of active trading onfixing the flaws of correlation numbers for high-frequency intervals. In order to sterilize theirfindings on synchronicity, Toth and Kertesz (2009) focuses on stocks where lead-lag relationship isignorable. In that regard, Coca Cola/PepsiCo, Caterpillar/ Deere, Wal-Mart Stores/Sprint NextelCorp. etc. are taken for deeper analysis. Correlation structure (dependent of sampling timescale) ofCoca Cola/PepsiCo pair for the period 1993-2003 is printed for visual inspection and displayed toincrease as the time interval gets larger to reach out its asymptotical value. More interestingly, thiscorrelation coefficients are graphed separately for the years 1993, 1997, 2000 and 2003 whichconverge to different correlation levels as the timescale is enlarged. Although correlation numbersof 2003 are above those of 1993 at the very short time intervals for instance, figures for both yearsstart to increase as the time interval gets bigger. Toth and Kertesz (2009) scales the correlations ofthe years 1993, 1997, 2000 and 2003 with their asymptotic values and curves this time nearlyoverlaps in all timescales with concave shape of correlation figures still existent. Hence authorsconclude that level of trading activity, as asserted in their earlier study, cannot be responsible for theEpps Effect solely and points out some other more reasonable factors shaping the pattern; mostprobably the reaction times of humans. Later, Toth and Kertesz (2009) divides time concept intothree market time scales: frequency of trading in the market (market activity), market periodicitiesand reaction time of traders to news and events. First two were shown to be not bringing asatisfactory explanation in Toth and Kertesz (2009). Regarding the last one, it will be a highlyoptimistic expectation for investors to react instantly to newly arriving information. There arestudies showing that prices absorb disclosed information within first fifteen minutes after it isreleased. Chordia et al. (2008), Busse and Green (2002) and Barclay and Litzenberger (1988) are among many others.
- Data consists of tick-by-tick trades of highly liquid XU030 index stocks in Borsa Istanbul equitymarket and listed in Table 1. Prices are stored for the third quarter of 2018. Even tough Epps (1979)applies 10 minutes intervals as the narrowest intervals, this study shortens it even to 5-second longintervals. Also, as is known, there may be more than one trades which coincide on the same second.In other words, there are trades on sub-second levels. Following Barndorff-Nielsen et al. (2009), median of these trades are taken as the sole price quotation for that second.
- Index constituents are updated quarterly at Borsa Istanbul. Even though the analyzed stocks arefrom XU030 index in the third quarter of 2018, this condition is additionally checked if it was alsothe case in second and fourth quarter of the same year. This is crucial in the sense that stocks’ betasconverge to that of the index they are added to. Vijh (1994) shows that non-S&P 500 stocks’ betasincrease after their inclusion to S&P 500. Barberis et al. (2005) similarly reports this co-movementwhen stocks are put into certain index and touches upon the factors of “friction-based”convergence. Even though days are analyzed separately in the study, requirement of indexmembership before and after the third quarter of 2018 eliminates these latent drivers in correlation structure.
- Numbers in the time series are the percentage changes of log prices between respective intervals. Incase there is no quoted price for the a given time stamp, previous tick rule is applied to fill in the data set as applied in Epps (1979).
- Findings reveal valuable insights for interested parties of finance community. Unconditional hand-in-hand movements vary depending on the methodology chosen as pictured in Epps (1979) decadesago. Hence, one needs to be careful about the adopted procedure. However, one of the critical facetsof empirical outcomes is related with the stock pairs. Whether each item in pairs belongs to thesame sector or not determines the shape of correlation path. For the same sector, correlation doesincrease almost in all successive intervals whereas it makes plato after 5-minute intervals and startsmostly declining towards the largest intervals when items of the pairs are from different sectors.
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