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. 2013:3:2110.
doi: 10.1038/srep02110.

How high frequency trading affects a market index

Dror Y Kenett  1 , Eshel Ben-Jacob, H Eugene Stanley, Gitit Gur-Gershgoren
Affiliations

How high frequency trading affects a market index

Dror Y Kenett et al. Sci Rep. 2013.

Erratum in

  • Sci Rep. 2013;3:2265

Abstract

The relationship between a market index and its constituent stocks is complicated. While an index is a weighted average of its constituent stocks, when the investigated time scale is one day or longer the index has been found to have a stronger effect on the stocks than vice versa. We explore how this interaction changes in short time scales using high frequency data. Using a correlation-based analysis approach, we find that in short time scales stocks have a stronger influence on the index. These findings have implications for high frequency trading and suggest that the price of an index should be published on shorter time scales, as close as possible to those of the actual transaction time scale.

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Figures

Figure 1
Figure 1. Daily correlation between the synthetic index and the market index.
Figure 2
Figure 2. Box-plot representation of the XCF, as function of the lag, for the (A) low, (B) medium, and (C) high STD groups, as categorized by the second classification rule.
The bottommost vertical line represents the minimum of the sample, the bottom line of the box represents the 25th percentile, the line inside the box represents the median, the uppermost line of the box represents the 75th percentile, and the topmost vertical line represents the maximum of the sample.
Figure 3
Figure 3. Correlation values for Lag = + 1 for 1025 days.
In panel A we present the histogram of the values, where the y-axis represents the percentage out of the whole for the value in each bin. This clearly shows that there is a higher probability for positive correlationvalues. In panel B we present the commutative distribution function (CDF) of values. The CDF shoes that 90% of the days have positive correlation values for this lag, 10% of the days (n = 102) have correlation >0.4, 1% of the days (n = 12) have correlation >0.7, and 0.7% of the days (n = 7) have correlation >0.8.
Figure 4
Figure 4. Average XCF, as function of lag, for each year separately.
The average is calculated over days categorized into the low (A), medium (B), and high (C) STD.
Figure 5
Figure 5. We calculate the ratio between the number of stocks influenced by the synthetic index and the number of stocks influenced by the market index.
The x-axis is days in which there was a nonzero influence, and the y-axis is the value of the II, in a logarithmic scale. The days are color-coded: blue, II ≤ 0.5; green, 0.5 < II ≤ 1.0; and red, II > 1.0.
Figure 6
Figure 6. Ranking of stocks and indices, according to their influence, for each day.
The color represents the number of the stock/index, where for the majority of the days there were 25 stocks, and then the synthetic index was number 26, and the market index was 27. For a small percentage of the days, there were 26 stocks, and then the indices were numbered 27 and 28, respectively.
Figure 7
Figure 7. Interday price change of TEVA for the trade period 2006–2010.
The time axis (x-axis) is time in the sense of transactions, starting from 1.0 at the beginning of the continuous trade stage for the first trading day (01/01/2006) until the end of the continuous trade stage of the last trading day (31/12/2009).
See this image and copyright information in PMC

References

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