Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm
Abstract
:1. Introduction
2. Layer Detection and Data Adjustment
3. Precise Adjustment of Data and an Improved Detection Algorithm
3.1. Finding the No-Information Cluster
- Sort the clusters by increasing the trade intensity, defined as the sum of average buys and sells within each cluster, and store them in a list .
- Let the no-information cluster be the cluster with the lowest trade intensity, . Initialize : .
- In each iteration,
- 4.1.
- Merge the no-information cluster with the next cluster in the list: .
- 4.2.
- Run the -Skellam test on the no-information cluster .
- 4.3.
- If passes the -Skellam test, then , and run step .
- 4.4.
- If fails the -Skellam test, the algorithm stops, and the no-information cluster is .
3.2. Adjusting the Data for Displacement
- [1].
- First, we use the values and —estimated from the identified no-information cluster in the previous step—as the reliable estimates of the theoretical and .
- [2].
- Second, instead of generating values from the Poisson distributions centered on and , we simply add to all the observations and to all the observations . Such approximation is justified by the fact that a Poisson distribution is centered on its mean, especially when and are relatively large.
3.3. Detecting the Information Layers
- Cluster trading days into layers based on the adjusted absolute order imbalance .
- Run the -Skellam test on all the layers:
- 2.1.
- If the test fails for one or more layers, increase the number of layers by , and run step 1.
- 2.2.
- If all clusters pass the α-Skellam test, the algorithm stops, and the number of layers is equal to .
4. Empirical Evidence
- (1)
- (2)
- E (the same algorithm with the correction that uses minimum numbers of buys and sells in the data, as suggested in (Ersan 2016)).
- (3)
- EG (the suggested method of this paper that refers to the modified layer detection algorithm and the new correction).
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Eps Ratio-Layers | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Panel A: No correction | ||||||||
0 | 84.88 | 88.28 | 93.24 | 92.76 | 92.04 | 92.56 | 91.16 | 89.52 |
0.001 | 86.32 | 89.96 | 93.12 | 92.68 | 92.56 | 91.88 | 91 | 89.92 |
0.01 | 77.08 | 81.2 | 88.2 | 86.96 | 88.68 | 87.84 | 87.92 | 87.16 |
0.05 | 60.44 | 49.16 | 41.6 | 35.24 | 30.24 | 29.44 | 27.8 | 30.36 |
0.1 | 29.72 | 32.32 | 33.12 | 27.48 | 21.24 | 17.96 | 16.44 | 14.72 |
0.25 | 12.2 | 10.04 | 14.04 | 16 | 15.12 | 13.64 | 12.6 | 10.28 |
Panel B: E2016 correction | ||||||||
0 | 98.88 | 91.48 | 78.44 | 61.2 | 53.04 | 49 | 44.44 | 42.56 |
0.001 | 98.84 | 91.12 | 78.2 | 61.92 | 54.28 | 47.6 | 44.8 | 40.4 |
0.01 | 98.64 | 91.08 | 79.88 | 60 | 53.48 | 48.16 | 44.12 | 41.76 |
0.05 | 98.84 | 90.28 | 79.6 | 62.56 | 54.92 | 50.08 | 44.6 | 42.72 |
0.1 | 98.88 | 92.2 | 78.84 | 61.84 | 50.88 | 49.88 | 43.84 | 42.64 |
0.25 | 98.72 | 90.36 | 79.6 | 63.12 | 54.8 | 50.08 | 45.04 | 43.12 |
Panel C: EG correction | ||||||||
0 | 93.36 | 95.32 | 94.68 | 92.92 | 92.6 | 90.32 | 87.84 | 86.36 |
0.001 | 93.48 | 95.12 | 94.64 | 93.52 | 92.68 | 90.76 | 88.12 | 85.68 |
0.01 | 93.8 | 94.12 | 94.88 | 94.44 | 93.36 | 91.44 | 88.24 | 86.56 |
0.05 | 92.76 | 95.08 | 94.68 | 93.96 | 93.32 | 90.24 | 89.04 | 86.8 |
0.1 | 93.32 | 94.6 | 94.04 | 94.96 | 91.56 | 90.32 | 89.24 | 87.12 |
0.25 | 94.64 | 94.72 | 94.76 | 93.28 | 92.88 | 90.76 | 88.64 | 86.16 |
Mean | sd | Min | Median | Max | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Buys | 6149 | 3358 | 107 | 382 | 952 | 3349 | 6138 | 8835 | 11,476 | 13,469 | 20,793 |
Sells | 6142 | 3467 | 95 | 369 | 931 | 3286 | 6024 | 8706 | 11,974 | 14,159 | 23,046 |
OI | 7 | 1325 | −12,526 | −3615 | −2160 | −665 | 20 | 688 | 2136 | 3581 | 9240 |
AOI | 2405 | 1879 | 20 | 143 | 327 | 985 | 1899 | 3349 | 6169 | 8359 | 17,037 |
MPIN | 0.20 | 0.15 | 0.00 | 0.01 | 0.03 | 0.09 | 0.17 | 0.28 | 0.48 | 0.66 | 0.92 |
alpha | 0.76 | 0.19 | 0.02 | 0.13 | 0.37 | 0.68 | 0.80 | 0.90 | 0.97 | 0.98 | 0.98 |
delta | 0.50 | 0.20 | 0.00 | 0.03 | 0.17 | 0.37 | 0.50 | 0.63 | 0.83 | 0.97 | 1.00 |
mu | 2693 | 2096 | 85 | 241 | 462 | 1046 | 2106 | 3791 | 6859 | 9317 | 19,093 |
eps.b | 5043 | 2858 | 95 | 200 | 593 | 2571 | 5039 | 7515 | 9507 | 9901 | 10,040 |
eps.s | 5040 | 2976 | 79 | 197 | 580 | 2516 | 4947 | 7342 | 10,088 | 11,436 | 12,476 |
Mean | sd | Min | Median | Max | |||
---|---|---|---|---|---|---|---|
1 | 0.24 | 0.14 | 0.01 | 0.12 | 0.21 | 0.33 | 0.85 |
2 | 0.19 | 0.11 | 0.01 | 0.1 | 0.17 | 0.26 | 0.69 |
3 | 0.17 | 0.09 | 0.03 | 0.09 | 0.16 | 0.23 | 0.61 |
4 | 0.16 | 0.09 | 0.02 | 0.09 | 0.15 | 0.22 | 0.55 |
5 | 0.16 | 0.08 | 0.03 | 0.09 | 0.15 | 0.22 | 0.63 |
6 | 0.16 | 0.08 | 0.03 | 0.09 | 0.15 | 0.22 | 0.7 |
7 | 0.17 | 0.09 | 0.03 | 0.09 | 0.16 | 0.23 | 0.67 |
8 | 0.17 | 0.09 | 0.03 | 0.09 | 0.16 | 0.24 | 0.67 |
1 | Firm-specific events such as CEO resignations, financial reports, mergers, and strategic alliances exert varying impacts on trading activity due to the nature and significance of the information they convey. The growing frequency of information events, along with the proliferation of data sources, has amplified their impact on market behavior, making it crucial to accurately assess their effects on trading activity (Fang and Peress 2009; Loughran and McDonald 2016). The recent literature on information overload document that stricter disclosure requirements in the last two decades have led to a substantial increase in the amount of data shared in annual reports (e.g., Guay et al. 2016; Chapman et al. 2019; Impink et al. 2022). Dyer et al. (2017) examined 10-K filing texts for more than 10,000 firms between 1996 and 2013 and found that the median text length doubled from 23,000 words in 1996 to nearly 50,000 in 2013. Boudoukh et al. (2019) employ textual analysis to identify fundamental information in public news. They find that this information accounts for 50% of the overnight idiosyncratic volatility in stock returns and most of this large share is due to the days with multiple news. They examine the impact of 18 event categories such as financials, ratings, earnings factors, forecasts, and mergers and acquisitions, composing 90 subcategories, and show the differing contributions of each event category to stock return variance. Thus, they show that stock returns and volatility vary greatly with the type of news and the magnitude of information is not the same across days. |
2 | The PIN model divides trading days among three types: no-information days with solely uninformed trading intensities ; good-information days with uninformed trading intensities and informed buying intensity ; and bad-information days with uninformed trading intensities and informed selling intensity . The straightforward generalization presented in Ersan (2016) assumes the existence of different levels of informed trading activities, i.e., instead of having a unique parameter , common to all information days, information days can be divided into multiple types (or layers), where each layer is associated with a distinct level of informed trading intensity . Consequently, a good-information day of type has the trading intensity rates of , while a bad-information day of type has the trading intensity rates of ; Ersan (2016) has been the only work relaxing the three assumptions in the PIN model and proposing the generalized model (MPIN). It estimates the probability of informed trading after simultaneously accounting for multiple information layers. Both models yield identical estimates when there is one type of information event in the data, whereas the traditional PIN model fails to provide accurate estimates when there are multiple layers. This is a natural consequence of the PIN model’s assumption of a single-event type. |
3 | The PIN model presented by Easley et al. (1996) has a single uninformed rate while Easley et al. (2002) incorporate uninformed buy and sell rates separately, reaching marginally different estimates on them. In the following literature, the mean estimates of buy-side and sell-side uninformed rates have differed from each other while the differences are relatively low (i.e., <20%). |
4 | PINstimation is an R software package that is developed for the estimation of various PIN models. The package includes the functions and arguments covering the computational improvements and extensions of the original PIN model, and it provides extensive data simulation and data aggregation tools. |
5 | Please check the R code of the function detectlayers_eg() that implements the introduced algorithm in this paper and the R code of the function detectlayers_e() for the algorithm of Ersan (2016), available at https://cran.r-project.org/web/packages/PINstimation/index.html (accessed on 1 February 2024). |
6 | Ghachem and Ersan (2023b) suggest using the expectation maximization (EM) algorithm to simultaneously estimate the number of layers and PIN parameters. However, this method requires the estimation of the model for all the possible numbers of information layers, which is time-consuming. |
7 | If , then and . These are two Skellam distributions with the same parameters but in reverse order, so they are symmetric around zero. |
8 | The Skellam test performed in the functions detectlayers_e and detectlayers_eg() is conducted using the function qskellam() from the R package Skellam (Lewis et al. 2016). |
9 | Theoretically, dividing the data into a sufficiently large number of clusters ensures that the order imbalance (OI) observations within each cluster are sufficiently similar due to the clustering algorithm’s focus on similarity. We have chosen to start with ⌊n/2⌋ initial clusters. This approach only fails in very unusual datasets, such as those containing more than ⌊n/2⌋ layers. For datasets representative of a quarter (e.g., 60 days), this would imply 30 layers, which is extremely unlikely. Ersan (2016) works with 8190 stock-quarter datasets. The largest number of layers detected in these datasets is 16. The number of layers is less than 10 in 98% of the datasets and less than 15 in 99.96% of the datasets. Change in the computation time is marginal when increasing the initial number of clusters; thus, we set the initial cluster number large enough to provide high confidence. |
10 | The actual step is slightly more complex than this but is equivalent to the described step in almost all the cases. It clusters trading days based on OI into clusters where , then runs the -Skellam test on all the clusters. Among all the configurations with clusters for which all the clusters pass the Skellam test, the clustering configuration that has the largest cluster with minimum trading intensity is selected as the clustering used in step 2. This modification aims to reduce the running time of the algorithm but does not alter its essence. |
11 | As our suggested algorithm specifically targets detecting the information layers in a dataset, the three compared methods involve the algorithm in our paper as well as the only two alternative layer detection methods that are available in the literature. Other comparisons among the overall estimation accuracy of the various PIN models are beyond the scope of our study. |
12 | Detailed information regarding the data simulation can be found in the PINstimation package documentation and Ghachem and Ersan (2023a). |
13 | |
14 | Buys and sells are the mean buys and sells in each dataset. Therefore, the mean statistic is the mean of these mean values. |
References
- Aktas, Nihat, Eric de Bodt, Fany Declerck, and Hervé Van Oppens. 2007. The PIN anomaly around M&A announcements. Journal of Financial Markets 10: 169–91. [Google Scholar]
- Amnas, Muhammed Basid, Murugesan Selvam, and Satyanarayana Parayitam. 2024. FinTech and Financial Inclusion: Exploring the Mediating Role of Digital Financial Literacy and the Moderating Influence of Perceived Regulatory Support. Journal of Risk and Financial Management 17: 108. [Google Scholar] [CrossRef]
- Arifovic, Jasmina, Xue-Zhong He, and Lijian Wei. 2019. High frequency trading in FinTech age: AI with speed (15 November 2019). Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2771153 (accessed on 12 August 2024).
- Bazzana, Flavio, and Andrea Collini. 2020. How does HFT activity impact market volatility and the bid-ask spread after an exogenous shock? An empirical analysis on S&P 500 ETF. The North American Journal of Economics and Finance 54: 101240. [Google Scholar]
- Berkman, Henk, Paul D. Koch, and P. Joakim Westerholm. 2014. Informed trading through the accounts of children. The Journal of Finance 69: 363–404. [Google Scholar] [CrossRef]
- Boehmer, Ekkehart, Charles M. Jones, Xiaoyan Zhang, and Xinran Zhang. 2021. Tracking retail investor activity. The Journal of Finance 76: 2249–305. [Google Scholar] [CrossRef]
- Bogousslavsky, Vincent, Vyacheslav Fos, and Dmitry Muravyev. 2024. Informed trading intensity. The Journal of Finance 79: 903–48. [Google Scholar] [CrossRef]
- Boudoukh, Jacob, Ronen Feldman, Shimon Kogan, and Matthew Richardson. 2019. Information, trading, and volatility: Evidence from firm-specific news. The Review of Financial Studies 32: 992–1033. [Google Scholar]
- Brennan, Michael J., Sahn-Wook Huh, and Avanidhar Subrahmanyam. 2016. Asymmetric effects of informed trading on the cost of equity capital. Management Science 62: 2460–80. [Google Scholar] [CrossRef]
- Brennan, Michael J., Sahn-Wook Huh, and Avanidhar Subrahmanyam. 2018. High-frequency measures of informed trading and corporate announcements. The Review of Financial Studies 31: 2326–76. [Google Scholar] [CrossRef]
- Brogaard, Jonathan. 2010. High frequency Trading and Its Impact on Market Quality. Northwestern University Kellogg School of Management Working Paper. Evanston: Northwestern University Kellogg School of Management. [Google Scholar]
- Chapman, Kimball L., Nayana Reiter, Hal D. White, and Christopher D. Williams. 2019. Information overload and disclosure smoothing. Review of Accounting Studies 24: 1486–522. [Google Scholar] [CrossRef]
- Chen, Mark A., Qinxi Wu, and Baozhong Yang. 2019. How valuable is FinTech innovation? The Review of Financial Studies 32: 2062–106. [Google Scholar] [CrossRef]
- Cheng, Tsung-Chi, and Hung-Neng Lai. 2021. Improvements in estimating the probability of informed trading models. Quantitative Finance 21: 771–96. [Google Scholar] [CrossRef]
- Dang, Viet Anh, Dinh Trung Nguyen, Thu Phuong Pham, and Ralf Zurbruegg. 2024. The dynamics of informed trading around corporate bankruptcies. Finance Research Letters 63: 105385. [Google Scholar] [CrossRef]
- Duarte, Jefferson, and Lance A. Young. 2009. Why is PIN priced? Journal of Financial Economics 91: 119–38. [Google Scholar]
- Duarte, Jefferson, Edwin Hu, and Lance A. Young. 2015. What does the PIN model identify as private information. Unpublished working paper, Rice University, University of Washington. [Google Scholar]
- Dyer, Travis, Mark Lang, and Lorien Stice-Lawrence. 2017. The evolution of 10-K textual disclosure: Evidence from Latent Dirichlet Allocation. Journal of Accounting and Economics 64: 221–45. [Google Scholar] [CrossRef]
- Easley, David, Nicholas M. Kiefer, Maureen O’Hara, and Joseph B. Paperman. 1996. Liquidity, information, and infrequently traded stocks. The Journal of Finance 51: 1405. [Google Scholar]
- Easley, David, Soeren Hvidkjaer, and Maureen O’Hara. 2010. Factoring information into returns. Journal of Financial and Quantitative Analysis 45: 293–309. [Google Scholar] [CrossRef]
- Easley, David, Soeren Hvidkjaer, and Maureen O’Hara. 2002. Is information risk a determinant of asset returns? The Journal of Finance 57: 2185–221. [Google Scholar] [CrossRef]
- El Hajj, Mohammad, and Jamil Hammoud. 2023. Unveiling the influence of artificial intelligence and machine learning on financial markets: A comprehensive analysis of AI applications in trading, risk management, and financial operations. Journal of Risk and Financial Management 16: 434. [Google Scholar] [CrossRef]
- Ersan, Oguz. 2016. Multilayer Probability of Informed Trading (November 22, 2016). Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2874420 (accessed on 25 March 2024).
- Ersan, Oguz, and Asli Alıcı. 2016. An unbiased computation methodology for estimating the probability of informed trading (PIN). Journal of International Financial Markets, Institutions and Money 43: 74–94. [Google Scholar] [CrossRef]
- Fang, Lily, and Joël Peress. 2009. Media coverage and the cross-section of stock returns. The Journal of Finance 64: 2023–52. [Google Scholar] [CrossRef]
- Gan, Quan, Wang Chun Wei, and David Johnstone. 2015. A faster estimation method for the probability of informed trading using hierarchical agglomerative clustering. Quantitative Finance 15: 1805–21. [Google Scholar] [CrossRef]
- Ghachem, Montasser, and Oguz Ersan. 2023a. PINstimation: An R Package for estimating probability of informed trading models. The R Journal 15: 145–68. [Google Scholar] [CrossRef]
- Ghachem, Montasser, and Oguz Ersan. 2023b. Estimation of the probability of informed trading models via an Expectation-Conditional Maximization Algorithm (12 March 2023). Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4386172 (accessed on 25 March 2024).
- Guay, Wayne, Delphine Samuels, and Daniel Taylor. 2016. Guiding through the fog: Financial statement complexity and voluntary disclosure. Journal of Accounting and Economics 62: 234–69. [Google Scholar] [CrossRef]
- Hendershott, Terrence, Xiaoquan (Michael) Zhang, J. Leon Zhao, and Zhiqiang (Eric) Zheng. 2021. FinTech as a game changer: Overview of research frontiers. Information Systems Research 32: 1–17. [Google Scholar] [CrossRef]
- Impink, Joost, Mari Paananen, and Annelies Renders. 2022. Regulation-induced Disclosures: Evidence of Information Overload? Abacus 58: 432–78. [Google Scholar] [CrossRef]
- Jackson, David. 2013. Estimating PIN for firms with high levels of trading. Journal of Empirical Finance 24: 116–20. [Google Scholar] [CrossRef]
- Ke, Wen-Chyan, Hueiling Chen, and Hsiou-Wei William Lin. 2019. A note of techniques that mitigate floating-point errors in PIN estimation. Finance Research Letters 31: 458–462. [Google Scholar] [CrossRef]
- Lai, Sandy, Lillian Ng, and Bohui Zhang. 2014. Does PIN affect equity prices around the world? Journal of Financial Economics 114: 178–95. [Google Scholar] [CrossRef]
- Lewis, Jerry W., Patrick E. Brown, and Michail Tsagris. 2016. Package ‘skellam’. Available online: https://cran.r-project.org/web/packages/skellam/index.html (accessed on 1 February 2024).
- Lin, Hsiou-Wei William, and Wen-Chyan Ke. 2011. A computing bias in estimating the probability of informed trading. Journal of Financial Markets 14: 625–40. [Google Scholar] [CrossRef]
- Lof, Matthijs, and Jos van Bommel. 2023. Asymmetric information and the distribution of trading volume. Journal of Corporate Finance 82: 102464. [Google Scholar] [CrossRef]
- Loughran, Tim, and Bill McDonald. 2016. Textual analysis in accounting and finance: A survey. Journal of Accounting Research 54: 1187–230. [Google Scholar] [CrossRef]
- O’Hara, Maureen. 2015. High frequency market microstructure. Journal of Financial Economics 116: 257–70. [Google Scholar] [CrossRef]
- Roşu, Ioanid. 2019. Fast and slow informed trading. Journal of Financial Markets 43: 1–30. [Google Scholar] [CrossRef]
- Yan, Yuxing, and Shaojun Zhang. 2012. An improved estimation method and empirical properties of the probability of informed trading. Journal of Banking & Finance 36: 454–67. [Google Scholar]
- Yan, Yuxing, and Shaojun Zhang. 2014. Quality of PIN estimates and the PIN-return relationship. Journal of Banking & Finance 43: 137–49. [Google Scholar]
- Yang, Yung Chiang, Bohui Zhang, and Chu Zhang. 2020. Is information risk priced? Evidence from abnormal idiosyncratic volatility. Journal of Financial Economics 135: 528–54. [Google Scholar] [CrossRef]
[Bad News] | No-Info Cluster | [Good News] | |
---|---|---|---|
Buys [B] | |||
Sells [S] | |||
Order Imbalance [OI] |
[Bad News] | No-Information Cluster | [Good News] | |
---|---|---|---|
Real\Estimate | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | >8 |
---|---|---|---|---|---|---|---|---|---|
Panel A: No correction | |||||||||
1 | 85.86 | 13.97 | 0.17 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 0.07 | 88.79 | 10.96 | 0.18 | 0 | 0 | 0 | 0 | 0 |
3 | 0 | 0.55 | 92.97 | 6.35 | 0.13 | 0 | 0 | 0 | 0 |
4 | 0 | 0 | 1.69 | 92.73 | 5.43 | 0.14 | 0.01 | 0 | 0 |
5 | 0 | 0 | 0 | 3.2 | 92.5 | 4.23 | 0.07 | 0 | 0 |
6 | 0 | 0 | 0 | 0.01 | 4.19 | 91.86 | 3.88 | 0.06 | 0 |
7 | 0 | 0 | 0 | 0 | 0.04 | 5.62 | 91.11 | 3.2 | 0.03 |
8 | 0 | 0 | 0 | 0 | 0 | 0.08 | 6.95 | 89.92 | 3.05 |
Panel B: E2016 correction | |||||||||
1 | 98.9 | 1.1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 8.17 | 90.91 | 0.92 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 0.01 | 20.89 | 78.68 | 0.42 | 0 | 0 | 0 | 0 | 0 |
4 | 0 | 0.52 | 37.04 | 62.19 | 0.25 | 0 | 0 | 0 | 0 |
5 | 0 | 0.01 | 1.81 | 44.27 | 53.64 | 0.27 | 0 | 0 | 0 |
6 | 0 | 0 | 0.02 | 3.27 | 47.59 | 48.87 | 0.25 | 0 | 0 |
7 | 0 | 0 | 0 | 0.06 | 4.36 | 50.44 | 44.89 | 0.25 | 0 |
8 | 0 | 0 | 0 | 0 | 0.12 | 5.63 | 51.16 | 42.92 | 0.17 |
Panel C: EG correction | |||||||||
1 | 93.7 | 6.12 | 0.18 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 0.31 | 94.82 | 4.53 | 0.34 | 0 | 0 | 0 | 0 | 0 |
3 | 0 | 0.73 | 94.57 | 3.95 | 0.68 | 0.07 | 0 | 0 | 0 |
4 | 0 | 0 | 1.73 | 93.77 | 3.47 | 0.84 | 0.18 | 0.01 | 0 |
5 | 0 | 0 | 0.02 | 3.15 | 91.91 | 3.26 | 1.23 | 0.31 | 0.12 |
6 | 0 | 0 | 0 | 0.04 | 4.08 | 90.57 | 3.6 | 0.97 | 0.74 |
7 | 0 | 0 | 0 | 0 | 0.04 | 6.02 | 88.46 | 3.59 | 1.89 |
8 | 0 | 0 | 0 | 0 | 0 | 0.13 | 6.98 | 85.99 | 6.9 |
Real\Estimate | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | >8 |
---|---|---|---|---|---|---|---|---|---|
Panel A: No correction | |||||||||
1 | 31.5 | 60.93 | 7.42 | 0.15 | 0 | 0 | 0 | 0 | 0 |
2 | 1.06 | 32.82 | 51.64 | 13.84 | 0.63 | 0.01 | 0 | 0 | 0 |
3 | 0 | 2.17 | 34.18 | 46.88 | 15.75 | 1.02 | 0 | 0 | 0 |
4 | 0 | 0.02 | 2.67 | 31.63 | 41.39 | 20.93 | 3.21 | 0.15 | 0 |
5 | 0 | 0 | 0.1 | 2.99 | 28.97 | 35.27 | 25.02 | 6.92 | 0.73 |
6 | 0 | 0 | 0.01 | 0.08 | 3.58 | 26.49 | 30.53 | 25.51 | 13.8 |
7 | 0 | 0 | 0 | 0.02 | 0.15 | 3.65 | 24.49 | 25.03 | 46.66 |
8 | 0 | 0 | 0 | 0 | 0.01 | 0.19 | 4.33 | 24.43 | 71.04 |
Panel B: E2016 correction | |||||||||
1 | 98.81 | 1.19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 7.25 | 91.71 | 1.04 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 0.01 | 20.41 | 79.11 | 0.46 | 0.01 | 0 | 0 | 0 | 0 |
4 | 0 | 0.73 | 36.63 | 62.13 | 0.51 | 0 | 0 | 0 | 0 |
5 | 0 | 0 | 2.06 | 44.1 | 53.53 | 0.31 | 0 | 0 | 0 |
6 | 0 | 0 | 0.04 | 3.26 | 46.53 | 49.95 | 0.22 | 0 | 0 |
7 | 0 | 0 | 0 | 0.12 | 4.71 | 50.16 | 44.77 | 0.23 | 0.01 |
8 | 0 | 0 | 0 | 0 | 0.14 | 5.83 | 52.35 | 41.54 | 0.14 |
Panel C: EG correction | |||||||||
1 | 93.9 | 5.94 | 0.16 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 0.22 | 94.63 | 4.73 | 0.4 | 0.02 | 0 | 0 | 0 | 0 |
3 | 0 | 0.87 | 94.64 | 3.77 | 0.63 | 0.09 | 0 | 0 | 0 |
4 | 0 | 0 | 1.66 | 93.12 | 3.93 | 0.95 | 0.31 | 0.03 | 0 |
5 | 0 | 0 | 0.01 | 2.79 | 92.53 | 3.17 | 0.92 | 0.48 | 0.1 |
6 | 0 | 0 | 0 | 0.03 | 3.88 | 91.03 | 3.44 | 1.06 | 0.56 |
7 | 0 | 0 | 0 | 0 | 0.08 | 5.21 | 89.39 | 3.62 | 1.7 |
8 | 0 | 0 | 0 | 0 | 0 | 0.13 | 6.94 | 86.25 | 6.68 |
Layers\Missed Days | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 5.15 | 0.12 | 0.19 | 0.37 | 0.81 | 89.6 | 3.18 | 0.42 | 0.1 | 0.03 | 0.03 |
2 | 3.27 | 0.08 | 0.18 | 0.16 | 0.75 | 91.49 | 3.23 | 0.5 | 0.19 | 0.06 | 0.09 |
3 | 2.05 | 0.09 | 0.1 | 0.19 | 0.49 | 92.53 | 3.55 | 0.62 | 0.26 | 0.07 | 0.05 |
4 | 1.67 | 0.1 | 0.16 | 0.12 | 0.26 | 92.5 | 3.78 | 0.84 | 0.32 | 0.05 | 0.2 |
5 | 1.32 | 0.05 | 0.07 | 0.06 | 0.54 | 92.94 | 3.71 | 0.77 | 0.32 | 0.12 | 0.1 |
6 | 1.03 | 0.08 | 0.05 | 0.06 | 0.34 | 93.6 | 3.27 | 0.91 | 0.4 | 0.1 | 0.16 |
7 | 0.57 | 0.07 | 0.07 | 0.08 | 0.32 | 94.06 | 3.48 | 0.83 | 0.29 | 0.09 | 0.14 |
8 | 0.7 | 0.03 | 0.08 | 0.06 | 0.52 | 93.55 | 3.36 | 0.91 | 0.42 | 0.2 | 0.17 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Ersan, O.; Ghachem, M. Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm. J. Risk Financial Manag. 2024, 17, 409. https://doi.org/10.3390/jrfm17090409
Ersan O, Ghachem M. Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm. Journal of Risk and Financial Management. 2024; 17(9):409. https://doi.org/10.3390/jrfm17090409
Chicago/Turabian StyleErsan, Oguz, and Montasser Ghachem. 2024. "Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm" Journal of Risk and Financial Management 17, no. 9: 409. https://doi.org/10.3390/jrfm17090409
APA StyleErsan, O., & Ghachem, M. (2024). Identifying Information Types in the Estimation of Informed Trading: An Improved Algorithm. Journal of Risk and Financial Management, 17(9), 409. https://doi.org/10.3390/jrfm17090409