# The Flow of Information in Trading: An Entropy Approach to Market Regimes

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Entropy, Information Flows and Trading

#### 2.1.1. Entropy Measures

#### 2.1.2. Entropy as a Causality Measure

**Theorem**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

#### 2.1.3. Information Flow Measures

- -
- market returns → market returns (${I}_{R\to R}$)$${I}_{R\to R}=\frac{{\Delta}_{R}}{{H}_{R}}=1-\frac{{h}_{R}}{{H}_{R}}$$
- -
- news sentiment → market returns (${I}_{S\to R}$)$${I}_{S\to R}=\frac{{T}_{S\to R}}{{h}_{R}}$$

#### 2.2. Trading Activities Identification

- -
- Return-driven trading: Investors are used to follow the market price patterns when making their trading decisions, which is called technical analysis. Such behavior can be identified through self-information flows of market returns. In other words, the memory of market return flow ${I}_{R\to R}$ is the evidence of return-driven trading according to our model.
- -
- News-driven trading: This often reflects digitization of textual information that allows investors to effectively form beliefs through news and incorporate them into their trading decisions. Such trading strategies pass news sentiment to the market; hence, ${I}_{S\to R}$ indicates occurrence of news-driven trading.

#### 2.3. Market Information Regime

- (1)
- The return-driven regime: The market is purely driven by chasing of return patterns. We often obtain stronger return memory in this regime.
- (2)
- The news-driven regime: The market prices moves entirely from responses to news and no self-causality in returns are detected.
- (3)
- The mixed regime: Both return-driven and news-driven trading were identified and they co-exist.
- (4)
- Other types: Neither return-driven nor news-driven trading were detected. The market either react to news and market data too slow to produce significant information flows, or have too few traders using these types of information to form market-level price impacts.

#### 2.4. Parameter Settings and Some Calibration Issues

## 3. Data

#### 3.1. Financial Market Data

#### 3.2. News Sentiment Data

- -
- $datetime$: The date and time of a news article.
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- $ric$: Reuters Instrument Code (RIC) of a stock for which the sentiment scores apply.
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- $pos$, $obj$, $neg$: Positive, neutral, and negative sentiment probabilities (i.e., $pos+obj+neg=1$).
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- $relevance$: A real-valued number between 0 and 1 indicating the relevance of a piece of news to a stock. One news article may refer to multiple stocks. A stock with more mentions will be assigned a higher relevance.

#### 3.3. Stationarity Test

## 4. Results

- -
- There are two periods within which the market regime is driven by a single type of trading activity: (1) from the Q3 of 2008 to the Q4 of 2010, the single source of market-wide trading is news sentiment (blue bars only); while (2) from the Q4 of 2011 to the Q3 of 2012, the return memory clustering indicates return-driven activities that drive the market movements (green bars only). Before and after the news-driven regime (period 1 here), we spot a swift switch from returns to sentiment. However, for the return-driven regime (period 2 here), instead, it is more of the fact that news influence disappears from a mixed-regime. These signs are important because they could be highly indicative. They show that news sentiment always requires longer time to form compared to the belief towards some fast updating changes in the market (e.g., reflected in returns).
- -
- During the rest of the time, price movements are caused by mixed types of trading. In addition, the mixed regime demonstrates strong features associated with the market crisis timeline. In the pre-crisis period (before 2008), although there exists trading of both returns and news, often return-driven trading overpowers the news-driven (apart from one exceptional spike of news event around October 2010); while in the post-crisis period (after 2013), the dominance more often resides in the power of news-driven trading, moreover, at a much higher level than the return-driven. This finding is of great interest to us because it provides strong evidence of the change in the market regimes’ dynamics before and after the double crisis period. Furthermore, the imbalance between their dominants within the mixed regime has changed dramatically and more frequently in the post-crises years. We see a few flash spikes in news-driven trading, while there was only one spike showing clear imbalance around October 2004 during the pre-crisis period. All these suggest that the complexity of the market may have increased after the crises with the growth of modern technology and big data [42].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Theorem**

**A1.**

**Proof.**

**Theorem**

**A2.**

**Proof.**

**Theorem**

**A3.**

**Proof.**

## Appendix B

Coefficient | T-Stat | P-Value | |
---|---|---|---|

Const. | $0.0000$ | $0.235$ | $0.814$ |

Lag-1 return | $0.0018$ | $0.352$ | $0.725$ |

Lag-1 sentiment | $0.0003$ | $1.086$ | $0.278$ |

Lag-2 return | $\mathbf{0.0129}$ | $\mathbf{2.546}$ | $\mathbf{0.011}$ |

Lag-2 sentiment | $-0.0001$ | $-0.227$ | $0.821$ |

Lag-3 return | $0.0079$ | $1.574$ | $0.116$ |

Lag-3 sentiment | $-0.0002$ | $-0.900$ | $0.368$ |

Lag-4 return | $0.0014$ | $0.278$ | $0.781$ |

Lag-4 sentiment | $\mathbf{0.0006}$ | $\mathbf{2.320}$ | $\mathbf{0.020}$ |

Lag-5 return | $-0.0025$ | $-0.489$ | $0.625$ |

Lag-5 sentiment | $-0.0003$ | $-1.057$ | $0.290$ |

Lag-6 return | $-\mathbf{0.0208}$ | $-\mathbf{4.121}$ | $\mathbf{0.000}$ |

Lag-6 sentiment | $0.0001$ | $0.290$ | $0.771$ |

Lag-1 | Lag-2 | Lag-3 | Lag-4 | Lag-5 | Lag-6 | |
---|---|---|---|---|---|---|

Sentiment → Return | $0.2235$ | $0.4793$ | $0.6106$ | $0.1492$ | $0.1654$ | $0.2340$ |

Return → Sentiment | $0.2906$ | $0.4838$ | $0.0861$ | $0.1299$ | $0.0028$ | $0.0047$ |

## Appendix C

$\mathit{\mu}$ | d | ${\mathit{D}}_{\mathbf{KL}}(\mathit{P}\Vert \mathit{Q})$ | |
---|---|---|---|

Return | $0.0$ | $0.000631$ | $0.00046$ |

Sentiment | $0.05$ | $0.029146$ | $0.0025$ |

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**Figure 2.**Conditional entropy ${h}_{X}\left(k\right)$ vs. reduced uncertainty ${\Delta}_{X}\left(k\right)$. Note: These results are calibrated through a simulation sample of $\mathrm{1,000,000}$ observations.

**Figure 3.**Small sample bias of ${h}_{I}\left(k\right)$. Note: This is an interpretation of systematically undervaluing conditional entropy due to small sample size. This calibration issue exists in transfer entropy as well. These values are calibrated through a simulation sample of $\mathrm{1,000,000}$ and 3000 observations.

t-Statistic | p-Value | |
---|---|---|

Price level | $-0.631$ | $0.864$ |

Log-return | $-27.092$ | $0.000$ |

News sentiment | $-10.901$ | $0.000$ |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Liu, A.; Chen, J.; Yang, S.Y.; Hawkes, A.G.
The Flow of Information in Trading: An Entropy Approach to Market Regimes. *Entropy* **2020**, *22*, 1064.
https://doi.org/10.3390/e22091064

**AMA Style**

Liu A, Chen J, Yang SY, Hawkes AG.
The Flow of Information in Trading: An Entropy Approach to Market Regimes. *Entropy*. 2020; 22(9):1064.
https://doi.org/10.3390/e22091064

**Chicago/Turabian Style**

Liu, Anqi, Jing Chen, Steve Y. Yang, and Alan G. Hawkes.
2020. "The Flow of Information in Trading: An Entropy Approach to Market Regimes" *Entropy* 22, no. 9: 1064.
https://doi.org/10.3390/e22091064