# How News May Affect Markets’ Complex Structure: The Case of Cambridge Analytica

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Correlations

#### 2.1.1. Correlation Network

#### 2.1.2. Correlation Threshold Sensitivity

#### 2.2. Mutual Information

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Data

#### 4.2. Methods

#### 4.2.1. Correlations

#### 4.2.2. Correlation Network

#### 4.2.3. Mutual Information

## Author Contributions

## Funding

**A**nalysis and

**M**odeling

**OF**social med

**I**a). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessary reflect the views of the funding parties.

## Conflicts of Interest

## Abbreviations

FB: | |

CA: | Cambridge Analytica |

MI: | Mutual Information |

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**Figure 1.**Bloomberg intraday time series for the Facebook (FB) stock. (

**a**) Time series for the price. (

**b**) Time series for the log-returns. The Cambridge Analytica (CA) event happens at time 313 (the first observation on March 19th, 2018 in the price chart); notice that after the CA event, the price of the stock decreases and its volatility increases.

**Figure 2.**Distribution of cross-correlation among the time series of the NASDAQ-100 components.

**Left panel:**Cross-correlation of the time series before the CA event.

**Right panel:**Cross-correlation of the time series after the CA event. Cross-correlations have been computed on two samples of 15-minute intraday stock returns consisting of 311 observations each. Notice that the average correlation of the stock market experiences a $\sim 50\%$ increase.

**Figure 3.**Average cross-correlation among the time series of the NASDAQ-100 components calculated with a moving window of 150 intraday observations. The dashed vertical red lines indicate a window centered around the CA event. Notice the sharp rise of correlations experienced by the stock market around the CA event.

**Figure 4.**Graph displaying the NASDAQ-100 components grouped by industry. The list of industries is reported here below:

- • Technology • Consumer Services • Health Care • C. Non-Durables
- • Miscellaneous • Capital Goods • Transportation • Public Utilities

- • Technology • Consumer Services • Health Care • C. Non-Durables
- • Miscellaneous • Capital Goods • Transportation • Public Utilities

**Figure 5.**Correlation graphs with threshold, $c=0.55$.

**Left panel:**Correlation graph before the CA event.

**Right panel:**Correlation graph after the CA event. Nodes are ordered anticlockwise by industry (color) and node’s degree (size). Edge thickness varies according to absolute correlation. However, edge-thickness scales differ in the two panels to improve readability. Notice the increase in the number of edges, i.e., an increase in correlation, after CA.

**Figure 6.**Edge density (

**a**) and clustering coefficient (

**b**) calculated with a moving window of 150 intraday observations. The dashed vertical red lines indicate respectively when CA enters and is fully within the moving window. Notice the sharp rise in both edge density and clustering coefficient.

**Figure 7.**The sensitivity of the number of nodes belonging to the Giant Component before (

**red**squares) and after (

**blue**dots) CA. Notice that the size of the Giant Component grows after CA for all the meaningful correlation thresholds.

**Figure 8.**Distribution of the Mutual Information among the time series of the NASDAQ-100 stock market index.

**Left panel:**Mutual Information among the time series before the CA event.

**Right panel:**Mutual Information among the time series after the CA event. Mutual Information for each pair of stocks has been computed on two samples of 15-minute intraday stock returns consisting in 311 observations each. Notice that the average Mutual Information among the assets of the stock market experiences a $\sim 10\%$ increase.

**Figure 9.**Scatter plot coupling Correlation and MI for every pair of stocks before (

**red**pluses) and after (

**blue**crosses) the events of CA. Notice that the all the points seem to follow a master curve.

**Table 1.**The table reports a ranking of the 10 highest-volatility stocks in the NASDAQ-100 before and after Cambridge Analytica (CA). Volatility has been computed on two samples of 15-minute intraday returns consisting of 311 observations each.

Top-10 Highest Volatility Stocks | ||||||
---|---|---|---|---|---|---|

Before CA | After CA | |||||

Stock | Industry | SD(x) | Stock | Industry | SD(x) | |

DLTR | Consumer Services | 0.01031 | SHPG | Health Care | 0.01013 | |

ESRX | Health Care | 0.00757 | TSLA | Capital Goods | 0.00857 | |

JD | Consumer Services | 0.00732 | MU | Technology | 0.00721 | |

ADSK | Technology | 0.00724 | NFLX | Consumer Services | 0.00704 | |

MU | Technology | 0.00703 | NVDA | Technology | 0.00684 | |

ALXN | Health Care | 0.00671 | FB | Technology | 0.00668 | |

ROST | Consumer Services | 0.00576 | AMZN | Consumer Services | 0.00640 | |

WYNN | Consumer Services | 0.00533 | LRCX | Technology | 0.00623 | |

ULTA | Consumer Services | 0.00496 | AMAT | Technology | 0.00564 | |

LRCX | Technology | 0.00477 | INTC | Technology | 0.00563 |

© 2018 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/).

## Share and Cite

**MDPI and ACS Style**

Peruzzi, A.; Zollo, F.; Quattrociocchi, W.; Scala, A.
How News May Affect Markets’ Complex Structure: The Case of Cambridge Analytica. *Entropy* **2018**, *20*, 765.
https://doi.org/10.3390/e20100765

**AMA Style**

Peruzzi A, Zollo F, Quattrociocchi W, Scala A.
How News May Affect Markets’ Complex Structure: The Case of Cambridge Analytica. *Entropy*. 2018; 20(10):765.
https://doi.org/10.3390/e20100765

**Chicago/Turabian Style**

Peruzzi, Antonio, Fabiana Zollo, Walter Quattrociocchi, and Antonio Scala.
2018. "How News May Affect Markets’ Complex Structure: The Case of Cambridge Analytica" *Entropy* 20, no. 10: 765.
https://doi.org/10.3390/e20100765