# Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Experimental Results

**Figure 1.**Minimally-spanning tree for the Shanghai Stock Exchange based on partial mutual information between studied stocks. Stocks with the highest node degrees have been named with their ticker symbols. The size of the nodes is proportional to their node degree.

**Figure 2.**Planar maximally-filtered graph for the Shanghai Stock Exchange based on partial mutual information between studied stocks. Stocks with the highest node degrees have been named with their ticker symbols. The size of the nodes is proportional to their node degree.

**Figure 3.**Pearson’s correlation coefficients between distances associated with the three used dependency measures (δ based on Pearson’s correlation (Corr), d based on mutual information (MI) and D based on partial mutual information (PMI)) for all pairs of stocks within the studied set. It is clear that using partial mutual information changes the analysis very slightly with regards to mutual information, but both give significantly different results from the analysis using Pearson’s correlation coefficients.

**Table 1.**Percentage of links between instruments belonging to the same economic sector in all links within the studied networks. As a reference, the same is shown for an unrestricted network or a full graph. Both mutual information (d) and partial mutual information (D) reproduce the sector structure from price changes slightly more accurately than Pearson’s correlation coefficient (δ), which is in agreement with similar studies of other markets. MST, minimally-spanning tree; PMFG, maximally-filtered graph.

Distance | MST | PMFG |
---|---|---|

δ | 64.97% | 53.85% |

d | 66.24% | 56.84% |

D | 66.88% | 58.12% |

None | 13.96% | 13.96% |

**Figure 4.**Degree distributions (with fitted power law and log-normal distribution) for: (

**a**) a minimally-spanning tree based on correlation; (

**b**) a planar maximally-filtered graph based on correlation; (

**c**) MST based on mutual information; (

**d**) PMFG based on MI; (

**e**) MST based on partial mutual information; and (

**f**) PMFG based on PMI.

**Table 2.**The sum of node degrees for stocks belonging to the studied economic sectors in MST (1) and PMFG (3) based on partial mutual information, the average node degree for stocks belonging to the studied sectors in MST (2) and PMFG (4) based on partial mutual information and the average earnings per share (EPS) ratio for stocks belonging to the studied sectors (5). There is a negative correlation between the EPS ratio in a sector and the sector’s average importance in the network.

Sector | (1) | (2) | (3) | (4) | (5) |
---|---|---|---|---|---|

Communications | 7 | 2.33 | 22 | 7.33 | 0.29 |

Consumer Discretionary | 46 | 1.92 | 136 | 5.67 | 0.58 |

Consumer Staples | 14 | 1.56 | 37 | 4.11 | 2.17 |

Energy | 37 | 2.06 | 117 | 6.50 | 0.49 |

Financials | 80 | 2.11 | 228 | 6.00 | 0.92 |

Healthcare | 17 | 2.13 | 47 | 5.88 | 0.54 |

Industrials | 38 | 2.00 | 113 | 5.95 | 0.15 |

Materials | 55 | 2.12 | 171 | 6.58 | 0.33 |

Technology | 10 | 1.43 | 39 | 5.57 | 0.53 |

Utilities | 10 | 1.67 | 26 | 4.33 | 0.46 |

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

You, T.; Fiedor, P.; Hołda, A. Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information. *J. Risk Financial Manag.* **2015**, *8*, 266-284.
https://doi.org/10.3390/jrfm8020266

**AMA Style**

You T, Fiedor P, Hołda A. Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information. *Journal of Risk and Financial Management*. 2015; 8(2):266-284.
https://doi.org/10.3390/jrfm8020266

**Chicago/Turabian Style**

You, Tao, Paweł Fiedor, and Artur Hołda. 2015. "Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information" *Journal of Risk and Financial Management* 8, no. 2: 266-284.
https://doi.org/10.3390/jrfm8020266