# Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information?

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## Abstract

**:**

## 1. Introduction

## 2. Exponentially Distributed Cross-Sectional Analyst Coverage

#### 2.1. Evidence from the Shanghai, Shenzhen, and Hong Kong Stock Markets

#### 2.2. Difference in Exponential Fitting between SSE, SZSE, and HK

#### 2.3. Predicting Stock-Market Uncertainty

#### 2.3.1. Distribution Changes during the Period 2011–2020

#### 2.3.2. Predictive Regression Results

## 3. MEP Generates the Exponential Distribution

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Yearly Results for the Shanghai Stock Market (SSE)

**Figure A1.**Exponential fits of complementary cumulative distribution functions (CCDFs) of cross-sectional analyst coverage (x) on the linear (blue) and semi-log (red) scales for each year from 2011 to 2020 in the Shanghai stock market (SSE).

## References

- Kelly, B.; Ljungqvist, A. Testing asymmetric-information asset pricing models. Rev. Financ. Stud.
**2012**, 25, 1366–1413. [Google Scholar] [CrossRef] - Lee, C.; So, E. Uncovering expected returns: Information in analyst coverage proxies. Rev. Financ. Stud.
**2017**, 124, 331–348. [Google Scholar] [CrossRef] - Guo, L.; Li, F.; Wei, K. Security analysts and capital market anomalies. J. Financ. Econ.
**2020**, 137, 204–230. [Google Scholar] [CrossRef] - Yu, F. Analyst coverage and earnings management. J. Financ. Econ.
**2008**, 88, 245–271. [Google Scholar] [CrossRef] - Derrien, F.; Kecskes, A. The real effects of financial shocks: Evidence from exogenous changes in analyst coverage. J. Financ.
**2013**, 68, 1407–1440. [Google Scholar] [CrossRef] - He, J.; Tian, X. The dark side of analyst coverage: The case of innovation. J. Financ. Econ.
**2013**, 109, 856–878. [Google Scholar] [CrossRef] - Chen, T.; Harford, J.; Lin, C. Do analysts matter for governance? Evidence from natural experiments. J. Financ. Econ.
**2006**, 115, 383–410. [Google Scholar] [CrossRef] - Chan, K.; Hameed, A. Stock price synchronicity and analyst coverage in emerging markets. J. Financ. Econ.
**2006**, 80, 115–147. [Google Scholar] [CrossRef] - Gao, K.; Lin, W.; Yang, L.; Chan, K. The impact of analyst coverage and stock price synchronicity: Evidence from brokerage mergers and closures. Financ. Res. Lett.
**2020**, 33, 101190. [Google Scholar] [CrossRef] - Scharfenaker, E.; dos Santos, P. The distribution and regulation of Tobin’s q. Econ. Lett.
**2015**, 137, 191–194. [Google Scholar] [CrossRef] - Newey, W.; West, K. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica
**1987**, 55, 703–708. [Google Scholar] [CrossRef] - Frankel, A.; Kamenica, E. Quantifying information and uncertainty. Am. Econ. Rev.
**2019**, 109, 3650–3680. [Google Scholar] [CrossRef] - Shannon, C. A mathematical theory of communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Minton, B.; Schrand, C. The impact of cash flow volatility on discretionary investment and the costs of debt and equity financing. J. Financ. Econ.
**1999**, 54, 423–460. [Google Scholar] [CrossRef] - Bloom, N. The impact of uncertainty shocks. Econometrica
**2009**, 77, 623–685. [Google Scholar] - Da, Z.; Engelberg, J.; Gao, P. In search of attention. J. Financ.
**2011**, 66, 1461–1499. [Google Scholar] [CrossRef] - Benamar, H.; Foucault, T.; Vega, C. Demand for information, uncertainty, and the response of US Treasury securities to news. Rev. Financ. Stud.
**2021**, 34, 3403–3455. [Google Scholar] [CrossRef] - Neilson, J. Investor information gathering and the resolution of uncertainty. J. Account. Econ.
**2022**, 74, 101513. [Google Scholar] [CrossRef] - White, H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica
**1980**, 48, 817–838. [Google Scholar] [CrossRef] - Loh, R.; Stulz, R. Is sell-side research more valuable in bad times? J. Financ.
**2018**, 73, 959–1013. [Google Scholar] [CrossRef] - Hou, Y.; Hu, C. Understanding the role of aggregate analyst attention in resolving stock market uncertainty. Financ. Res. Lett.
**2023**, 57, 104183. [Google Scholar] [CrossRef] - Jaynes, E. Information theory and statistical mechanics. Phys. Rev.
**1957**, 106, 620. [Google Scholar] [CrossRef] - Foley, D. A statistical equilibrium theory of markets. J. Econ. Theory
**1994**, 62, 321–345. [Google Scholar] [CrossRef] - Sims, C. Implications of rational inattention. J. Monet. Econ.
**2003**, 50, 665–690. [Google Scholar] [CrossRef]

**Figure 1.**Exponential fits of complementary cumulative distribution functions (CCDFs) of cross-sectional analyst coverage (x) on the linear (blue) and semi-log (red) scales for each month from 2011 to 2020 in the Shanghai stock market (SSE).

**Figure 2.**Exponential fits of complementary cumulative distribution functions (CCDFs) of cross-sectional analyst coverage (x) on the linear (blue) and semi-log (red) scales for each month from 2011 to 2020 in the Hong Kong stock market (HK).

**Figure 3.**Exponential fits of complementary cumulative distribution functions (CCDFs) of cross-sectional analyst coverage (x) on the linear (blue) and semi-log (red) scales for each month from 2011 to 2020 in the Shenzhen stock market (SZSE).

**Figure 4.**Exponential fits of complementary cumulative distribution functions (CCDFs) of cross-sectional analyst coverage (x) on the linear (blue) and log-linear (red) scales during the period 2011–2020 in the SSE (

**a.1**,

**a.2**), SZSE (

**b.1**,

**b.2**), and HK (

**c.1**,

**c.2**) stock markets.

**Figure 5.**Exponential fits of CCDFs in two scaling regimes (denoted as ${\lambda}_{1}$ and ${\lambda}_{2}$) for cross-sectional analyst coverage (x) of the SSE (

**a**), SZSE (

**b**), and HK (

**c**) stock markets during the period 2011–2020.

**Figure 6.**Fitted values of parameter $\lambda $ (

**a**) and sample mean $\mu $ (

**b**) for cross-sectional analyst coverage of the Shanghai stock market (SSE) for each year from 2011 to 2020.

Mean | S.D. | Min | Max | Med. | Skew. | Kurt. | No. | |
---|---|---|---|---|---|---|---|---|

${x}_{\mathrm{SSE}}$ | 5.44 | 6.24 | 1 | 49 | 3 | 1.95 | 6.93 | 108,282 |

${x}_{\mathrm{SZSE}}$ | 5.19 | 5.64 | 1 | 49 | 3 | 1.98 | 7.34 | 165,678 |

${x}_{\mathrm{HK}}$ | 4.30 | 4.99 | 1 | 47 | 2 | 2.09 | 8.62 | 88,794 |

$\lambda $ | ${\lambda}_{1}$ | ${\lambda}_{2}$ | $\overline{\lambda}$ | ($\lambda -{\lambda}_{1}$) | ($\lambda -{\lambda}_{2}$) | (${\lambda}_{1}-{\lambda}_{2}$) | ($\lambda -\overline{\lambda}$) | |||

Panel A. Monthly exponential fitting for SSE and SZSE | ||||||||||

${x}_{\mathrm{SSE}}$ | $0.1876$ | $0.1484$ | $0.2530$ | $0.2007$ | $0.04$ *** | $-0.07$ *** | $-0.10$ *** | $-0.01$ *** | ||

NW t | $\left[8.75\right]$ | $[-6.56]$ | $[-7.54]$ | $[-3.84]$ | ||||||

${x}_{\mathrm{SZSE}}$ | $0.2061$ | $0.1680$ | $0.2712$ | $0.2196$ | $0.04$ *** | $-0.07$ *** | $-0.10$ *** | $-0.01$ *** | ||

NW t | $\left[11.6\right]$ | $[-7.55]$ | $[-8.83]$ | $[-4.46]$ | ||||||

Panel B. Monthly exponential fitting for HK | ||||||||||

${x}_{\mathrm{HK}}$ | $0.2549$ | $0.2041$ | $0.3149$ | $0.2595$ | $0.05$ | $-0.06$ | $-0.11$ | $-0.00$ | ||

NW t | $\left[1.58\right]$ | $[-1.33]$ | $[-1.44]$ | $[-0.69]$ |

Panel A. Predicting future manager uncertainty proxied by cash-flow volatility ${\mathrm{CFV}}_{t,t+h}$ | ||||||

(1) | (2) | (3) | (4) | (5) | (6) | |

${\mathrm{CFV}}_{t,t+1}$ | ${\mathrm{CFV}}_{t,t+1}$ | ${\mathrm{CFV}}_{t,t+6}$ | ${\mathrm{CFV}}_{t,t+6}$ | ${\mathrm{CFV}}_{t,t+12}$ | ${\mathrm{CFV}}_{t,t+12}$ | |

${\lambda}_{t}^{-1}$ | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-1.38$ *** | $\phantom{\rule{1.em}{0ex}}-0.16$ ** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-1.42$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.52$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-1.42$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.61$ *** |

$[-8.29]$ | $[-2.27]$ | $[-8.68]$ | $[-3.57]$ | $[-9.47]$ | $[-5.25]$ | |

Trend | No | Yes | No | Yes | No | Yes |

Lagged CFV | No | Yes | No | Yes | No | Yes |

N | 108 | 108 | 102 | 102 | 96 | 96 |

${\mathrm{adj}.\mathrm{R}}^{2}$ | 0.31 | 0.86 | 0.42 | 0.82 | 0.50 | 0.86 |

ADF.prob | 1 × ${10}^{-3}$ | 1 × ${10}^{-3}$ | 5 × ${10}^{-3}$ | 1 × ${10}^{-3}$ | 2 × ${10}^{-3}$ | 5 × ${10}^{-3}$ |

Panel B. Predicting future investor uncertainty proxied by information demand ${\mathrm{Search}}_{t,t+h}$ | ||||||

${\mathrm{Search}}_{t,t+1}$ | ${\mathrm{Search}}_{t,t+1}$ | ${\mathrm{Search}}_{t,t+6}$ | ${\mathrm{Search}}_{t,t+6}$ | ${\mathrm{Search}}_{t,t+12}$ | ${\mathrm{Search}}_{t,t+12}$ | |

${\lambda}_{t}^{-1}$ | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.40$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.34$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.39$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.20$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.34$ *** | $\phantom{\rule{1.em}{0ex}}\phantom{\rule{4pt}{0ex}}-0.26$ *** |

$[-4.65]$ | $[-4.04]$ | $[-9.22]$ | $[-7.16]$ | $[-8.87]$ | $[-6.22]$ | |

Trend | No | Yes | No | Yes | No | Yes |

Lagged Search | No | Yes | No | Yes | No | Yes |

N | 108 | 108 | 102 | 102 | 96 | 96 |

${\mathrm{adj}.\mathrm{R}}^{2}$ | 0.22 | 0.58 | 0.40 | 0.65 | 0.42 | 0.71 |

ADF.prob | 1 × ${10}^{-3}$ | 1 × ${10}^{-3}$ | 1 × ${10}^{-2}$ | 5 × ${10}^{-3}$ | 1 × ${10}^{-2}$ | 1 × ${10}^{-2}$ |

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**MDPI and ACS Style**

Hou, Y.; Hu, C.
Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information? *Entropy* **2024**, *26*, 285.
https://doi.org/10.3390/e26040285

**AMA Style**

Hou Y, Hu C.
Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information? *Entropy*. 2024; 26(4):285.
https://doi.org/10.3390/e26040285

**Chicago/Turabian Style**

Hou, Yunfei, and Changsheng Hu.
2024. "Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information?" *Entropy* 26, no. 4: 285.
https://doi.org/10.3390/e26040285