# Multiple Blockholders and Firm Value: A Simulation Analysis

## Abstract

**:**

## 1. Introduction

## 2. The Model

## 3. Simulations and Results

#### 3.1. ${D}^{*}\left(S{H}_{1}\right)$ at Different Values of B Fixing R

#### 3.2. ${D}^{*}\left(S{H}_{1}\right)$ at Different Values of R Fixing B

## 4. Conclusions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | Linear dichroism |

## Notes

1 | We focus on the pecuniary private benefits of control defined by Gilson (2006) as “the non-proportional flow of real resources from the company to the controlling shareholder”. Such benefits broadly include theft, tunnelling, consumption of perks, empire building and in general any use of corporate resources that is not in the best interests of all shareholders. |

2 | The basic structure of the model is inspired by Russino et al. (2019). |

3 | We can think at the two blocks in terms of a block of insiders, that is a block of shareholders that can directly affect the firm’s operations (shareholders being directors, officers or having representatives on the board simultaneously), and a block of outsiders or blockholders that do not have any inside role but can nevertheless affect firm governance gathering information and exerting their voice. |

4 | In this paper, we do not investigate how the blocks of shares arise or the process of coalition formation. We assume that there is a controlling block and a non-controlling block and we try to understand how the distribution of ownership between these two blocks affects the ownership–firm value relationship. For the sake of simplicity, from now on we consider the two blocks as individual blockholders. |

5 | The restriction on the value of the parameter representing the amount of private benefits of control per unit of company resources diverted is needed to model the more interesting case of inefficient controlling shareholder structures. Assuming $B<1$ ensures that the extraction of private benefits of control generates a reduction in the company value and implies expropriation of non-controlling shareholders. |

6 | Note that $(B-S{H}_{1})$ measures the per unit gain from diversion of company resources realized by the controlling blockholder. Clearly, when the per unit gain is zero there will be no diversion. |

7 | Note that the additive functional form used for $D(e,m)$ implies that the cross derivative is equal to zero. |

8 | The Matlab code used for the simulations is available upon request. |

9 | That advantage can be related to the fact that the largest shareholder may have an insider position and therefore have a greater ability in gathering information, understanding and influencing the firm’s operations and strategic choices. |

10 | Given two generic twice-differentiable functions f and g on $(L,H)$, the curvature of the two functions is measured by the ratio of the second derivative to the absolute value of the first derivative. The ratios ${f}^{\u2033}/\left|{f}^{\prime}\right|$ and ${g}^{\u2033}/\left|{g}^{\prime}\right|$ provide a measure of the curvature of the functions, therefore they can be used to determine the relative curvature ordering of the functions: f is more convex than g on $(L,H)$, if ${f}^{\u2033}/|{f}^{\prime}|\ge {g}^{\u2033}/\left|{g}^{\prime}\right|$ uniformly on $(L,H)$, or if f is a convex transformation of g. |

11 | As underlined by Nagar et al. (2011), three features characterize closely held corporation: a small number of shareholders; no market for corporate control; involvement of the largest shareholder in the management of the company. |

12 | For instance, Maury and Pajuste (2005), Laeven and Levine (2008), and Attig et al. (2009) are examples of analyses based on samples of listed firms, while Gutiérrez et al. (2012) and Russino et al. (2019) mainly use samples of unlisted firms. |

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**Figure 1.**${D}^{*}\left(S{H}_{1}\right)$ at two levels of R ($a<b$ and $c=d$). In the two panels, the highest graph corresponds to the case where $B=0.95$, and the lowest to the case where $B=0.6$. The intermediate plots follow the order of the legend.

**Figure 2.**${D}^{*}\left(S{H}_{1}\right)$ at two levels of R ($a<b$ and $c>d$). In the two panels, the highest graph corresponds to the case where $B=0.95$ and the lowest to the case where $B=0.6$. The intermediate plots follow the order of the legend.

**Figure 3.**${D}^{*}\left(S{H}_{1}\right)$ at $B=0.6$ ($a<b$ and $c=d$). In the two panels, the highest graph corresponds to the case where $R=0.30$ and the lowest to the case where $R=0$. The intermediate plots follow the order of the legend.

**Figure 4.**${D}^{*}\left(S{H}_{1}\right)$ at two levels of B ($a<b$ and $c>d$). In the two panels, the highest graph corresponds to the case where $R=0.30$, and the lowest to the case where $R=0$. The intermediate plots follow the order of the legend.

Variable | Description | Range of Values | Constraints |
---|---|---|---|

V | Firm value | $V\in [0,1]$ | |

D | Total amount of corporate resources diverted | $D\in [0,V)$ | ${D}^{*}<V$ |

$S{H}_{1}$ | Percentage ownership of the largest blockholder | $S{H}_{1}\in (0.10,(1-S{H}_{2}-R)]$ | $S{H}_{1}>10\%$ |

$S{H}_{2}$ | Percentage ownership of the second largest blockholder | $S{H}_{2}\in [0.10,(1-S{H}_{1}-R)]$ | $S{H}_{1}>S{H}_{2}\ge 10\%$ |

R | Residual diffused ownership | $R\in [0,(1-S{H}_{1}-S{H}_{2})]$ | |

B | Per unit private benefits of control | $B\in (0.10,1)$ | $B>S{H}_{1}$ |

e | Intensity of effort to extract private benefits of control | $e\in [0,1]$ | |

m | Intensity of monitoring | $m\in [0,1]$ |

First Case: $\mathit{a}<\mathit{b}$ and $\mathit{c}=\mathit{d}$ | |||
---|---|---|---|

$R=0$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

max ${D}^{*}$ | $0.1640$ | $0.1347$ | $0.0981$ |

$S{H}_{1}$ | $0.66$ | $0.51$ | $0.51$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | inverted U-shape | monotone decreasing | monotone decreasing |

max: interior point | max: lowest extreme point | max: lowest extreme point | |

$R=0.20$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

max ${D}^{*}$ | $0.2775$ | $0.2080$ | $0.1640$ |

$S{H}_{1}$ | $0.7$ | $0.62$ | $0.46$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | monotone increasing | inverted U-shape | inverted U-shape |

max: highest extreme point | max: interior point | max: interior point | |

$R=0.30$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

max ${D}^{*}$ | $0.3116$ | $0.2775$ | $0.2080$ |

$S{H}_{1}$ | $0.6$ | $0.6$ | $0.52$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | monotone increasing | monotone increasing | inverted U-shape |

max: highest extreme point | max: highest extreme point | max: interior point | |

Second Case: $\mathit{a}<\mathit{b}$ and $\mathit{c}>\mathit{d}$ | |||

$R=0$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

max ${D}^{*}$ | $0.2648$ | $0.2282$ | $0.20$ |

$S{H}_{1}$ | $0.74$ | $0.62$ | $0.51$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | inverted U-shape | inverted U-shape | monotone decreasing |

max: interior point | max: interior point | max: lowest extreme point | |

$R=0.20$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

${D}^{*}$ | $0.3771$ | $0.3204$ | $0.2648$ |

$S{H}_{1}$ | $0.7$ | $0.67$ | $0.54$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | monotone increasing | inverted U-shape | inverted U-shape |

max: highest extreme point | max: interior point | max: interior point | |

$R=0.30$ | $B=0.8$ | $B=0.7$ | $B=0.6$ |

max ${D}^{*}$ | $0.3956$ | $0.3771$ | $0.3204$ |

$S{H}_{1}$ | $0.6$ | $0.6$ | $0.57$ |

Shape ${D}^{*}\left(S{H}_{1}\right)$ | monotone increasing | monotone increasing | inverted U-shape |

max: highest extreme point | max: highest extreme point | max: interior point |

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**MDPI and ACS Style**

Russino, A.
Multiple Blockholders and Firm Value: A Simulation Analysis. *Int. J. Financial Stud.* **2023**, *11*, 56.
https://doi.org/10.3390/ijfs11020056

**AMA Style**

Russino A.
Multiple Blockholders and Firm Value: A Simulation Analysis. *International Journal of Financial Studies*. 2023; 11(2):56.
https://doi.org/10.3390/ijfs11020056

**Chicago/Turabian Style**

Russino, Annalisa.
2023. "Multiple Blockholders and Firm Value: A Simulation Analysis" *International Journal of Financial Studies* 11, no. 2: 56.
https://doi.org/10.3390/ijfs11020056