# Asymmetric Mean Reversion in Low Liquid Markets: Evidence from BRVM

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## Abstract

**:**

## 1. Introduction

## 2. Model

## 3. Data and Summary Statistics

## 4. Estimation Results

#### 4.1. Mean Reversion on the Overall Sample

#### 4.2. Dynamics of Mean Reversion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The BRVM Main Indices

**Figure A2.**Dynamics of the returns for the BRVMC and BRVM10. (

**a**) Dynamics of the BRVMC returns; (

**b**) Dynamics of the BRVM10 returns.

## Appendix B. Correlogram

**Figure A3.**Correlogram of the BRVMC and BRVM10 returns. (

**a**) Correlogram of the BRVMC; (

**b**) Correlogram of the BRVM10.

BRVM C | BRVM 10 | |||||||
---|---|---|---|---|---|---|---|---|

Lag 1 | Lag 4 | Lag 5 | Lag 6 | Lag 1 | Lag 4 | Lag 5 | Lag 6 | |

LL | 11,255.22 | 11,243.42 | 11,276.25 | 11,277.33 | 10,495.79 | 10,490.59 | 10,493.63 | 10,531.81 |

AIC | −6.82 | −6.81 | −6.82 | −6.82 | −6.36 | −6.35 | −6.35 | −6.37 |

BIC | −6.80 | −6.77 | −6.79 | −6.78 | −6.34 | −6.32 | −6.31 | −6.33 |

SIC | −6.82 | −6.81 | −6.82 | −6.82 | −6.36 | −6.35 | −6.35 | −6.37 |

HQ | −6.81 | −6.79 | −6.81 | −6.81 | −6.35 | −6.34 | −6.34 | −6.36 |

## Appendix C. Stationary Test

Lag | Type 1 | Type 2 | Type 3 | |||
---|---|---|---|---|---|---|

ADF | p-Value | ADF | p-Value | ADF | p-Value | |

BRVMC return | ||||||

0 | $-55.513$ | $0.010$ | $-55.597$ | $0.010$ | $-55.664$ | $0.010$ |

1 | $-38.768$ | $0.010$ | $-38.857$ | $0.010$ | $-38.928$ | $0.010$ |

2 | $-28.747$ | $0.010$ | $-28.830$ | $0.010$ | $-28.897$ | $0.010$ |

3 | $-23.596$ | $0.010$ | $-23.677$ | $0.010$ | $-23.742$ | $0.010$ |

4 | $-20.827$ | $0.010$ | $-20.911$ | $0.010$ | $-20.980$ | $0.010$ |

5 | $-19.498$ | $0.010$ | $-19.586$ | $0.010$ | $-19.660$ | $0.010$ |

6 | $-18.429$ | $0.010$ | $-18.522$ | $0.010$ | $-18.601$ | $0.010$ |

7 | $-17.854$ | $0.010$ | $-17.953$ | $0.010$ | $-18.037$ | $0.010$ |

8 | $-17.070$ | $0.010$ | $-17.174$ | $0.010$ | $-17.262$ | $0.010$ |

BRVM10 return | ||||||

0 | $-58.345$ | $0.010$ | $-58.367$ | $0.010$ | $-58.419$ | $0.010$ |

1 | $-40.131$ | $0.010$ | $-40.157$ | $0.010$ | $-40.214$ | $0.010$ |

2 | $-30.613$ | $0.010$ | $-30.640$ | $0.010$ | $-30.697$ | $0.010$ |

3 | $-25.351$ | $0.010$ | $-25.378$ | $0.010$ | $-25.435$ | $0.010$ |

4 | $-21.540$ | $0.010$ | $-21.569$ | $0.010$ | $-21.630$ | $0.010$ |

5 | $-20.183$ | $0.010$ | $-20.214$ | $0.010$ | $-20.279$ | $0.010$ |

6 | $-19.874$ | $0.010$ | $-19.909$ | $0.010$ | $-19.982$ | $0.010$ |

7 | $-18.599$ | $0.010$ | $-18.635$ | $0.010$ | $-18.712$ | $0.010$ |

8 | $-16.970$ | $0.010$ | $-17.006$ | $0.010$ | $-17.083$ | $0.010$ |

## Appendix D. Dynamics of Half-Time

**Figure A4.**Dynamics of half-time for the BRVMC index using recursive rolling regression. These graphs plot the half-time estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the half-time is 14 days using recursive rolling regression with a window whose end date is 1 July 2007. (

**a**) Dynamics of half-time for the BRVMC index using recursive rolling regression with a 2-year window; (

**b**) Dynamics of half-time for the BRVMC index using recursive rolling regression with a 4-year window; (

**c**) Dynamics of half-time for the BRVMC index using recursive rolling regression with a 6-year window; (

**d**) Dynamics of half-time for the BRVMC index using recursive rolling regression with an 8-year window.

**Figure A5.**Dynamics of half-time for the BRVMC index using standard rolling regression. These graphs plot the half-time estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the half-time is 14 days using recursive rolling regression with a window whose end date is 1 July 2007. (

**a**) Dynamics of half-time for the BRVMC index using standard rolling regression with a 2-year window; (

**b**) Dynamics of half-time for the BRVMC index using standard rolling regression with a 4-year window; (

**c**) Dynamics of half-time for the BRVMC index using standard rolling regression with a 6-year window; (

**d**) Dynamics of half-time for the BRVMC index using standard rolling regression with an 8-year window.

**Figure A6.**Dynamics of half-time for the BRVM10 index using recursive rolling regression. These graphs plot the half-time estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the half-time is 1.2 days using recursive rolling regression with a window whose end date is 1 July 2007. (

**a**) Dynamics of half-time for the BRVM10 index using recursive rolling regression with a 2-year window; (

**b**) Dynamics of half-time for the BRVM10 index using recursive rolling regression with a 4-year window; (

**c**) Dynamics of half-time for the BRVM10 index using recursive rolling regression with a 6-year window; (

**d**) Dynamics of half-time for the BRVM10 index using recursive rolling regression with an 8-year window.

**Figure A7.**Dynamics of half-time for the BRVM10 index using standard rolling regression. These graphs plot the half-time estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the half-time is 1.4 days using recursive rolling regression with a window whose end date is 1 July 2007. (

**a**) Dynamics of half-time for the BRVM10 index using standard rolling regression with a 2-year window; (

**b**) Dynamics of half-time for the BRVM10 index using standard rolling regression with a 4-year window; (

**c**) Dynamics of half-time for the BRVM10 index using standard rolling regression with a 6-year window; (

**d**) Dynamics of half-time for the BRVM10 index using standard rolling regression with an 8-year window.

## Appendix E. Dynamics of the Persistence Parameter in EGARCH

**Figure A8.**Dynamics of the persistence parameter for the BRVMC index using recursive rolling regression. These graphs plot the persistence parameter estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the persistence parameter is around 0.95 using recursive rolling regression with a window whose end date is 1 July 2007. The dot lines denote the 95% level confidence interval. The persistence parameter declines slightly over the estimation period. This decrease in the persistence parameter can be considered an insight into the improvement of the efficiency of the market. (

**a**) Dynamics of the persistence parameter using rolling regression with a 2-year window; (

**b**) Dynamics of the persistence parameter using rolling regression with a 4-year window; (

**c**) Dynamics of the persistence parameter using rolling regression with a 6-year window; (

**d**) Dynamics of the persistence parameter using rolling regression with an 8-year window.

**Figure A9.**Dynamics of the persistence parameter for the BRVM10 index using recursive rolling regression. These graphs plot the persistence parameter estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the persistence parameter is around 0.6 using recursive rolling regression with a window whose end date is 1 July 2007. The dot lines denote the 95% level confidence interval. (

**a**) Dynamics of the persistence parameter using rolling regression with a 2-year window; (

**b**) Dynamics of the persistence parameter using rolling regression with a 4-year window; (

**c**) Dynamics of the persistence parameter using rolling regression with a 6-year window; (

**d**) Dynamics of the persistence parameter using rolling regression with an 8-year window.

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1. | The markets studied in this paper are Egypt, Kenya, Zimbabwe, Morocco, Mauritius, Tunisia, Ghana, Namibia, Botswana and Côte d’Ivoire |

2. | It was the weak-form efficiency that was tested. |

3. | Appendix D provides the dynamics of the half-life for both BRVMC and BRVM10 indices using each of the four windows considered for each of the two schemes of rolling regression. In Appendix E, the dynamics of the persistence parameter (EGARCH coefficient) is plotted for both BRVMC and BRVM10 indices under the two schemes and for all four windows. The dynamics for all other coefficients of the models using the rolling regression under the two schemes and for all the windows are available upon request to the authors. |

**Figure 1.**Dynamics of half-life for BRVM indices using rolling regression. These graphs plot the half-life estimated using rolling regression. The date is the end date for a selected window. In (

**a**), the half-time is 14 days at the beginning using recursive rolling regression with a window whose end date is 1 July 2007. (

**a**) Dynamics of the BRVMC half-time using recursive rolling regression with a 2-year window; (

**b**) Dynamics of the BRVMC half-time using standard rolling regression with a 2-year window; (

**c**) Dynamics of the BRVM10 half-time using recursive rolling regression with a 2-year window; (

**d**) Dynamics of the BRVM10 half-time using standard rolling regression with a 2-year window.

Indices | N | Mean | St. Dev. | Min | Pctl(25) | Pctl(75) | Max |
---|---|---|---|---|---|---|---|

BRVMC returns | 3299 | $0.0004$ | $0.0087$ | $-0.0879$ | $-0.003$ | $0.004$ | $0.0951$ |

BRVM10 returns | 3299 | $0.0002$ | $0.0105$ | $-0.1045$ | $-0.0040$ | $0.0042$ | $0.0848$ |

BRVMC Return | BRVM10 Return | |||
---|---|---|---|---|

+ | − | + | − | |

2c | 426 | 356 | 409 | 373 |

3c | 232 | 176 | 214 | 179 |

4c | 117 | 101 | 103 | 89 |

5c | 62 | 64 | 64 | 49 |

6c | 42 | 33 | 45 | 28 |

7c | 22 | 20 | 28 | 21 |

8c | 15 | 12 | 19 | 11 |

9c | 11 | 6 | 11 | 6 |

10c | 9 | 2 | 7 | 1 |

11c | 5 | 1 | 4 | 0 |

12c | 4 | 1 | 4 | 0 |

13c | 3 | 0 | 2 | 0 |

14c | 3 | 0 | 2 | 0 |

15c | 1 | 0 | 0 | 0 |

16c | 1 | 0 | 0 | 0 |

BRVMC | BRVM10 | |||
---|---|---|---|---|

Criteria | ANAR | ANARMA | ANAR | ANARMA |

LL | $\mathrm{11,222}$ | $\mathrm{11,255}$ | $\mathrm{10,481}$ | $\mathrm{10,496}$ |

AIC | $-6.800$ | $-6.820$ | $-6.350$ | $-6.360$ |

BIC | $-6.790$ | $-6.800$ | $-6.340$ | $-6.340$ |

HQ | $-6.790$ | $-6.810$ | $-6.350$ | $-6.350$ |

SIC | $-6.800$ | $-6.820$ | $-6.350$ | $-6.360$ |

Parameters | BRVMC | BRVM10 |
---|---|---|

$\mu $ | 0.00 ** | −0.00 ** |

$(0.00)$ | $(0.00)$ | |

$\varphi $ | 0.98 *** | 0.91 *** |

$(0.01)$ | $(0.01)$ | |

$\theta $ | −0.93 *** | −0.87 *** |

$(0.00)$ | $(0.01)$ | |

$\rho $ | −0.12 *** | −0.19 *** |

$(0.02)$ | $(0.03)$ | |

$\omega $ | −0.87 *** | −2.88 ** |

$(0.09)$ | $(0.97)$ | |

$\alpha $ | 0.04 * | −0.01 |

$(0.02)$ | $(0.03)$ | |

$\beta $ | 0.91 *** | 0.68 *** |

$(0.01)$ | $(0.11)$ | |

$\gamma $ | 0.23 *** | 0.26 *** |

$(0.04)$ | $(0.05)$ | |

Half-life (h2l) | 7.05 days | 1.8 days |

Parameters | BRVMC | BRVM10 | ||||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |

$\mu $ | 0.00 ** | 0.00 *** | $0.00$ | −0.00 ** | $0.00$ | 0.00 *** |

$(0.00)$ | $(0.00)$ | $(0.00)$ | $(0.00)$ | $(0.00)$ | $(0.00)$ | |

$\varphi $ | 0.98 *** | −0.11 *** | −0.06 * | 0.91 *** | $-0.18$ | −0.14 * |

$(0.01)$ | $(0.02)$ | $(0.03)$ | $(0.01)$ | $(0.31)$ | $(0.07)$ | |

$\theta $ | −0.93 *** | 0.04 *** | $0.00$ | −0.87 *** | $0.15$ | $0.10$ |

$(0.00)$ | $(0.01)$ | $(0.01)$ | $(0.01)$ | $(0.25)$ | $(0.06)$ | |

$\rho $ | −0.12 *** | 0.17 * | $0.22$ | −0.19 *** | $-0.02$ | $0.05$ |

$(0.02)$ | $(0.07)$ | $(0.16)$ | $(0.03)$ | $(0.29)$ | $(0.06)$ | |

$\omega $ | −0.87 *** | −0.85 *** | $-0.84$ | −2.88 ** | −2.83 ** | −2.81 ** |

$(0.09)$ | $(0.02)$ | $(1.55)$ | $(0.97)$ | $(1.00)$ | $(0.96)$ | |

$\alpha $ | 0.04 * | $0.04$ | $0.05$ | $-0.01$ | $-0.01$ | $-0.01$ |

$(0.02)$ | $(0.02)$ | $(0.14)$ | $(0.03)$ | $(0.03)$ | $(0.03)$ | |

$\beta $ | 0.91 *** | 0.91 *** | 0.91 *** | 0.68 *** | 0.69 *** | 0.69 *** |

$(0.01)$ | $(0.00)$ | $(0.19)$ | $(0.11)$ | $(0.11)$ | $(0.11)$ | |

$\gamma $ | 0.23 *** | 0.21 *** | $0.21$ | 0.26 *** | 0.26 *** | 0.26 *** |

$(0.04)$ | $(0.04)$ | $(1.50)$ | $(0.05)$ | $(0.05)$ | $(0.05)$ | |

LL | 11,255.22 | 11,227.17 | 11,227.18 | 10,495.79 | 10,479.01 | 10,479.31 |

AIC | −6.82 | −6.80 | −6.80 | −6.36 | −6.35 | −6.35 |

BIC | −6.80 | −6.79 | −6.79 | −6.34 | −6.33 | −6.33 |

SIC | −6.82 | −6.80 | −6.80 | −6.36 | −6.35 | −6.35 |

HQ | −6.81 | −6.80 | −6.80 | −6.35 | −6.34 | −6.34 |

© 2019 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**

Gbenro, N.; Moussa, R.K.
Asymmetric Mean Reversion in Low Liquid Markets: Evidence from BRVM. *J. Risk Financial Manag.* **2019**, *12*, 38.
https://doi.org/10.3390/jrfm12010038

**AMA Style**

Gbenro N, Moussa RK.
Asymmetric Mean Reversion in Low Liquid Markets: Evidence from BRVM. *Journal of Risk and Financial Management*. 2019; 12(1):38.
https://doi.org/10.3390/jrfm12010038

**Chicago/Turabian Style**

Gbenro, Nathaniel, and Richard Kouamé Moussa.
2019. "Asymmetric Mean Reversion in Low Liquid Markets: Evidence from BRVM" *Journal of Risk and Financial Management* 12, no. 1: 38.
https://doi.org/10.3390/jrfm12010038