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doi: 10.3934/jimo.2018191

Empirical analysis and optimization of capital structure adjustment

1. 

Business School, Hunan Normal University, Changsha 410081, China

2. 

School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, 6185, Australia

3. 

School of Information Science and Engineering, Fujian University of Technology, Fuzhou 350118, China

* Corresponding author: Honglei Xu

Received  July 2018 Revised  August 2018 Published  January 2019

Fund Project: The second author is supported by ARC Discovery grant DP160102819

This paper analyzes capital structure's characteristics and presents its simplified mathematical model. Panel data analysis shows that the listed companies prefer equity financing rather than debt financing. Furthermore, we propose a capital structure optimization model with uncertain equity financing constraints. We formulate the capital structure optimization problem as a two-stage stochastic optimization problem and solve it. Finally, numerical examples show that our optimization approach can improve the statistics result of capital structure adjustment.

Citation: Jinying Ma, Honglei Xu. Empirical analysis and optimization of capital structure adjustment. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018191
References:
[1]

J. AngF. Meng and J. Sun, Two-stage stochastic linear programs with incomplete information on uncertainty, European Journal of Operational Research, 233 (2014), 16-22. doi: 10.1016/j.ejor.2013.07.039.

[2]

M. Baker and J. Wurgler, Market timing and capital structure, The Journal of Finance, 57 (2002), 1-32.

[3]

Y. DangJ. Sun and H. Xu, Inertial accelerated algorithms for solving a split feasibility problem, Journal of Industrial and Management Optimization, 13 (2017), 1383-1394. doi: 10.3934/jimo.2016078.

[4]

E. Dudley, Capital structure and large investment projects, Journal of Corporate Finance, 18 (2012), 1168-1192.

[5]

E. O. FischerH. Robert and Z. Jose, Dynamic capital structure choice: theory and tests, The Journal of Finance, 44 (1989), 19-40.

[6]

M. J. Flannery and P. R. Kasturi, Partial adjustment toward target capital structures, Journal of Financial Economics, 79 (2006), 469-506.

[7]

P. Grier and E. Zychowicz, Institutional investors, corporate discipline and the role of debt, Journal of Economics and Business, 46 (1994), 1-11.

[8]

M. Harris and R. Artur, The theory of capital structure, The Journal of Finance, 46 (1991), 297-355.

[9]

H. Hu, Dynamic Adjustment of Capital Structure of listed companies in China: Speed, Path and Efficiency (in Chinese), Southwest University of Finance and Economics Press, 2012

[10]

S. HuangZ. Wan and S. Deng, A modified projected conjugate gradient algorithm for unconstrained optimization problems, The ANZIAM Journal, 54 (2013), 143-152. doi: 10.1017/S1446181113000084.

[11]

R. A. KorajczykJ. L. Deborah and L. M. Robert, Equity issues with time-varying asymmetric information, Journal of Financial and Quantitative Analysis, 27 (1992), 397-417.

[12]

M. C. Jensen and H. M. William, Theory of the firm: Managerial behavior, agency costs and ownership structure, Journal of Financial Economics, 3 (1976), 305-360.

[13]

B. Li, Irrational Investment behavior, debt soundness and dynamic adjustment of capital structure (in Chinese), Economic Science, 4 (2013), 103-115.

[14]

A. Shleifer and W. V. Robert, Large shareholders and corporate control, Journal of Political Economy, 94 (1986), 461-488.

[15]

H. Xu, K. L. Teo and Y. Zhang, Optimization and Control Techniques and Applications, Springer, Heidelberg, 2014.

[16]

H. Xu, S. Wang and S. Y. Wu, Optimization Methods, Theory and Applications, Springer-Verlag, Berlin, 2015.

[17]

H. Xu and X. Wang, Optimization and Control Methods in Industrial Engineering and Construction, Springer Netherlands, 2014.

[18]

J. Ye, H. Xu, E. Feng and Z. Xiu, et al., Optimization of a fed-batch bioreactor for 1, 3-propanediol production using hybrid nonlinear optimal control, Journal of Process Control, 24(2014), 1556-1569.

[19]

Z. WanY. ChenS. Huang and D. Feng, A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations, Optimization Letters, 8 (2014), 1845-1860. doi: 10.1007/s11590-013-0678-6.

[20]

Z. WanK. L. TeoX. Shen and C. Hu, New BFGS method for unconstrained optimization problem based on modified Armijo line search, Optimization, 63 (2014), 285-304. doi: 10.1080/02331934.2011.644284.

[21]

Z. W. WangD. Q. Zhao and W. X. Zhu, Capital market friction and capital structure adjustment (in Chinese), Financial Research, 2 (2007), 109-119.

show all references

References:
[1]

J. AngF. Meng and J. Sun, Two-stage stochastic linear programs with incomplete information on uncertainty, European Journal of Operational Research, 233 (2014), 16-22. doi: 10.1016/j.ejor.2013.07.039.

[2]

M. Baker and J. Wurgler, Market timing and capital structure, The Journal of Finance, 57 (2002), 1-32.

[3]

Y. DangJ. Sun and H. Xu, Inertial accelerated algorithms for solving a split feasibility problem, Journal of Industrial and Management Optimization, 13 (2017), 1383-1394. doi: 10.3934/jimo.2016078.

[4]

E. Dudley, Capital structure and large investment projects, Journal of Corporate Finance, 18 (2012), 1168-1192.

[5]

E. O. FischerH. Robert and Z. Jose, Dynamic capital structure choice: theory and tests, The Journal of Finance, 44 (1989), 19-40.

[6]

M. J. Flannery and P. R. Kasturi, Partial adjustment toward target capital structures, Journal of Financial Economics, 79 (2006), 469-506.

[7]

P. Grier and E. Zychowicz, Institutional investors, corporate discipline and the role of debt, Journal of Economics and Business, 46 (1994), 1-11.

[8]

M. Harris and R. Artur, The theory of capital structure, The Journal of Finance, 46 (1991), 297-355.

[9]

H. Hu, Dynamic Adjustment of Capital Structure of listed companies in China: Speed, Path and Efficiency (in Chinese), Southwest University of Finance and Economics Press, 2012

[10]

S. HuangZ. Wan and S. Deng, A modified projected conjugate gradient algorithm for unconstrained optimization problems, The ANZIAM Journal, 54 (2013), 143-152. doi: 10.1017/S1446181113000084.

[11]

R. A. KorajczykJ. L. Deborah and L. M. Robert, Equity issues with time-varying asymmetric information, Journal of Financial and Quantitative Analysis, 27 (1992), 397-417.

[12]

M. C. Jensen and H. M. William, Theory of the firm: Managerial behavior, agency costs and ownership structure, Journal of Financial Economics, 3 (1976), 305-360.

[13]

B. Li, Irrational Investment behavior, debt soundness and dynamic adjustment of capital structure (in Chinese), Economic Science, 4 (2013), 103-115.

[14]

A. Shleifer and W. V. Robert, Large shareholders and corporate control, Journal of Political Economy, 94 (1986), 461-488.

[15]

H. Xu, K. L. Teo and Y. Zhang, Optimization and Control Techniques and Applications, Springer, Heidelberg, 2014.

[16]

H. Xu, S. Wang and S. Y. Wu, Optimization Methods, Theory and Applications, Springer-Verlag, Berlin, 2015.

[17]

H. Xu and X. Wang, Optimization and Control Methods in Industrial Engineering and Construction, Springer Netherlands, 2014.

[18]

J. Ye, H. Xu, E. Feng and Z. Xiu, et al., Optimization of a fed-batch bioreactor for 1, 3-propanediol production using hybrid nonlinear optimal control, Journal of Process Control, 24(2014), 1556-1569.

[19]

Z. WanY. ChenS. Huang and D. Feng, A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations, Optimization Letters, 8 (2014), 1845-1860. doi: 10.1007/s11590-013-0678-6.

[20]

Z. WanK. L. TeoX. Shen and C. Hu, New BFGS method for unconstrained optimization problem based on modified Armijo line search, Optimization, 63 (2014), 285-304. doi: 10.1080/02331934.2011.644284.

[21]

Z. W. WangD. Q. Zhao and W. X. Zhu, Capital market friction and capital structure adjustment (in Chinese), Financial Research, 2 (2007), 109-119.

Table 1.  Asset-liability ratio and institutional investor's shareholding ratio in various sectors
Trade Asset-Liability Ratio IIShare
Mining 48.19% 18.39%
Electric Heating Water 60.33% 28.55%
Real Estate 62.77% 21.12%
Construction 70.69% 16.66%
Traffic 49.62% 21.01%
Agriculture 41.71% 17.6%
Wholesale and Retail 56.37% 18.1%
Entertainment 46.19% 13.15%
Information Technology 37.02% 18.16%
Manufacturing 29.86% 16.88%
52.21% 17.19%
Trade Asset-Liability Ratio IIShare
Mining 48.19% 18.39%
Electric Heating Water 60.33% 28.55%
Real Estate 62.77% 21.12%
Construction 70.69% 16.66%
Traffic 49.62% 21.01%
Agriculture 41.71% 17.6%
Wholesale and Retail 56.37% 18.1%
Entertainment 46.19% 13.15%
Information Technology 37.02% 18.16%
Manufacturing 29.86% 16.88%
52.21% 17.19%
Table 2.  Institutional investor's shareholding ratio
Trade Public Offering Funds Securities Insurance Trader Social Insurance Funds Other Sum
Mining 4.71% 3.23% 4.03% 3.76% 2.66% 18.39%
Electric Heating Water 6.31% 3.17% 3.48% 4.76% 10.83% 28.55%
Real Estate 5.08% 3.23% 5.21% 2.66% 4.94% 21.12%
Construction 5.73% 2.16% 2.33% 3.09% 3.35% 16.66%
Traffic 3.14% 2.64% 3.72% 3.53% 7.98% 21.01%
Agriculture 5.32% 2.26% 3.14% 3.05% 3.83% 17.6%
Wholesale and Retail 6.62% 1.79% 2.93% 2.77% 3.99% 18.1%
Entertainment 2.33% 0.74% 1.67% 1.24% 7.17% 13.15%
Information Technology 8.91% 2.27% 2.71% 2.73% 1.54% 18.16%
Manufacturing 6.24% 2.36% 2.7% 2.87% 2.71% 16.88%
Synthesize 4.26% 1.93% 3.65% 3.28% 4.07% 17.19%
Trade Public Offering Funds Securities Insurance Trader Social Insurance Funds Other Sum
Mining 4.71% 3.23% 4.03% 3.76% 2.66% 18.39%
Electric Heating Water 6.31% 3.17% 3.48% 4.76% 10.83% 28.55%
Real Estate 5.08% 3.23% 5.21% 2.66% 4.94% 21.12%
Construction 5.73% 2.16% 2.33% 3.09% 3.35% 16.66%
Traffic 3.14% 2.64% 3.72% 3.53% 7.98% 21.01%
Agriculture 5.32% 2.26% 3.14% 3.05% 3.83% 17.6%
Wholesale and Retail 6.62% 1.79% 2.93% 2.77% 3.99% 18.1%
Entertainment 2.33% 0.74% 1.67% 1.24% 7.17% 13.15%
Information Technology 8.91% 2.27% 2.71% 2.73% 1.54% 18.16%
Manufacturing 6.24% 2.36% 2.7% 2.87% 2.71% 16.88%
Synthesize 4.26% 1.93% 3.65% 3.28% 4.07% 17.19%
Table 3.  Descriptive Statistics
Variables N Mean Sd Min Max
IIShare 8559 0.181 0.179 0 0.9102
Mortgage Capacity 8559 0.239 0.179 0 0.971
Grow 8559 5.712 235.6 -57.96 20,371
Size 8559 21.86 1.350 15.60 28.51
Ownership Concentration 8559 59.53 35.75 7.32 100
NDTS 8559 0.0311 0.0333 -0.114 1.529
Profitability 8559 0.0526 0.310 -6.353 22.00
Deb 8559 0.0321 0.2801 -8.1073 6.1282
Capital Cost 8559 5.9239 3.501 1.6552 25.7761
Variables N Mean Sd Min Max
IIShare 8559 0.181 0.179 0 0.9102
Mortgage Capacity 8559 0.239 0.179 0 0.971
Grow 8559 5.712 235.6 -57.96 20,371
Size 8559 21.86 1.350 15.60 28.51
Ownership Concentration 8559 59.53 35.75 7.32 100
NDTS 8559 0.0311 0.0333 -0.114 1.529
Profitability 8559 0.0526 0.310 -6.353 22.00
Deb 8559 0.0321 0.2801 -8.1073 6.1282
Capital Cost 8559 5.9239 3.501 1.6552 25.7761
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