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How do capital structure and economic regime affect fair prices of bank’s equity and liabilities?

  • S.I.: Financial Economics
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Abstract

This paper considers the capital structure of a bank in a continuous-time regime-switching economy. The modeling framework takes into account various categories of instruments, including equity, contingent convertible debts, straight debts, deposits and deposits insurance. Whereas previous researches concentrate on the determination of the capital structure that maximizes shareholders’ equity, this work focuses on the fair pricing of liabilities that ensures no cross-subsidization among stakeholders. This is discussed in a case study where the bank’s EBIT is modeled by a four-regime process and is fitted to real market data. A numerical analysis reveals that convertible debts can significantly reduce the cost of deposits insurance and straight debts as well as probabilities of bankruptcy. Although it is found that the risk of dilution for shareholders is important, paradoxically, a high conversion rate for the contingent convertible debt, compensated by a low interest cost before conversion, can delay this dilution. Finally, we find that in case of change of economic regime, there exists an optimal capital structure from the shareholder’s perspective.

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Notes

  1. Notice that the economic regime is assumed observable. However, as explained in the last paragraph of Sect. 6, most of our results may be extended to hidden regimes.

  2. In the model, the EBIT is used as an estimate of the firm’s cash-flow.

  3. The equity net of the deposit insurance is defined later as the equity value decreased by the premium for the deposit insurance.

  4. Decreasing the volatility \(\sigma _{4}\) from 41.44 to 31.44 % , leads to an asset growth rate equal to \(\left( \mu _{4}+\frac{1}{2}\sigma _{4}^{2}\right) = - 3.45\) % and for this volatility, the equity is lower in state 4 than in state 3.

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Authors and Affiliations

  1. ESC Rennes Business School and CREST, Rennes, France

    Donatien Hainaut

  2. York University, Toronto, Canada

    Yang Shen

  3. Lingnan (University) College, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Yan Zeng

Authors
  1. Donatien Hainaut
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  2. Yang Shen
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  3. Yan Zeng
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Correspondence to Donatien Hainaut.

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Hainaut, D., Shen, Y. & Zeng, Y. How do capital structure and economic regime affect fair prices of bank’s equity and liabilities?. Ann Oper Res 262, 519–545 (2018). https://doi.org/10.1007/s10479-016-2210-8

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  • DOI: https://doi.org/10.1007/s10479-016-2210-8

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