How does equity capital cost affect bank performance during a financial crisis?

Abstract

This article theoretically examines how equity capital cost affects return performance and safety of a bank and how this effect varies across a financial crisis comparing to a normal time when the bank manager’s performance reveals the like of higher equity return and the dislike of higher equity risk. We derive two main results. First, an increase in the bank’s equity capital cost from an increase of the interest rate of the Federal funds results in a reduced loan risk-taking at an increased optimal bank interest margin, implying better bank performance. Second, by ignoring the dislike, we find that the better performance is reinforced during a financial crisis but is reduced during a normal time. Financial crises and the dislike preference as such contribute a relatively low return and the stability of banking activities.

Keywords:

• bank interest margin
• equity capital cost
• barrier
• utility maximization

JEL Classification:

• G21
• G33

Acknowledgements

A previous version of this article was entitled ‘A path-dependent utility call option framework for bank spread behavior in response to equity capital cost’. We would like to thank Jyh-Horng Lin and two anonymous referees for their helpful comments and suggestions.

Notes

¹ Related literature includes, for example, Kashyap et al. (2008), Acharya et al. (2011) and Hart and Zingales (2011).

² Academic literature argues that the perspective of the bankers need to be more nuanced (e.g. Jimenéz et al., 2012; Osborne et al., 2012).

³ Two divergent approaches have been employed in the literature to model the financial intermediary (Sealey, 1980). The Markowitz–Tobin portfolio theory has the principal advantage of the explicit treatment of uncertainty. However, this approach assumes that asset and deposit markets are perfectly competitive. Klein (1971) bases his criticism on the existence of imperfectly competitive structures and shows that basic theorems of portfolio theory are not applicable under imperfect market structures. This article follows the spirit of the firm-theoretic approach.

⁴ However, we note that there are many aspects of the debate over the cost of market power in banking, particularly related to social welfare loss versus cost inefficiency (see Maudos and De Guevara, 2007) that we are silent on.

⁵ Alternatively, it is recognized that the utility function may be superadditive, subadditive or multiplicative. We argue that the aforementioned issue may provide an ample opportunity for future research.

⁶ Results to be derived from our model do not extend to the case where the bank is a price taker in the loan market (see Baltensperger, 1980).

⁷ For the Basel Accord and bank bankruptcy analysis, see Chiu et al. (2009) and Cebula (2010).

⁸ Given separation of management from ownership, the firm’s managers may have incentives to make decisions that maximize their own expected utility (Jensen and Meckling, 1976).

⁹ This dislike need not be particularly revealed. One could as easily interpret it as an amount a risk-averse manager is willing to forego in order to avoid a random level of equity returns. We will consider an alternative utility function without such a dislike in the following section.

¹⁰ Lin et al. (2012) also discuss the issue of equity quality during a financial crisis.

¹¹ In general, the standard down-and-out call option includes a standard call, a down-and-in call and the rebate payment. For simplicity, we follow Brockman and Turtle (2003) and consider only the case without the debate term.

¹² The riskless rate R% is given by the compounded return on 1-year US treasuring bills. According to Brockman and Turtle (2003), the mean value of R% is 5.81% with a corresponding SD of 2.07%. For simplicity, our numerical analysis is limited to the range between 2.75% and 4.50%.

¹³ According to the empirical study of Brockman and Turtle (2003), the average barrier is 0.6920 with a corresponding SD of 0.2259, and the barrier in retail is 0.6681 with a corresponding SD of 0.2024 during the sample period of 1981–1998. In our numerical exercises, we assume that the barrier is equal to 0.60, allowing the inclusion of a more realistic state.

¹⁴ The number of $\mathrm{\partial }{R}_{\mathrm{L}}/\mathrm{\partial }R$ evaluated at the optimal loan rate is rather small. This result is understood because the dependent variable R_L is a function of $R$, R_D, $B$, $D$, $q$, $\sigma$, $\mu$ and $\alpha$ in our model. According to the empirical results observed from Slovin and Sushka (1983), the effects of $\mathrm{\partial }{R}_{\mathrm{L}}/\mathrm{\partial }R$ are 0.2573, 0.0958, 0.0282, 0.0466, 0.0221, 0.0253, 0.031 and 0.0758 as the independent variables are increased.

¹⁵ Note that the bank’s objective in Wong (1997) is to set the loan rate to maximize the expected value of a Von Neumann–Morgenstern utility function defined in terms of profits, subject to the bank’s liquidity constraint. The comparative static result obtained above is based on a constant level of capital. Wong (1997) demonstrates that an increase in the bank’s equity capital will decrease the optimal bank interest. Zarruk and Madura (1992) also argue that an increase in the capital-to-deposits ratio decreases the optimal bank interest margin. In this article, we do not address the issue of capital regulation.

Additional information

Funding

This article received an aid of research fund from the Ministry of Science and Technology of Taiwan [grant number 102-2410-H-032-005].