Equities of scope as merger incentives under capital regulation: narrow versus synergy banking valuation

ABSTRACT

The call options theory of corporate security valuation is applied to narrow-banking contingent claims of one bank, while the cap options theory is applied to synergy-banking contingent claims of another bank. This article investigates efficiency gains specified as equities of scope associated with the likelihood of the two banks involved in merger under capital regulation. We find that merger incentives are encouraged when the narrowing banking is conducted by the consolidated bank, whereas discouraged when the synergy banking is conducted. Raising bank capital requirement leads to an increased interest margin of the consolidated bank with the narrow banking valuation; however, to a decreased margin of the consolidated bank with the synergy banking valuation. An increase in the capital regulation reduces the merger incentives in the narrow banking valuation whereas increases the merger disincentive in the synergy banking valuation. These findings are consistent with the organizational theory that predicts a comparative advantage of narrow banking proposals in bank mergers.

KEYWORDS:

• Scope equities
• merger
• narrow banking
• synergy banking
• capital regulation

JEL CLASSIFICATION:

• G21
• G28
• G34

Acknowledgements

The authors would like to thank Jyh-Horng Lin, and two anonymous referees for their helpful comments and suggestions. The usual disclaimer applies.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ Beccalli and Frantz (2013) argue that overall merger and acquisition operations appear to result in financial gains, as measured by a straight ratio analysis on efficiency frontiers, for the EU and U.S. banking industries (see for an extensive review, DeYoung, Evanoff, and Molyneux 2009).

² Tsai and Hung (2013) develop a model of a bank with exactly this structure.

³ Ogura and Uchida (2014) focus on soft information and bank consolidation under the bank-complexity hypothesis, while this article emphasizes bank interest margin and consolidation related to the financial intermediation efficiency under the hypothesis.

⁴ See Bossone (2002) for a discussion of the narrow banking perspective.

⁵ See Strahan (2008) for a review of deposit-lending synergies.

⁶ Episcopos (2008) proposes a framework for bank equity valuation based on a barrier option model instead of the commonly used call option approach. The main contribution is to explicitly consider default risk in a contingent claim model to value the equity of a bank. In particular, default can occur at any time before the maturity date. Adding this complexity, ceteris paribus, is expected to affect none of the qualitative results in our model.

⁷ Ogura and Uchida (2014) demonstrate that financing costs for merged banks may decrease as a result of acquiring the ability to construct more diversified portfolios.

⁸ Mullins and Pyle (1994) develop a banking-firm model with exactly this time structure. In particular, the authors argue that deposits are renewed each period, based on the status of the bank at that time. The bank can also change its capital structure at the beginning of each period based on the past performance of its assets and its future prospects. In nature, their as well as our model is multiperiodic and dynamic.

⁹ We note that there are many aspects of the loan rate competition that we silent on. For example, as pointed out by Boyd and De Nicoló (2005), there is a large body of literature that concludes that when confronted increased with increased competition, banks rationally choose more risky portfolios.

¹⁰ Results to be derived from our model may not extend to the case where the liquidity constraint is not binding. We follow Zarruk and Madura (1992), and Wong (1997), and do not attempt to discuss the non-binding case.

¹¹ Alternatively, the discount factor can be specified as the weighted-average form $(L_2/(L_2+B_2))R_2+(B_2/(L_2+B_2))R-R_D$ with the specification of the total repayments from lending and liquid-asset investments and the payments to depositors. Adding this complexity affects none of the quantitative results.

¹² Longstaff, Santa-Clara, and Schwartz (2001) develop a cap option with this structure.

¹³ In Black’s (1976) model, the principal repayment vanishes since the principal is not exchanged at the end of a swap. In our model, we focus on bank equity valuation including the interest and principal repayments.

¹⁴ Baumol, Panzar, and Willig (1982) use the cost concept to define economies of scope. Their definition describes the basic phenomena that distinguish the multiproduct case from that of the single product.

¹⁵ This result can be realized from the observations presented in Table 1, $S_1>S_2$ and $P_1<P_2$.

¹⁶ The comparative static results of $\mathrm{\partial }{R}_2/\mathrm{\partial }q$ at a constant level of $R_1=4.5\mathrm{\%}$ are identical to those of $\mathrm{\partial }{R}_1/\mathrm{\partial }q$ at a constant level of $R_2=4.5\mathrm{\%}$ presented in Table 3. These results are understood because bank 1 and bank 2 are homogeneous in Equation 10.