Mean Variance Optimization of Non-Linear Systems and Worst-case Analysis

Scharfstein and Stein (2000) and Rajan et al. (2000) warn that they might also become
inefficient if internal incentive problems and power struggles lead to excessive cross-divisional
subsidies, the empirical results of Graham et al. (2002) suggest that ‘value destruction’ in
firms is not related to consolidation, supporting the idea of efficiently functioning internal
capital markets. Concerning banks, Houston et al. (1997) provide evidence that loan growth
at subsidiaries of US bank holding companies (BHCs) is more sensitive to the holding
company’s cash flow than to the subsidiaries’ own cash flow; and Campello (2002) shows
that the funding of loans by small affiliates of US BHCs is less sensitive to affiliate-level
cash flows than independent banks of comparable size. Focusing on short-term assets, we
show how the creation of an internal money market can cushion external liquidity shocks
and how it affects banks’ reserve choices and banking system liquidity. We also show that
the financing cost advantages associated with the internal money market lead the merged
banks, ceteris paribus, to be more aggressive on the loan market.

The remainder of the paper is structured as follows. Section 2 sets up the model.
Section 3 derives the equilibrium before a merger (‘status quo’). The subsequent section
characterizes the effects of a merger on individual banks’ behavior; and Section 5 looks at its
implications for aggregate liquidity. Section 6 contains a discussion of the different scenarios
for competition and liquidity effects of bank consolidation. Section 7 concludes. All proofs
are in the Appendix.

2 The Model

Consider a three date (T =0, 1, 2) economy with three classes of risk neutral agents: N
banks (N>3), numerous entrepreneurs, and numerous individuals. At date 0 banks raise
funds from individuals in the form of retail deposits, and invest the proceeds in loans to
entrepreneurs and in liquid short-term assets denoted as reserves. Thus, the balance sheet
for each bank i is

Li + Ri = Di,                                   (1)

where Li denotes loans, Ri reserves, and Di deposits.

Competition in the loan market

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