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



this sense, this result provides a new bank-specific motive to merge, in addition to the
well-known market power and diversification motives.

To sum up, the possibility for merged banks to estimate more precisely their liquidity
needs allows them to better assess the reserve-deposit ratio they should hold and adjust it
accordingly. Furthermore, the possibility for the merged banks to exchange reserves in the
internal money market implies that banks can benefit from scope economies in their liquidity
management by raising deposits in two imperfectly correlated deposit markets. This result
is consistent with Hughes et al. (1996), who find that banks active in imperfectly correlated
deposit markets
-especially as a result of consolidation- can reduce the cost of controlling
liquidity risk by appropriately adjusting deposit collection and reserve holdings. In this
respect, our result is also related to Kashyap et al. (2002), who show that combining
the activities of lending and deposit taking produces synergies that allow banks to reduce
the volume of liquid assets that banks need to hold to satisfy their customers’ unexpected
demands. However, whereas in their paper such an advantage in providing liquidity arises as
a consequence of two imperfectly correlated markets on different sides of the balance sheet,
in our model it emerges from two imperfectly correlated markets on the same side of the
balance sheet.

4.2 Choice of Loan Rates and Balance Sheets

We now examine how the merger modifies the loan market equilibrium and banks’ balance
sheets. The effect of the merger on loan rates depends on how it affects banks’ market
power and cost structures. As already noticed, competitors have the same total costs as
in the status quo. By contrast, the total costs of the merged banks change. As stated in
Corollary 2, their financing costs are lower than competitors’. Furthermore, their lending
costs reach βc, where the parameter β
1 represents the potential non-financial efficiency
gains that the merger induces for granting loans. The lower the parameter β the greater
are the efficiency gains. The idea is to include, for example, the possibility for economies
of scale, which are often put forward by bank managers in favor of mergers and have been
questioned in the literature, as we discuss in Section 6.
8

8We could also allow for β > 1, in which case the merger would even lead to diseconomies. Already the
market power of merged banks tends to increase loan rates, and β > 1 would only strengthen this effect. So,
none of our results would be qualitatively altered by further generalizing β.

17



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