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



try reduce both the variance of aggregate liquidity demand and expected aggregate liquidity
needs. The impact of consolidation on aggregate liquidity depends on the interaction be-
tween the reserve and the asymmetry channel. In particular, whether the two effects work
in the same or opposite directions depends on the size of the relative cost of refinancing and
on how mergers affect the asymmetry of banks’ balance sheets.

The model delivers several insights, which can be interpreted according to size of merger
and type of country or financial system. First, mergers between large banks leading to a
‘polarization’ of the banking system with large and small institutions are more likely to lead
to higher aggregate liquidity needs than mergers involving small banks, since they increase
the asymmetry in banks’ balance sheets. This result is particularly noteworthy in light of
Table 1, which suggests that the banking sector consolidation of the 1990s may have led
to greater asymmetry in the size of banks in most industrialized countries. In particular,
in Belgium, Canada, France, the Netherlands and Sweden, the five top players enlarged
their market shares significantly to very high levels. Second, mergers are more likely, ceteris
paribus, to increase aggregate liquidity needs in developing countries than in industrial ones,
since they induce lower individual reserve holdings in less efficient markets, where banks
face higher refinancing costs. Third, the effects of consolidation on loan competition and
aggregate liquidity tend to be complementary in industrial countries but not in developing
ones. In fact, whereas mergers are likely to affect competition and liquidity in the same
direction when the cost of refinancing is low (i.e., mergers between large banks are likely to
increase both loan rates and expected aggregate liquidity needs, and vice versa for mergers
involving small banks), they always push towards larger expected liquidity needs when the
cost of refinancing is high, independently of the effect on loan competition. Finally, the
impact of bank mergers on reserve holdings and aggregate liquidity may depend on the
phase of the business cycle. Mergers happening in upturns may affect reserves and private
aggregate liquidity more negatively than mergers happening in downturns, at least in the
short run.

Relation with the literature

Our approach to study the joint implications of bank mergers for competition, individual
and aggregate liquidity combines elements of the industrial organization literature on the



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