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



1 Introduction

The last decade has witnessed an intense process of consolidation in the financial sectors of
many industrial countries. This ‘merger movement’, documented in a number of papers and
official reports, was particularly concentrated among banking firms and occurred mostly
within national borders.
1 As shown in Figure 1, in countries like Canada, Italy and Japan
more than half of the banks combined forces over the 1990s.

[FIGURE 1 ABOUT HERE]

As a consequence, many countries (e.g., Belgium, Canada, France, the Netherlands, and
Sweden) reached a situation of high banking concentration or faced a further deterioration
of an already concentrated sector. As can be seen from Table 1, a small number of large
banks often constitutes more than 70 per cent of the national banking sector.

[TABLE 1 ABOUT HERE]

This extensive consolidation process raises a number of important questions, including the
effects on a nation’s financial stability. The conventional wisdom is that consolidation may
lower liquidity needs and reduce activity in the interbank market. For example, according
to the G-10 ‘Report on Financial Sector Consolidation’, ‘...by internalizing what had pre-
viously been interbank transactions, consolidation could reduce the liquidity of the market
for central bank reserves, making it less efficient in reallocating balances across institutions
and increasing market volatility’ (Group of Ten, 2001, p. 20).
2 However, this statement may
not survive in a moderately general model. Merging banks may either increase or decrease
their demand for reserve assets. Moreover, mergers affect loan markets as well as deposit
markets, and loan market competition also affects the demand for reserves.

1See, e.g., Boyd and Graham (1996), Berger et al. (1999), Hanweck and Shull (1999), Dermine (2000),
ECB (2000), OECD (2000) and Group of Ten (2001).

2 The effects of consolidation on interbank market liquidity are of course most pronounced in smaller
countries with national money markets, such as Denmark, Sweden or Switzerland. For example, the Swiss
banking system is now dominated by two main players. In order to moderate adverse effects on liquidity,
the Swiss National Bank considerably facilitated foreign banks’ access to the Swiss franc money market.
“With this opening the influence of the main banks on the conditions in the money market was reduced.
Their share of total outstanding liquidity transactions declined from more than 80% to now around 50%”
(quote from the SNB Board Member Bruno Gehrig at the Jahresend-Mediengesprach of 8 December 2000,
see
http://www.snb.ch/d/aktuelles/referate/ref_001208_bge.html; translation by the authors).



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