  Network theory proved recently to be useful in the quantification of many
properties of financial systems. The analysis of the structure of investment
portfolios is a major application since their eventual correlation and overlap
impact the actual risk diversification by individual investors. We investigate
the bipartite network of US mutual fund portfolios and their assets. We follow
its evolution during the Global Financial Crisis and analyse the interplay
between diversification, as understood in classical portfolio theory, and
similarity of the investments of different funds. We show that, on average,
portfolios have become more diversified and less similar during the crisis.
However, we also find that large overlap is far more likely than expected from
models of random allocation of investments. This indicates the existence of
strong correlations between fund portfolio strategies. We introduce a
simplified model of propagation of financial shocks, that we exploit to show
that a systemic risk component origins from the similarity of portfolios. The
network is still vulnerable after crisis because of this effect, despite the
increase in the diversification of portfolios. Our results indicate that
diversification may even increase systemic risk when funds diversify in the
same way. Diversification and similarity can play antagonistic roles and the
trade-off between the two should be taken into account to properly assess
systemic risk.
