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G. Marti et al.
together and indicates the presence of correlations that pervade the entire system
[118].
• The measure of the average length of shortest path in the PMFG shows a small
world effect present in the networks at any time horizon [145].
• Among the 100 largest market capitalization stocks in the NYSE, the auto and
lagged intraday correlations play a much more prominent role in 2011-2013 than
in 2001-2003 [33].
• Authors in [33] find striking periodicities in the validated lagged correlations,
characterized by surges in network connectivity at the end of the trading day.
• At short time scales, measured synchronous correlations among stock returns tend
to be lower in magnitude [45], but lagged correlations among assets may become
non-negligible [32, 140].
• Banks may be of more concern than hedge funds from the perspective of connectedness [14].
• A lack of distinct sector identity in emerging markets [105, 113]; Few largest
eigenvalues deviate from the bulk of the spectrum predicted by RMT (far fewer
than for the NYSE) [104, 113].
• Emergence of an internal structure comprising multiple groups of strongly coupled
components is a signature of market development [113].
10.7.2 Moot Points and Controversies
Though most of the conclusions of empirical studies do agree, we find some claims
that seem to be contradictory:
• Reference [69] finds that eccentricity-based risk budgeting portfolios have
improved return to risk ratios, hence better invest in centrality (of the minimum
spanning tree). On the contrary, [108, 116, 119] conclude that it is better to invest
in the peripheries (of the minimum spanning tree).
• Volatility shocks always start at the fringe and propagate inwards [155], but in
[129], authors assert that the credit crisis spreads among affected stocks from more
centralized to more outer ones, as spread the news about the extent of damage to
the global economy.
• One might expect that the higher the correlation associated to a link in a correlationbased network is, the higher the reliability of the link is. The paper [144] shows
that it is not always observed empirically. However, the Cramér–Rao lower bound
(CRLB) for correlation [93] points out that the higher the correlation, the easier
its estimation, i.e. less statistical uncertainty for high correlations.
• For filtering the correlation matrix, SLCA is more stable than ALCA according
to [148], but ALCA is more stable and appropriate than SLCA according to [115,
139].
G. Marti et al.
together and indicates the presence of correlations that pervade the entire system
[118].
• The measure of the average length of shortest path in the PMFG shows a small
world effect present in the networks at any time horizon [145].
• Among the 100 largest market capitalization stocks in the NYSE, the auto and
lagged intraday correlations play a much more prominent role in 2011-2013 than
in 2001-2003 [33].
• Authors in [33] find striking periodicities in the validated lagged correlations,
characterized by surges in network connectivity at the end of the trading day.
• At short time scales, measured synchronous correlations among stock returns tend
to be lower in magnitude [45], but lagged correlations among assets may become
non-negligible [32, 140].
• Banks may be of more concern than hedge funds from the perspective of connectedness [14].
• A lack of distinct sector identity in emerging markets [105, 113]; Few largest
eigenvalues deviate from the bulk of the spectrum predicted by RMT (far fewer
than for the NYSE) [104, 113].
• Emergence of an internal structure comprising multiple groups of strongly coupled
components is a signature of market development [113].
10.7.2 Moot Points and Controversies
Though most of the conclusions of empirical studies do agree, we find some claims
that seem to be contradictory:
• Reference [69] finds that eccentricity-based risk budgeting portfolios have
improved return to risk ratios, hence better invest in centrality (of the minimum
spanning tree). On the contrary, [108, 116, 119] conclude that it is better to invest
in the peripheries (of the minimum spanning tree).
• Volatility shocks always start at the fringe and propagate inwards [155], but in
[129], authors assert that the credit crisis spreads among affected stocks from more
centralized to more outer ones, as spread the news about the extent of damage to
the global economy.
• One might expect that the higher the correlation associated to a link in a correlationbased network is, the higher the reliability of the link is. The paper [144] shows
that it is not always observed empirically. However, the Cramér–Rao lower bound
(CRLB) for correlation [93] points out that the higher the correlation, the easier
its estimation, i.e. less statistical uncertainty for high correlations.
• For filtering the correlation matrix, SLCA is more stable than ALCA according
to [148], but ALCA is more stable and appropriate than SLCA according to [115,
139].