Correlation Analysis of Financial Contagion: What One Should Know Before Running a Test



contributions.

Assume that the rates of return of the stock markets in country i and country
j are generated by the process

ri = ai + yi ■ f + εi                           (1)

rj  = a1 + Tj ■ f + εj

where a,ι and a.j are constant numbers, yi and yj are market-specific factor
loadings, f is a global factor, ε⅛ and ε7 denote idiosyncratic risks, and where
f,
ε-i and εj are mutually independent random variables with finite and strictly
positive variance.7

For simplicity, let both yi and yj be strictly positive. From the process
above, the correlation coefficient between r⅛ and rj∙ can be written as:8

о = Corr(r- r 1 =    c°<TT3ï

ρ = corr[rl,r1 )         ------- -----

ʌ/vɑr(r) ■ Var(rj■)

_                 1

+ Var(εt) 1 ɪ/2 ι+ Var(εj) 11/2

[1+ fiVar( f)    [1+7j2M∕)J

For given factor loadings yi and yj∙, a rise in correlation must correspond to
shocks increasing the variance of the global factor f relative to the variance of the
idiosyncratic noise
ε-ι and/or εj∙. Given the variances of the global factor and the
idiosyncratic components, however, a rise in correlation could also correspond to
an increase in the magnitude of the factor loadings
yi and yj, or to an increase
in the correlation between the idiosyncratic risks.

This distinction is at the root of recent empirical studies contrasting conta-
gion to interdependence. Consider a financial crisis in country
j. The increase
in the variance of the stock market return in such a country may be due to
an increase in the variance of either the global factor f, or the country specific
component
εj∙, or both. It is apparent that, if the change in the variance of the
global factor f is large enough relative to the change in the variance of the coun-
try specific component
εj, cross-market correlation must increase during a crisis
in country j. This change in correlation is
interdependence, in the sense that,
conditional on the occurrence of a financial crisis in country j, it is consistent
with the data generating process
(1). Contagion, as opposed to interdependence,
occurs if the increase in correlation turns out to be ‘too strong’ relative to what
is implied by the process (1); i.e. it is too strong to be explained by the behavior
of the global factor and the country specific component. In other words, con-
tagion occurs when, conditional on a crisis, correlations are stronger because of
some structural change in the international economy — affecting the link across
markets.

In a related definition, contagion occurs when a country-specific shock be-
comes ‘regional’ or ‘global’. This means that there is some factor
η for which
factor loadings are zero in all countries but one during tranquil periods, and be-
come positive during crisis periods. An illustration of this concept of contagion

7Allowing for some covariance across country-specific terms does not substantially modify
the main result of our analysis, on the need to adjust correlation coefficients for the variance
of country-specific shocks.

8We denote with Var the variance operator, Cov the covariance operator and Corr the
linear correlation operator.



More intriguing information

1. The East Asian banking sector—overweight?
2. Multi-Agent System Interaction in Integrated SCM
3. The name is absent
4. Conservation Payments, Liquidity Constraints and Off-Farm Labor: Impact of the Grain for Green Program on Rural Households in China
5. The name is absent
6. Female Empowerment: Impact of a Commitment Savings Product in the Philippines
7. TOMOGRAPHIC IMAGE RECONSTRUCTION OF FAN-BEAM PROJECTIONS WITH EQUIDISTANT DETECTORS USING PARTIALLY CONNECTED NEURAL NETWORKS
8. Micro-strategies of Contextualization Cross-national Transfer of Socially Responsible Investment
9. Climate Policy under Sustainable Discounted Utilitarianism
10. Behaviour-based Knowledge Systems: An Epigenetic Path from Behaviour to Knowledge
11. The name is absent
12. The name is absent
13. Weak and strong sustainability indicators, and regional environmental resources
14. Credit Market Competition and Capital Regulation
15. The Shepherd Sinfonia
16. Self-Help Groups and Income Generation in the Informal Settlements of Nairobi
17. Are Public Investment Efficient in Creating Capital Stocks in Developing Countries?
18. Party Groups and Policy Positions in the European Parliament
19. BUSINESS SUCCESS: WHAT FACTORS REALLY MATTER?
20. Conditions for learning: partnerships for engaging secondary pupils with contemporary art.