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

‘instantaneous’ correlation coefficient between stock market returns in Hong
Kong and the Philippines, both measured in US dollars, during 1997. The daily
correlation provides a proxy for p (during tranquil periods) and pɑ (during
crises). Note that, before October 20, which is the starting day of the crisis,
we only report the instantaneous correlation, p_t; from October 20 on, we report
both the instantaneous correlation, pɛ, and a set of coefficients of instantaneous
correlation under the null hypothesis of interdependence, calculated assuming
different values of λ_j∙.

For the purpose of the graph, we find it useful to calculate and plot an inverse
transformation of φ, instead of φ itself. This transformation, denoted by φ_t(λ_j■'),
is given below

pɑ

Φi (ʌ,) = I ʌ ʌ ^P₂
ʌ/l + ^s - S [pf )

where S is estimated from the sample data.⁹ According to the logic of our test,
this coefficient of correlation is adjusted so as to allow for the fact that changes
in the volatility of stock prices in Hong Kong will per se affect cross-border
comovements during the Hong Kong crisis. Thus, the observed pɑ is adjusted
on the basis of the estimated increase in the variance of r_j-, that is S. Given S,
a smaller λ_j (shifting weight towards an increase in the variance of the global
factor) entails a smaller adjusted coefficient.

A visual inspection of figure 5 suggests that the unadjusted correlation co-
efficient pɑ increased significantly during the Hong Kong crisis in October 1997
relative to the previous months. Is this evidence of contagion? In light of what
discussed in the previous section, we can test of contagion vs. interdependence
by comparing φ_t (λ_j) and p_t. Specifically, the null hypothesis of interdependence
is accepted when φ_i(λ_j) is not significantly larger than p_t. Figure 5 plots differ-
ent estimates of φ_t (λ_j) conditional on values of λ_j between 0 and 5. The graph
shows that the adjusted coefficient φ_t (X_l) is close to p_t for low values of the
variance ratio, while it gets significantly larger for values of λ_j around 5. The
graph thus suggests that the hypothesis of interdependence could be accepted
conditional on some λ_j smaller than 5.

The literature provides a few examples of conditional correlation tests of
contagion — but in most cases the maintained assumption on the Xs is only
implicit. In the following section, we will review these tests, nesting them in
our framework.

4.1 Tests based on sample correlation coefficient or A =
l∕p² - 1

Early contributions on contagion, such as King and Wadhwani (1990), acknowl-
edge the problem of controlling for the relationship between volatility of return
and correlation, but implement no correction of their empirical tests.¹⁰ It is

⁹The coefficient φ' is obtained by substituting φ with ρ^c in equation (2), and then solving
the resulting expression for ρ.

¹⁰King and Wadhwani (1990) are aware of the relationship between volatility and correlation
as they write: “we might expect that the contagion coefficients would be an increasing function
of volatility” (pp. 20). However, in calculating correlation between markets, they do not
correct for the increase in volatility.

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