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

Hence, we obtain:

Var(ri I C)

Var(rj I C)

Var(r ) + ^7?Var(/)

(1 + δ) Var(r₁)

Var(r_i )             v7²

^{(1 +} è'^)Var(r_J) ^{+ (1 +} £^{)(1 + χ}_jφ7_j

(A.6)

From (A.3), the correlation coefficient during the crisis period in the hypothesis
that only the variance of f and εj change, while the factor loadings remain
constant — which is our coefficient of interdependence φ — can be written as:

φ(λ_j,λf,δ,p) = ⁷i

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1 Φ Var(r_i I C) ∖ “^1/2

1 + λf ∖Va^r(r_j ^{i c})J

Substituting (A.6) into (A.7), we finally obtain

φ^_j,^χf,δ,p)

^{(1 +} ʌɑ⁾² 7² Var(r_i) ₊ 'dl ⁺ ʌɑ⁾²

^{(1 +}    7²i^Var(r₃)   ^{(1 +} W ^{+ x}₃)

-, —1/2

^{(1 +} ʌf⁾²    ₊ ^^{(1 + X}j)(ɪ ⁺ ʌf^{)2 p}

(1 + δ)(1 + X_jɔ² p^{2 +} (1 + δ)(1 + X_jɔ² p²

ʃ^{(1 + χ )2} ■ [¹⁺^^{(1 + χ}'^)p2 ] 1

^p(       (1 + <5)(1 + Xj^p       ∫

which can be rearranged to give equation (2).

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(A.7)