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

Var(f ) =

Var (r_j)
(1 + >)

Var(ε_i )

7i ■ Var(f)

(A∙1)

_             1

^p [¹ + ⅛⅛⅛Γ'²-11 + >

(A.2)

Substituting (A.1) into (A.2), we obtain the unconditional correlation coefficient
as a function of the rates of return, the factor loadings and λ_j■:

7i

1   7 V ar (ri ) A ¹A

^{1 +} λ₃ ∖Var(r_jУ

(A∙3)

We now turn to the crisis period. From the data generating process of the
rate of return of the stock market in country i, the variance of r during the
crisis is:

Var(r_i I C) = 7² ■ Var(f ∣ C) + Var(ε_i)

(A.4)

Note that by the data generating process (1) and by the definition of λj and
ʌɑ, it follows that:

^Var(rj ^{i c)} = _{1 + δ} = ^{1 +} ʌɑ ^{Var(f i c)}

Var(r₁)              1 + λj Var(f )

(A.5)

By solving (A.5) for Var(f ∣ C) and substituting the resulting expression into
(A.4) we get:

Var(ri I C) = Var(ri) + ψ7²Var(f)

where ψ is defined as in follows

^^{(1 +} ʌj) ⁺ Q ^— > ⁾
1 + >7

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