And the unexpected US and regional returns are :
εUS,t = eUS,t
(5)
εreg,t = βreg,US,t -1 * eUS,t -1 + ereg,t
Letting i and j be two individual countries and assuming that the idiosyncratic shocks to the
US, regional and individual market are uncorrelated; this implies the following variance and
covariance expressions:
h (i tt ) = E (εltt εl,t )= β us,t-1 * σUS,t + β . -ɪi)* σR EG,t + σl t
h (i t us tt ) = E (ειt ,εus,t )= β-2υst—i
(6)
1
h(it regtt)= E(ε t t t εREGt t )= βitustt-1 * βREGtUSt t-1 * σUStt + βltREGtt-1 * σREGt t
_h(it jtt) = βι2UStt-1 * eUStt-1 + βι2REGtt-1 * eREGtt-1 + elt
The conditional covariance dynamics given in (6) have several important implications. Firstt a
market’s covariance with the U.S. (regional) market return is positively related to its country-
specific beta with the U.S. (or region). Secondt provided that the country specific beta
parameter is positivet higher volatility in the U.S. market induces higher return covariance
between the U.S. and market i. Thirdt the covariance with the regional market or any other
national market j within the same region increases in times of high return volatility in the U.S.
and/or the regional market. This natural implication of any factor modelt coupled with
asymmetric volatilityt could lead to the appearance of “contagious bear markets.” The
significant costs associated to this phenomenon have been underlined by a well-known series
of financial crises which had various causes but which spreaded worldwide equivalently.
These included the Mexican peso crisis of December 1994t the Asian crisis of 1997t the
Russian crisis of August 1998t the collapse of the Brazilian real in January 1999t the Turkish