statistique, théorie et gestion de portefeuille - Docs at ISFA

240 9. Mesure de la dépendance extrême entre deux actifs financiers
Introduction
The October 19, 1987, stock-market crash stunned Wall Street professionals, hacked about $1 trillion off
the value of all U.S. stocks, and elicited predictions of another Great Depression. On “Black Monday,” the
Dow Jones industrial average plummeted 508 points, or 22.6 percent, to 1, 738.74. Contrary to common
belief, the US was not the first to decline sharply. Non-Japanese Asian markets began a severe decline on
October 19, 1987, their time, and this decline was echoed first on a number of European markets, then in
North American, and finally in Japan. However, most of the same markets had experienced significant but
less severe declines in the latter part of the previous week. With the exception of the US and Canada, other
markets continued downward through the end of October, and some of these declines were as large as the
great crash on October 19.
On December 19, 1994, the Mexican government, facing a solvency crisis, chose to devaluate the peso and
abandoned its exchange rate parity. This devaluation plunged the country into a major financial crisis which
quickly propagated to the rest of the Latin American countries.
From July 1997 to December 1997, several East Asian markets crashed, starting with the Thai market on
July 2, 1997 and ending with the Hong Kong market on October 17, 1997. After this regional event, the
turmoil spread over to the American and European markets.
The “slow” crash and in particular the turbulent behavior of the stock markets worldwide starting midaugust
1998 are widely associated with and even attributed to the plunge of the Russian financial markets,
the devaluation of its currency and the default of the government on its debts obligations.
The Nasdaq Composite index dropped precipiteously with a low of 3227 on April 17, 2000, corresponding
to a cumulative loss of 37% counted from its all-time high of 5133 reached on March 10, 2000. The drop
was mostly driven by the so-called “New Economy” stocks which have risen nearly fourfold over 1998 and
1999 compared to a gain of only 50% for the S&P500 index. And without technology, the benchmark would
be flat.
All these events epitomize the observation often reported by market professionals that, “during major market
events, correlations change dramatically” (Bookstaber 1997). The possible existence of changes of correlation,
or more precisely of changes of dependence, between assets and between markets in different market
phases has obvious implications in risk assessment, portfolio management and in the way policy and regulation
should be performed. Concerning portfolio management, (Ang and Bekaert 2001, Ang and Chen 2001)
for instance, have stressed that these questions related to state-varying-dependence are important for practical
applications since in such a case the optimal portfolio will also become state-dependent, and neglecting
this point can lead to very inefficient asset allocations. In this spirit, the recent Argentine crisis in 2001 has
triggered fears of a contagion to other Latin American market. Also, the Enron financial scandal at the end
of 2001 seems to have opened a flux of similar bankrupcies in other “new economy” companies.
From an academic perspective, all these manifestations of propagating crisis have given birth to an intense
activity concerning the notion of contagion (see (Claessens et al. 2001) for a review) which is defined,
according to the most commonly accepted definition, as an increase in the correlation (or linkage) across
markets during turmoil periods. In fact, as we shall see, there are two distinct classes of mechanisms for
understanding “changes of correlations”, not necessarily mutually exclusive.
• It is possible that there are genuine changes with time of the unconditional (with respect to amplitudes)
correlations and thus of the underlying structure of the dynamical processes, as observed by identifying
shifts in ARMA-ARCH/GARCH processes (Silvapulle and Granger 2001), in regime-switching
models (Ang and Bekaert 2001, Ang and Chen 2001) or in contagion models
2