Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

JEL classification: C35 F37 G10 G15Keywords: Contagion Stock market crises Interdependence Systemic risk a b s t r a c t This paper shows that stock market contagion occurs as a domino effect, where confined local crashes evolve into more widespread crashes. Using a novel framework based on ordered logit regressions we model the occurrence of local, regional and global crashes as a function of their past occurrences and financial variables. We find significant evidence that global crashes do not occur abruptly but are preceded by local and regional crashes. Besides this form of contagion, interdependence shows up by the effect of interest rates, bond returns and stock market volatility on crash probabilities. When it comes to forecasting global crashes, our model outperforms a binomial model for global crashes only.

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The state of the equity market, often referred to as a bull or a bear market, is of key importance for financial decisions and economic analyses. Its latent nature has led to several methods to identify past and current states of the market and forecast future states. These methods encompass semi-parametric rule-based methods and parametric regime-switching models. We compare these methods by new statistical and economic measures that take into account the latent nature of the market state. The statistical measure is based directly on the predictions, while the economic measure is based on the utility that results when a risk-averse agent uses the predictions in an investment decision. Our application of this framework to the S&P500 shows that rule-based methods are preferable for (in-sample) identification of the market state, but regime-switching models for (out-of-sample) forecasting. In-sample only the direction of the market matters, but for forecasting both means and volatilities of returns are important. Both the statistical and the economic measures indicate that these differences are significant.