http://repub.eur.nl/res/aut/14698/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/12391/ 2000-01-01T00:00:00Z A safety-first investor maximizes expected return subject to a downside risk constraint. Arzac and Bawa [Arzac, E.R., Bawa, V.S., 1977. Portfolio choice and equilibrium in capital markets with safety-first investors. Journal of Financial Economics 4, 277–288.] use the Value at Risk as the downside risk measure. The paper by Gourieroux, Laurent and Scaillet estimates the optimal safety-first portfolio by a kernel-based method, we exploit the fact that returns are fat-tailed, and propose a semi-parametric method for modeling tail events. We also analyze a portfolio containing the two stocks used by Gourieroux et al. and discuss the merits of the safety-first approach. http://repub.eur.nl/res/pub/12408/ 1996-01-01T00:00:00Z The so-called Hill estimator for the shape parameter of the tail distribution is known to be downwardly biased. The Hill estimator is a moment estimator, based on the first conditional moment of the highest logarithmically transformed data. We propose a new estimator for the tail index based on the ratio of the second to the first conditional moment. This estimator has a smaller bias than the Hill estimator. We provide simulation results that demonstrate a sizable reduction in bias when a is large, while the MSE is moderated as well. The new estimator is applied to stock return data in order to resolve a long standing issue in economics. http://repub.eur.nl/res/pub/12429/ 1991-01-01T00:00:00Z Numerous articles have investigated the distribution of share prices, and find that the returns are fat tailed. Nevertheless, there is still controversy about the amount of probability mass in the tails, and hence about the most appropriate distribution to use in modeling returns. This controversy has proven hard to resolve, as the alternatives are non-nested. We employ extreme value theory, focusing exclusively on the larger observations in order to assess the tail shape within a unified framework. We find that at least the first two moments exist. This enables one to generate robust probabilities on large returns, which put the recent stock market swings into historical perspective.