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Title: Black-Litterman model for continuous distributions and general risk measures Authors:  Andrzej Palczewski - University of Warsaw (Poland) [presenting]
Abstract: The Black-Litterman methodology of portfolio optimization combines statistical information on asset returns with investors views within the Markowitz mean-variance framework. The main assumption underlying the Black-Litterman model is that asset returns and investors views are multivariate normally distributed. However, the empirical research demonstrates that the distribution of asset returns has fat tails and is asymmetric, which contradicts normality. Moreover, recent advances in risk measurement advocate replacing the variance by risk measures that take account of tail behavior of the portfolio return distribution. We extend Black-Litterman theory into general continuous distributions with the risk measured by general deviation risk measures. Using ideas from the Black-Litterman methodology, we design analytical and numerical methods (with variance reduction techniques) for the inverse portfolio optimization that extracts in a stable way statistical information from historical data. We introduce a quantitative model for stating investors views and blending them consistently with the market information via Bayes formula. The theory is complemented with the design of efficient numerical methods. We conclude with a number of practical examples that demonstrate significant impact of the choice of istributions on optimal portfolio weights to the extent that the classical Black-Litterman procedure cannot be viewed as an adequate approximation.