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Abstract: In this article we demonstrate that the optimal portfolios generated by the Black-Litterman asset allocation model have a very simple, intuitive property. The unconstrained optimal portfolio in the Black-Litterman model is the scaled market equilibrium portfolio (reflecting the uncertainty in the equilibrium expected returns) plus a weighted sum of portfolios representing the investor's views. The weight on a portfolio representing a view is positive when the view is more bullish than the one implied by the equilibrium and the other views. The weight increases as the investor becomes more bullish on the view, and the magnitude of the weight also increases as the investor becomes more confident about the view.
Baysian, Black-Litterman model, CAPM, mean-variance analysis, portfolio selection
Abstract: We solve the problem of constructing an optimal portfolio consisting of many risky assets to maximize the long-term growth rate of a representative agent's expected utility, subject to a set of general linear constraints on the portfolio weight vector as well as a constraint to prevent wealth drawdowns below a dynamic floor. The dynamic floor is defined as the time-decayed historical all-time high. Our results generalize those achieved by earlier authors, including Grossman and Zhou (1993) and Cvitannic and Karatzas (1994). Grossman and Zhou solved a special case of our problem by focusing on a single risky asset without portfolio weight constraints. Cvitanic and Karatzas solved a problem involving many risky assets but that ignored portfolio weight constraints and the time decay on the dynamic floor. To illustrate the usefulness of our method, we present several numerical examples based on both actual and simulated (Monte Carlo) returns. Finally, we suggest applications of our results to various practical investment management problems, including the management of hedge fund portfolios and 'principal-protected' investment strategies.
drawdown, optimal portfolio, dynamic programming, linear constraints
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