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  Volume 5, Issue 1, Article 16
Lower Bounds On Products Of Correlation Coefficients

    Authors: Frank Hansen,  
    Keywords: Correlation coefficient, Bessis-Moussa-Villani conjecture, Robust portfolio.  
    Date Received: 23/06/03  
    Date Accepted: 17/02/04  
    Subject Codes:

46C05, 26D15

    Editors: Neil S. Barnett,  

We consider square integrable stochastic variables $ X_1,\dots,X_n $ without imposing any further conditions on their distributions. If $ r_{i,j} $ denotes the correlation coefficient between $ X_i $ and $ X_j $ then the product $ r_{1,2}r_{2,3}\cdots r_{(n-1),n}r_{n,1} $ is bounded from below by $ -\cos^n(\pi/n). $ The configuration of stochastic variables attaining the minimum value is essentially unique.

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