2. A sufficient condition to produce positively weighted efficient portfolios is that the variance-covariance matrix be diagonal, that is, that σij = 0, for i≠j. By continuity, positively weighted portfolios will result if the offdiagonal elements of the variance-covariance matrix are sufficiently small compared to the diagonal. Consider a transformation of this matrix in which When ε = 1, this transformation will give the original variance-covariance matrix, and when ε = 0, the transformation will give a fully diagonal matrix.
For r = 10 percent find the maximum ε for which all portfolio weights are positive.