|Simulation|Modified VaR| Correlation| Regression| Cholesky Matrix| Distribution| Diversification|
|Skewness| Sharpe| Fund of Funds |4 Moment CAPM| Stress Test| Coskewness| Black-Litterman|
Diversification, a finance concept developed by Markowitz (born August 1927, PhD thesis in 1955, Nobel in 1990), is the basis for portfolio construction, assuming normally distributed assets.  In order to measure if a portfolio is diversified enough, a technique is to 'push' the assets correlation to 1.0 and compare the portfolio with the historical assets correlation and the portfolio with the assets correlation equal to 1.0.  The following formula allows to measure how much the portfolio is diversified (i.e. 100% implies highly diversified, 0% means no diversification):



where Ω is the portfolio covariance matrix and w is the portfolio weights vector.

Computing the rolling diversification ratio allows to visualize if a portfolio has been diversified enough and is worth the fees paid by the investor.  For example, in the graph below (i.e. 100% means a highly diversified portfolio, 0% means no diversification), one could argue this portfolio could and should be better diversified:



The diversification ratio is available in AlternativeSoft platform.