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2

You can also use the Herfindahl-Hirschman-Index (HCI) as a measure for concentration. In portfolio analysis, you can calculate it as $\frac{1}{N} \leq HCI(x) = \sum_{i=1}^N x_i^2 \leq 1$ where $x$ is a vector of $N$ portfolio asset weights. One can easily see that $HCI(x) = 1$ if 100% is invested in a single asset, and $HCI(x) = 1/N$ if the portfolio is ...

1

Alex C's and Kiwiakos' answers are definitely the most realistic approaches. If you are open to consider also other kinds of risk measures, further alternatives might be thought of. Variance / correlation based approaches interprete "diversification" as how much your assets are heterogeneous from the point of view of deviations from the historical mean. In ...

3

I use the 'implied correlation' defined as $$\rho = \frac{V^2_P-\sum V^2_j}{(\sum V_j)^2-\sum V^2_j}$$ for $V_p$ the VaR (or volatility) of the portfolio, and $V_j$ the VaRs (or volatilities) of the individual components. Essentially it shows what would be the common correlation that I would need to use in order to aggregate the stand-alone risks to the ...

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In 2006 Choueifaty proposed a measure of portfolio diversification, called the Diversification Ratio (DR), which he defined as the ratio of the weighted average of the volatilities of the assets in the portfolio, to the portfolios overall volatility. The DR of a long only portfolio is greater than or equal to one, and equals unity for a ...

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The correlation between the assets in the portfolio will give you a measure of the diversification in the portfolio.

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