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I think you might be looking for the portfolio return variance: $$\sigma_p^2 = \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij},$$ where $\rho_{ij}$ is the Pearson product-moment correlation coefficient between the returns on assets $i$ and $j$ and $\rho_{ij} = 1$ for $i=j$. In your case you could either weigh the assets equally or according to the real ...


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If you measure risk by the standard deviation of the portfolio return $$ \sigma = \sqrt{w^T \Sigma w}, $$ then it is usual to define risk contributions for each asset by $$ \sigma_i = w_i (\Sigma w)_i/\sigma, $$ then diversified could mean that these $\sigma_i$ are evenly spread over the assets in the portfolio. You find this approach and more in this paper ...


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This paper uses the following diversification measures to measure the diversification of retail investors: Normalized portfolio variance: $$ NV = \frac{\sigma_p ^2}{\bar{\sigma} ^2} $$ Sum of Squared Portfolio Weights (SSPW). Since the weight in the market portfolio is very small diversification could be approximated by the sum of squared portfolio ...


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In their paper on their S&P 500 Implied Correlation Index the CBOE has defined a measure for the market-capitalization weighted average correlation of the S&P 500 index which could be applied to portfolios in general. The equation $$ \rho_{av} = \frac{\sigma^2 - \sum_{i=1}^N w_i^2\sigma_i^2}{2 \sum_{i=1}^N \sum_{j>i}^N w_i w_j \sigma_i ...



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