What is the best way to score a portfolio's diversity based on it's returns covariance matrix?

I know that if my portfolio has two securities and their returns' correlation coefficient is -1 that is a good diversified portfolio. Now I would like to know how do I score a portfolio with more than 2 securities.

If the theory is valid, should I calculate the correlation coefficient of N variables ? What's the formula for that?


1 Answer 1


There are several measures discussed in the literature, the classical approach is Markowitz mean-variance portfolio optimization.

The formula for portfolio return variance is $$\sigma_p^2 = \sum_i w_i^2 \sigma_{i}^2 + \sum_i \sum_{j \neq i} w_i w_j \sigma_i \sigma_j \rho_{ij}$$ where $\rho_{ij}$ are the correlations betweent the assets.

Others suggeste measures are:

  • Normalized portfolio variance (NV), which is obtained by dividing the portfolio variance by the average variance of stock returns in the portfolio: $$ NV = \frac{\sigma^2_p}{\bar{\sigma}^2}$$

  • Sum of squared portfolio weights (SSPW), where $w_i$ is the portfolio weight assigned to stock $i$ in the portfolio and w_m is the portfolio weight assigned by the market (i.e. an index): $$\sum_N (w_i-w_m)^2 $$

For more references, see for example:
Goetzmann and Kumar, Equity portfolio diversification, Review of Finance, 2008
Google will give you a lot of results, I found this Minimum Correlation Algorithm interesting.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.