Editing Modern portfolio theory (section)

===Diversification===
{{unreferenced section|date=April 2021}}

An investor can reduce portfolio risk (especially <math>\sigma_p</math>) simply by holding combinations of instruments that are not perfectly positively [[correlation|correlated]] ([[Pearson product-moment correlation coefficient|correlation coefficient]] <math>-1 \le \rho_{ij}<  1</math>). In other words, investors can reduce their exposure to individual asset risk by holding a [[Diversification (finance)|diversified]] portfolio of assets.  Diversification may allow for the same portfolio expected return with reduced risk. 
<!-- The mean-variance framework for constructing optimal investment portfolios was first posited by Markowitz and has since been reinforced and improved by other economists and mathematicians who went on to account for the limitations of the framework. -->

*If all the asset pairs have correlations of 0 — they are perfectly uncorrelated — the portfolio's return variance is the sum over all assets of the square of the fraction held in the asset times the asset's return variance (and the portfolio standard deviation is the square root of this sum).

*If all the asset pairs have correlations of 1 — they are perfectly positively correlated — then the portfolio return's standard deviation is the sum of the asset returns' standard deviations weighted by the fractions held in the portfolio. For given portfolio weights and given standard deviations of asset returns, the case of all correlations being 1 gives the highest possible standard deviation of portfolio return.