The expected return of a portfolio is the weighted average of the expected returns of the securities that comprise it. However, the risk of a portfolio is a function of three factors:

• the relative weights of each of the assets which comprise the portfolio,
• the volatility of each of the portfolio's components as measured by the standard deviation of returns, and
• the correlation of the returns between each pair of assets which comprise the portfolio.

Analysts and academics use several tools to facilitate the evaluation of portfolios, one being the normality assumption. The normality assumption indicates that the returns on a security are clustered around a single number. Statisticians call this the central tendency towards the mean or average. This normality assumption allows an investor or portfolio manager to make selections of securities based on only two criteria: the expected return of the security, and the standard deviation of the security's return.

Standard deviation is a measure of the expected deviation or variability of returns in relation to the expected return. Standard deviation is a statistical measure of the spread of the security's returns. As a general rule, the higher the standard deviation, the higher the total risk of a security or a portfolio.

The standard deviation of a portfolio is always less than or equal to the weighted average of the standard deviations of the component securities.

The standard deviation of a portfolio can be calculated from the standard deviations of the individual securities that make up the portfolio. Even if the return distributions of the individual securities within a portfolio are not normally distributed, as the total number of securities held in the portfolio increases, the distribution of the portfolio's return tends towards normality.