Final answer:
The standard deviation of a portfolio is typically less than the weighted average of the standard deviations of the individual securities due to diversification. This is because the formula for portfolio standard deviation includes correlations between the securities.
Step-by-step explanation:
The standard deviation of a portfolio is not necessarily equal to the weighted average of the standard deviations of the individual securities in the portfolio. In fact, due to diversification effects, the portfolio's standard deviation is typically less than the weighted average of the standard deviations of its constituent securities.
This phenomenon is largely due to the covariance between the securities in the portfolio. When combining securities, one must consider both the individual standard deviations and the correlations between the returns of those securities. The reduction in portfolio risk through diversification is a fundamental concept in modern portfolio theory.
To calculate the standard deviation of a portfolio, you need to use the formula that incorporates both the standard deviations of the individual investments and the correlations (or covariances) between the pairs of investments. This is important because the presence of securities with imperfect correlations can reduce the overall risk of the portfolio.
Therefore, the correct completion of the statement would be: 'The standard deviation of a portfolio must be less than or equal to the weighted average of the standard deviations of returns of the individual securities' assuming there are diversification benefits.