Final answer:
The statement is false; a positive correlation between two securities does not guarantee the portfolio's standard deviation will be lower than the weighted average of the securities' individual standard deviations.
Step-by-step explanation:
The statement is false. If the correlation between two securities is positive, it does not necessarily mean that the standard deviation of their portfolio is less than the weighted average of the standard deviations of the individual securities. In reality, the total risk (or standard deviation) of a portfolio considering two assets with a positive correlation could be higher or lower depending on the degree of correlation.
If the assets are perfectly positively correlated (correlation coefficient of +1), the standard deviation of the portfolio would be a weighted average of the individual standard deviations. However, if they are less than perfectly correlated, diversification benefits come into play and can reduce the portfolio's total risk below the weighted average of the individual securities' standard deviations. Nevertheless, a positive correlation implies that the securities' returns move in the same direction, which limits the diversification benefits.