Final answer:
The standard deviation of a global minimum variance portfolio with two perfectly negatively correlated securities is always positive or zero, due to the fact that standard deviation cannot be negative and represents the dispersion of data around a mean.
Step-by-step explanation:
If we consider an investment opportunity set formed with two securities that are perfectly negatively correlated, the global minimum variance portfolio constructed from these two securities would have a standard deviation that is always positive or zero. This is because the standard deviation is a measure of the dispersion or variability of a set of data points. Since it represents a square root of variance, the standard deviation cannot be negative. When two assets are perfectly negatively correlated, this implies that as one asset's return goes up, the other's goes down by the same magnitude, which allows for a potential reduction in the portfolio's overall variability. However, due to the nature of standard deviation, the lowest possible value it can reach is zero, where no variability exists between the returns of the two securities.