Final answer:
In symmetric profit-loss distributions, using the Standard Deviation or the Mean will result in the same risk ranking of uncertain outcomes.
Step-by-step explanation:
If the profit-loss distribution is symmetric, the use of the Standard Deviation turns out to result in the exact same ranking of uncertain outcomes with respect to risk as the use of the Mean. This is because for symmetric distributions, measures of central tendency like the mean are equal to measures of the center of the distribution's spread. The standard deviation is a measure of the distribution's spread, and for a normally distributed set of data, it tells us how much variance there is from the mean.
A few key concepts involved in this question include the expected value or mean, which is the long-term average outcome of a repeated experiment, and the standard deviation, which measures the variability of these outcomes. In symmetric distributions, all measures of central tendency coincide at the same value. Therefore, using either the mean or the standard deviation would result in the same ranking when it comes to evaluating risk.