Final answer:
Variance is a measure of dispersion and cannot be negative as it represents the average squared deviations from the mean. Expected return and correlation can be negative, with the latter ranging between -1 and +1, representing inverse or direct relationships between variables.
Step-by-step explanation:
The question relates to different statistics that are used in finance and investments. The statistic that cannot be negative is variance. Variance is a measure of the dispersion of a set of data points around their mean value. By its definition, variance cannot be negative because it is calculated as the average squared deviation from the mean, which results in a positive number or zero. The other options, expected return and correlation, can indeed be negative. An expected return can be negative, indicating a loss rather than a profit. A correlation can range from -1 to +1, where a negative correlation implies that the variables move in opposite directions, and a positive correlation implies they move together.
When it comes to correlation, a positive correlation suggests that as one variable increases, so does the other, and vice versa. Conversely, a negative correlation suggests that as one variable increases, the other tends to decrease. However, as stated, variance differs from these because it represents the spread of a dataset and is always non-negative.