What is variance? How is ex-ante and ex-post variance calculated?

 What is variance? How is ex-ante and ex-post variance calculated? 

Ans. Variance is a measure of the dispersion in outcomes around the expected value. It is used as an indication of the risk inherent in the security. Standard deviation is the square root of variance. 

Ex-ante variance calculation The expected return is subtracted from the return within each state of nature; this difference is then squared. Each squared difference is multiplied by the probability of the state of nature. These weighted squared terms are then summed together

Ex-post variance calculation: The average return is subtracted from each single period return; this difference is then squared. The squared differences are summed. This sum is divided by the number of periods (using population data) or the number of periods minus 1 (using sample data).