The Carhart four-factor model is an extension of the Fama-French three-factor model including a momentum factor, also known in the industry as the MOM factor (monthly momentum). Momentum in a stock is described as the tendency for the stock price to continue rising if it is going up and to continue declining if it is going down. The MOM can be calculated by substracting the equal weighed average of the highest performing firms minus the equal weighed average of the lowest performing firms, lagged one month (Carhart, 1997). A stock is showing momentum if its prior 12-month average of returns is positive. Similar to the three factor model, momentum factor is defined by self-financing portfolio of (long positive momentum)+(short negative momentum).
The four factor model is commonly used as an active management and mutual fund evaluation model.