When examining the performance of mutual fund managers, academic researchers focus on abnormal (risk adjusted) returns rather than raw returns. Abnormal return is defined as the return earned by a manager relative to the return expected to be earned given the risk level chosen by the manager. Often, in both academic studies and the popular press, a fund’s abnormal return is referred to as alpha. As defined, a manager that generates a positive abnormal return is considered to be skilled at portfolio management.   

            In order to estimate a fund’s abnormal return, one must first have a model that quantifies the risk return relationship from investing in various sectors of the stock market. In this study, Carhart defines a model which includes four risk factors that explain the future expected return of any individual stock. Given that mutual funds represent a portfolio of individual stocks, the four factors together can provide an estimate of the expected return of the portfolio selected by the fund manager. The four factors included in the model are 1) the market factor - the return of all NYSE, Amex, and Nasdaq stocks in excess of the one month Treasury bill return, 2) the size factor - the average return on small market capitalization stocks minus the average return on large capitalization stocks, 3) the book to market factor - the average return on value stocks minus the average return on growth stocks, and 4) the momentum factor - the average return of stocks with the highest returns over the previous year minus the average return of the stocks with the lowest returns over the same period. 

            The logic behind the model is that a manager should not be rewarded simply for following various elementary stock picking strategies that could be mimicked by individuals with little financial knowledge. Thus, a manager is considered to be skilled at portfolio management only if the return he earns is greater than the expected return given the characteristics (i.e. risk) of the stocks held in his portfolio. Empirically, abnormal performance is measured by regressing a fund’s returns against the contemporaneous returns of the four risk factors.  The intercept of the regression represents the fund’s abnormal return.

            The Carhart model is an extension of the Capital Asset Pricing Model (CAPM) and the Fama French model which have been used historically to measure abnormal return. The CAPM explained returns using only the market factor while the Fama French model added the size and book to market factors to the CAPM. In this study, Carhart compares the relative effectiveness of the three models. Specifically, he examines how well each of the three models predicts the future returns of portfolios of NYSE, Amex, and Nasdaq stocks. He demonstrates that his model is significantly better at explaining both the future cross section and time series variation in the returns of the portfolios. Thus, this model has become widely accepted in academic circles and is almost always used by researchers when examining mutual fund performance.