The assumptions are – asset returns are described by a factor model, asset-specific risk can be eliminated, as there are multiple assets, and assets are priced in a way such that no arbitrage opportunities exist. It is similar to the CAPM model but with less strict assumptions. The arbitrage pricing theory (APT) is a model that is used to describe the expected return of an asset or portfolio as a linear function of the risk of the assets relative to certain factors. Given the number of factors, the Fama-French five-factor model is, at times, not practical to be implemented in certain economies. It is typically negatively correlated with the value factor. The investment factor recognizes the level of capital investment used to maintain and grow the business. It uses the return of stocks with high operating profitability minus the return of stocks with low or negative operating profitability.Īt times, the factor is replaced by a quality factor. The Fama-French five-factor model also builds on the three-factor model and introduces two more factors – Profitability (RMW) and Investment (CMA). The Cahart model is considered a superior one, given its explanatory power of around 95%. It is a bit controversial, as it uses risk-based, as well as behavioral-based, explanations to determine returns. ![]() The concept of the momentum of an asset can be used to predict future asset returns. The Cahart model builds onto the Fama-French three-factor model and introduces a fourth factor called momentum. R Mt – R ft= Excess return on the market portfolio (index).R ft= Risk-free rate of return at time t R Mt= Total market portfolio return at time t.R it = Total return of a stock or portfolio i at time t.The formula for the Fama-French three-factor model is given in the equation below: SMB characterizes publicly-traded companies with small market caps that generate higher returns, and HML uses value stocks with high book-to-market ratios that generate higher returns relative to the market. The Fama-French model employs three factors – namely SMB (small minus big), HML (high minus low), and the portfolio return minus the risk-free rate. It is a better approach than the Capital Asset Pricing Model (CAPM), as CAPM only explains 70% of a portfolio’s diversified returns, whereas Fama-French explains roughly 90%. Fama-French Three-Factor Modelįama-French uses the factors of size and value to derive asset returns. Below, we will discuss three different types of multi-factor models and their relevant factors used to derive returns: 1. The construction of multi-factor models is an interesting process, and over time, several different types of models have emerged in the field of finance. In statistical factor models, statistical methods are applied to historical data of returns and are used to explain covariances in data. Fundamental factor models use asset returns, and after determining the factor sensitivities, the returns are calculated by running regressions. Examples of such factors are price-to-earnings ratio, market capitalization, and financial leverage. In fundamental models, the factors are characteristics of stocks or companies that can be used to explain the changes in stock prices. The surprise or incremental return can be calculated as the actual value less the forecasted value, and the mean of the return is typically zero. In macroeconomic factor models, the factors are associated with surprises in macroeconomic variables that help explain returns of asset classes. ![]() Broadly, three types of multi-factor models can be classified based on the type of factors employed: 1. Multi-factor models can be used in all industries, be it finance, economics, or mathematics.
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