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Fama-French regression is a statistical technique used to analyze the relationship between security returns and various factors that may affect those returns. It was developed by economists Eugene Fama and Kenneth French in the 1990s, and has become a widely used tool in finance and investing.
The Fama-French model is based on the idea that the returns of a security, such as a stock or bond, are influenced by several factors beyond just the overall market. For example, a company's financial health, management team, and industry conditions can all impact the performance of its stock. The Fama-French model seeks to identify and quantify the influence of these "non-market" factors on security returns.
To perform a Fama-French regression, analysts begin by collecting data on the returns of the security or portfolio they are interested in analyzing. They also collect data on a number of potential explanatory variables, such as the size of the company, the book-to-market ratio (which compares the company's book value to its market value), and the company's beta (a measure of its risk relative to the overall market).
The analysts then use statistical techniques, such as linear regression, to determine the relationship between the security returns and the explanatory variables. The goal is to find the combination of variables that best explains the returns of the security.
One key insight of the Fama-French model is that small, value-oriented companies tend to outperform large, growth-oriented companies. This finding is known as the "small-firm effect" or the "value premium." It suggests that investors may be able to earn higher returns by focusing on smaller, undervalued companies rather than chasing after the biggest, most popular firms.
Another important insight from the Fama-French model is that the performance of a security is not solely determined by the overall market. Instead, other factors, such as a company's financial health and industry conditions, can also play a significant role. This finding has important implications for investors, as it suggests that they should consider a wide range of factors when evaluating potential investments, rather than relying solely on market movements.
In summary, Fama-French regression is a powerful tool that allows analysts to better understand the factors that influence the returns of securities. By identifying the variables that drive returns, investors can make more informed decisions about which securities to include in their portfolio.
Fama and French Three Factor Model Definition: Formula and Interpretation
Finally, we want only the FF factor data that aligns with our portfolio data, so we filter by the first and last date in our portfolio returns object. Then, you'd simply interpret the model outputs. Over all economic cycles since 1963, going long high quality stocks, or profitable firms, and shorting their low quality, unprofitable counterparts has been a great investment strategy. We refer to Gagliardini, Ossola, and Scaillet Hou, Xue, and Zhang The current chapter relies on this set of packages. Sometimes two data sets are thrown at us and we have to wrangle them from there. My view was a little more simple. What Is the Fama and French Three Factor Model? Furthermore, we also use the CAPM betas based on monthly returns we computed in the previous chapters.
Besides these outputs,the other miscellaneous pieces of information from the regression output are not-as-important to analyze and therefore will not be discussed in this article. Therefore, select these three columns and the same exact date range as the dependent variable. This is what's referred to as the " The single index model is identical to the " What's important here is that the FFTFM size and value factor. There has also been Regardless, although the FFFFM has its clear limitations and is not yet a proven universal model, the five-factor model still explains between 71-94% of the cross-section variance of expected returns. If you are testing the reaction of investors to realized vol, then you can just do a 21-day moving average realized vol or some backward-looking measure. If not, whatever this model does not capture will be absorbed into the firm's alpha or residuals, as discussed below , which will indicate a persistent firm-specific factor that investors are looking for. This also makes sense given that Home Depot has a strong balance sheet and is not really considered a growth stock.
After backtesting a lot of different portfolios, my conclusion is that more often than not, few years make big differences in long term, and sectors tend to perform very different in different market conditions. Newey and West Whitney K. In your regression, the average residual should be zero. Factor 3: Book-to-Market Value The book-to-market value factor, also known as HML high minus low is equal to the difference in returns between portfolios of high and low book-to-market firm. The fifth factor, referred to as "investment", relates the concept of internal investment and returns, suggesting that companies directing profit towards major growth projects are likely to experience losses in the stock market.
How to Calculate and Interpret the Fama and French and Carhart Multifactor Models
The Fama and French Three-Factor Model or the Fama French Model for short is an asset pricing model developed in 1992 that expands on the capital asset pricing model CAPM by adding size risk and value risk factors to the market risk factor in CAPM. Fama and Kenneth R. The application on thin trading also applies to this model as well. Carhart Four Factor Model In 1997, Mark Cahart momentum factor added. Afterwards, you'd solve for the FFTFM using its formula.
Absent specific reasons to believe that an investment will outperform or underperform the market, the alpha is generally not used in predictive Fama-French Three Factor models. CMA Cumulative Returns Which brings us to the quality factor, or RMW. To further understand the three risk factors of the FFTFM market, size, and value , see the sections below. RMW is the single factor that has consistently delivered excess returns. Reference the entire residuals column when doing so.
We can use the lubridate package to parse that date string into a nicer date format. Question 1: The Picture below is a screenshot of the monthly returns for the 25 portfolios sorted on size and Book-to-market value obtained from French's website. The Lambdas are the risk premia of the factors, right? The HML factor of 1. The Fama and French Three Factor model highlighted that investors must be able to ride out the extra volatility and periodic underperformance that could occur in the short term. However, you can take the standard deviation of these residuals, or even the variance of these residuals standard deviation is just the square root of variance , to evaluate yield idiosyncratic volatility. In fact, that formula is used as the basis for the Fama-French Three Factor model.
Otherwise, the next step may be to estimate vol using a GARCH model to better capture the persistence of realized vol in the future. If momentum is an important driver of stock returns and you've omitted this from the model, then you'll end up with a misleading alpha, which could be the case with the FFTFM. An excess return is the result of going long one portfolio return and short another such as risk risk free rate. This will be a step-by-step instruction. To reiterate, Fama and French put forth the argument that over the long-term, returns are higher on smaller firms versus large firms, as well as higher on value high book-to-market firms versus growth low book-to-market firms.
The FFFFM then goes even further by adding a profitability and investment factor, in an attempt to further explain the drivers of stock market returns. Note that the section below is a summary of my more in-depth article on the CAPM, which shows you how to calculate and interpret the CAPM following a similar format to this article. Through expanding on the Capital Asset Pricing Model CAPM , which proposes beta is its only risk factor and driver of stock market returns, these multifactor models have been able to improve the understanding on what contributes to stock market returns. To assist in this instruction, I've provided a completed Excel sheet model below: In short, to calculate any multifactor model on Excel, you regress the firm's risk-free adjusted returns onto the returns associated with the factors of the particular model. Step 2: Run a Regression Analysis The second step is to simply run a regression on the data set you just put together, given that you now have all of the inputs required to calculate the FFTFM. Newey and West NeweyWest. This factor is also referred to as the "monthly momentum factor" MOM or the "up-minus-down" UMD factor.