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1. Determine Factors Economically, the use of factor models can be either motivated using the ICAPM or the APT. Although there are some theoretical differences between the model, for empirical and practical work these differences are irrelevant. In the end, both models stipulate that returns and expected returns are linear functions of the factors: $$ r_{i,...


20

Then for each month $t$, you run a cross-section regression: $r_{i,t} = \lambda_0 + \hat{\beta}_i {\lambda}_t + \alpha_{i,t}$ Where: $\hat{\beta}_i \equiv [\beta_{i, MktRf}, \beta_{i, SMB}, \beta_{i, HML}]'$, is a vector of the coefficients estimated on the first step. What you are looking for is to estimate the vector of $\hat{\lambda}_t \equiv [\...


15

Clarification on the regression coefficients Cochrane (Asset Pricing, rev. edition, 2005) states (p. 247): It it easier to do this in a more standard setup, with left-hand variable $y$ and right-hand variable $x$. Consider a regression $$y_{it} = \beta´x_{it} + \epsilon_{it}$$ $$i = 1,2,..,N$$ $$t = 1,2,...,T$$ [...] In an expected return-beta asset pricing ...


12

The two step Fama-Macbeth regression works as follows: First, run a cross sectional regression in each period. I believe that you want to estimate risk premia for each of the Fama and French factors. Therefore you run: $$r_{i,t} = \lambda_{t,MKT} \hat{\beta}_{i,MKT}+\lambda_{t,HML} \hat{\beta}_{i,HML}+\lambda_{t,SMB} \hat{\beta}_{i,SMB}+ \alpha_{i,t} \quad ...


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This is actually a rather involved question, and different interpretations exist. A narrow, linear algebra based interpretation is that the stochastic discount factor lies in the linear span of the factors. (Recall that a linear asset pricing function implies the existence of a stochastic discount factor.) You can take an expansive, economics based ...


10

The following paper (and the references given within) focuses on the practical aspects of implementation of factor-based investing and gives an overarching framework for the more technical answers here: Practical Considerations for Factor-Based Asset Allocation by Kang, X. (Standard & Poor's), Ung, D. (Chartered Alternative Investment Analyst ...


10

You don't have a GRS test there that all the alphas are zero. You have a $\chi^2$ test that all the alphas are zero. (The p-value associated with that test statistic corresponds to a chi-squared distribution with 25 degrees of freedom. 1 - chi2cdf(81.338394, 25) = 7.029276349879154e-08) Perhaps examine this answer here. Quick review of the F-test (GRS test)...


7

You just need to check the definition of the variable. They basically represent Ordinary common shares (see below the exact definition).


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Time Series Factor modelling is a very good and practical manual to building time series factor models. FactorAnalytics is a very good R package that allows you to fit timeseries, fundamental and statistical factor models. A good reference to factor models would be Chapter 15 of this book.


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The clearest hands-on explanation I have seen so far is the following: Bernstein, W.: Rolling Your Own: Three-Factor Analysis Everything is explained very clearly and step-by-step with Excel. Concerning your question: The R-squared tells you how much percent are explained by the factors. The intercept is your alpha, the coefficients of the factors tell ...


6

To preface, just a minor quibble: French still tracks the momentum anomaly elsewhere on his library, under "Sorts involving Prior Returns"; it's just no longer part of the core FF framework for invalidating the mean-variance-covariance optimized portfolio implied by the CAPM. Originally, Fama-French (FF) developed a three-factor model to invalidate ...


6

No, you cannot interpret the average return for the factor as the risk premium. The second stage regression is equivalent to building a set of portfolios that have no net investment, a unit exposure to one factor and 0 exposure to all others. These unit exposure portfolios are then used to estimate the risk premia for those factors ($\lambda_t$). In that ...


6

How do the investment styles compare? KIS 10 is the only one with substantial exposure to Value and Size, the other two have negligible exposure to these two factors. GS1 is typical of a portfolio of big, growing companies, such as S&P 500, market beta near 1 and with very slightly negative value and size exposure. Most investors hold this kind of ...


6

The factors are not constructed to be market neutral. The factors are constructed from 6 subportfolios sorted by book-to-market and size. You can read more about how the factors are constructed at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_factors.html. Given that the Fama-French factors are long-short portfolios, it might be ...


6

Not exactly. People use those type of models (such as the fama-french model) to evaluate their portfolio. Literally, you run a regression of a stock/portfolio agains the FF factor model to understand if your portfolio beats known risk factors (i.e. whether its $\alpha$ is positive). If the $\alpha$ is negative you are better off taking the money out of your ...


5

There are issues with all three of these. @noob2 has pointed out the inconsistency in the first one. It also uses no subscripts. The second one is probably least wrong. However, there is no index to the error term and no intercept. The third one uses too many indices. It has an index on the intercept and indices on the slopes. Granted, it is possible to ...


5

You're compounding correctly but the discrepancy is not just because of rounding. SMB and HML are formed as averages of 6 and 4 different portfolios, respectively. As French's website explains, this results from cutting all stocks into 2x3 SizexBook portfolios. French compounds each of these portfolios to the proper horizon (eg monthly) and then averages ...


5

Preliminary The main result of the Fama-MacBeth procedure is to calculate standard errors that correct for cross-sectional correlation in a panel. It is a commonly used method due to it's easily approach, and with regards to the time it was developed (1973), modern techniques like clustered robust standard errors were not yet invented. In this context, it ...


5

You say: At this point I don't really get any further, as I am unsure about which "cross section" is being talked about here. Since I have created 25 portfolios, I can only have all in all 25 values in the cross section, right? Isn't that far too little for a sufficient regression? Or do I have to run new time series regressions for each company ...


5

As @skoestlmeier and @noob2 commented there's much research going on about the profitability anomaly. Firstly, there are different ways of measuring profitability. Novy-Marx (2013, JFE) uses gross profitability, Fama and French (2015, JFE) total profitability and Hou et al. (2015, RFS) return on equity. The $q$-theory model from Hou et al. claims to explain ...


4

You are doing it right. The differences are rounding issues and can be safely ignored for any practical purpose.


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First of all, it is not conceivable to do all that work by hand! You are crazy to have just thought it! Second, if you want to repeat your work with different datasets, I suggest you to use R, since, once you have written a script, you can use it all the times you want. But, there's a 'but': you cannot think we are going to write some code for you (you ...


4

Out of curiosity, I took a quick stab at replicating the Fama-French portfolios using CRSP data. I seem to be getting numbers reasonably close to Fama-French, so I think the issue is on your end. It's also possible though the difference is due to using the Russell 1000 rather than the full CRSP universe. That doesn't strike me as crazy. I'm for sure not ...


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In the long run, you'd probably be better off learning a real programming language like Python, R, or MATLAB. While you can do this in Excel using mmult, transpose, and minverse, it's rather horrible. In any case, you should know about the mathematical idea of a matrix, matrix multiplication, and the inverse of a matrix. (Multiplying by the inverse of a ...


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A conceptual problem with ESG as a factor is that ESG criteria seem to me about preferences over how firms operate rather than preferences over when cashflows occur? I don't think this is a strong reason not to go down the road of investigating ESG as a factor, but you'll want to think about how you frame your research question and how you discuss whatever ...


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Just finding factors based on regression is a poor idea. A statistically significant factor in all honesty may mean nothing. Read the fama French original paper, they were not just trying to find factors which explained risk( like in CAPM, beta is a measure of systematic risk), but they were trying to find out factors that provided a "risk premia". There are ...


4

That's indeed a very good question about the Fama-MacBeth approach and i would like to address both questions in separated statements. Fama-MacBeth (1973) - standard errors Your description of the procedure is right in general, so let's directly take a closer look on the cross-sectional regression: At each period of time, a cross-sectional regression is ...


4

Regards FFC, you refer to four portfolios, which are formed by using different weightings: The market portfolio, which is a value-weighted return with end-of-previous market cap. as weights: The excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 ...


4

If you just want to compare the portfolios you could work with a dummy variable (A column in your data which is "1" for the ESG firms and "0" for the non-ESG firms). The regression output will then state the impact of such a variable. Alternatively, if you intend to measure the impact of an ESG-Score/Rating on the individual portfolio constituents, you ...


4

You first run your FF three factor model. And get an estimate of $\alpha$ and $\beta$ for each factor. Then for each month $t$, you run a cross-section regression: $r_{i,t} = \lambda_0 + \hat{\beta}_i {\lambda}_t + \epsilon_{i,t}$ Where: $\hat{\beta}_i \equiv [\beta_{i, MktRf}, \beta_{i, SMB}, \beta_{i, HML}]'$, is a vector of the coefficients estimated ...


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