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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: $$r_{i,... 13 Clarification on the regression coefficients Cochrane (Asset Pricing, rev. edition, 2005) states (p. 247): It it easier to do this in a more standard setup, with left-hand variable y and right-hand variable x. Consider a regression$$y_{it} = \beta´x_{it} + \epsilon_{it}i = 1,2,..,Nt = 1,2,...,T$$[...] In an expected return-beta asset pricing ... 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 ... 9 There is no definitive answer to this question and there are infinite papers out there. I personally think they are better explained as mispricings. Several points: 1) Persistence of HML does not imply it has to be a risk factor. If there are idiosyncratic mispricings in individual stocks, then by construction, the ones that look cheap are going to be ... 9 Don't just run simple time-series regression to see if you get statistically significant betas. This procedure will not tell you if the factors are actually priced. You run a high risk of finding spurious correlations. There is a fairly well established standard program to test factor models, called the Fama-MacBeth method. It is based on two sets of ... 8 It appears that you are re-running the regression with each new data point. Instead, you should use an update/online formula (see an excellent answer by the famous Dr. Huber at stats.se). You can find an implementation in the R package biglm. If it doesn't have all the features you need (no windowing out of old data) you can at least adapt it and use it ... 8 Glad you've asked :) Technically speaking, in factor model \alpha stays for return or risk premia, which asset pays when all factor returns are zero. Then, to answer question in more details, we have to specify, are we dealing in our model with return (R_i for asset i) or with risk premia over risk free (R_i-R_f). In the first case, ... 8 The best overview I have seen so far is this paper which lists 214 (!) factors (or anomalies if you like) on over one hundred (!) pages: Harvey, Campbell R. and Liu, Yan and Zhu, Caroline, …and the Cross-Section of Expected Returns (February 3, 2015). Available at SSRN: https://ssrn.com/abstract=2249314 or http://dx.doi.org/10.2139/ssrn.2249314 Abstract: ... 8 Different portfolio risk decompositions answer different questions. Before discussing what method to use, first ask why you want a decomposition and what definition of risk are you using. Is the point to examine how portfolio return volatility is affected by a tiny change in portfolio weights? On the other hand, if the point is to make a statement like, "30%... 7 Quant investing has the same basic problem as any approach to asset management: capacity for capital invested. Unlike quant trading, quant investing deals with large assets. For this reason, the type of arbitrage opportunities pursued by quant traders are not feasible for investing - those strategies simply do not have the capacity necessary for asset ... 7 You might want to read this: Size, Value, and Momentum in International Stock Returns by Fama and French (2011) Abstract: In the four regions (North America, Europe, Japan, and Asia Pacific) we examine, there are value premiums in average stock returns that, except for Japan, decrease with size. Except for Japan, there is return momentum everywhere,... 6 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. 6 What you're describing sounds like the reverse of a Fama-Macbeth regression. The original Fama-Macbeth approach estimated rolling time series regressions to get CAPM betas and then doing a cross-sectional regression to estimate the overall sensitivity of returns to beta. If I were to write down what the model looks like, I think you're talking about ... 6 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 AP factors do not need to be excess returns. In case they are, corresponding prices of risk are conveniently equal to average factor values, since "factors price themselves":$$E[R_i] = \beta_{i} \cdot \lambda_f, \\ E[f] = 1 \cdot \lambda_f, \\ \Leftrightarrow \\ \lambda_f = E[f],$$where there is just one factor f, \beta_i is the loading of asset i ... 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 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 This isn't exactly what I would call advanced but running each regression on a separate core in a parallel foreach loop would help http://cran.r-project.org/web/packages/foreach/foreach.pdf 5 This is the question I've been waiting for! I work at a large outsourced CIO shop and spend a lot of time evaluating different managers and the strategies they come to us with. I also know a number of people I went to school with that are now at quant funds. There are a couple of important points to keep in mind: Every respectable quantitative manager has a ... 5 There's always a balance between model complexity and interpretability. Of course, it'll be great if we can perfectly capture the comovement of all the bonds in the deliverable basket, but that would require the volatilities of all the bond's yields and the correlations amongst all these bonds as well -- it's not easy to come up with reliable assumptions for ... 5 I would say the main difference between "risk factor" and "market anomaly" is that people demand to be compensated for risk and because there are different kinds of risks these can be systematized into risk factors whereas anomalies are results of behavioral biases. Another big difference would be that risk factors will stay because of the need for ... 5 You have started a huge job, an enormous number of anomalies have been reported. The web site quantpedia.com has a list, here for example is their writeup on momentum effect in stocks 5 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 ... 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 ... 4 In the following paper: "On the Cross-Section of Expected Stock Returns: Fama-French Ten Years Later" (by Chou, Chou, and Wang), the authors found, using the Fama-Mac Beth two-pass regression, that the size effect becomes insignificant during the post-1981 period, and the Book/Market effect becomes insignificant during the post-1990 period. It is important ... 4 There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ... 4 Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ... 4 Following @silencer's comment, your formula for variance is wrong. I would suggest that instead of trying to re-invent the wheel, you just use the formula that everyone else uses. So I'd replace your first indented line with$$ w^{*}\equiv argmin\left\{ \frac{1}{2}w'\varSigma w-\lambda\left(w'\mathbf{1}-1\right)\right\} $$which will give you$$ w^{*}=\...