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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 The regression requires orthogonalization of factors. However, we need to maintain the interpretation of factors (so PCA and Factor Analysis are out). Also, we could apply an iterative method (indeed this is very common practice) but this will bias the factor loadings on the sequence of factors. Best approach is that of Klein and Chow in their paper ... 10 Here is a structured list of your bullet points: covariance, correlation, PCA, factor analysis, Are similar. They are based on Gaussian assumptions (i.e. correlations means dependencies) and try to identify common factors (i.e. a variable in small dimension) explaining the observed relationships. co-integration is more specific in the sense that you ... 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: ... 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,... 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 ... 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 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 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%... 6 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 ... 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 ... 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 The first principal component of a large covariance matrix is extremely expensive to replicate in a real portfolio. While it is true principal components provide true (ex post) orthogonal factors, this is not necessarily relevant to the business of risk management. The market index is what most investors are benchmarked by, and is furthermore often ... 5 a) because it does not matter how you weigh each constituents as long as the methodology is publicly accessible and as long as it more or less reflects the original intent. That is why there are market cap weighted indexes but also why there are indexes that apply different weighting methodologies. b) because PCA is computationally way more expensive. Why ... 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 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 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 ... 5 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],$$where there is just one factor f, \beta_i is the loading of asset i ... 4 In the following paper: "On the Cross-Section of Expected Stock Returns: Fama-French Ten Years Later" (by Chou, Chou, and Wang), the authors found, using the Fama-Mac Beth two-pass regression, that the size effect becomes insignificant during the post-1981 period, and the Book/Market effect becomes insignificant during the post-1990 period. It is important ... 4 Most of the credit risk models are some derivative of survival models. Cox Proportional Hazard is one of the early and more popular models, Kaplan-Meier and Logrank tests are others you may have heard of. There are a few ways to go from here. The simplest is to model the sample as binomial with one population as current and the other as in default. A ... 4 There are a few reasons to use factor models. Most importantly, stocks tend to move together. Stated alternately, the first principal component of the securities in a domestic market tends to explain a large share of the variance. If you're concerned with multiple securities (as in portfolio optimization), then you have to account for this or you will ... 4 Portfolio returns are analyzed to account for risk factors only to determine what the risk factor contributed to the returns, was it the underlying assets or the skill of the portfolio manager. Fama French model explains the returns in terms of principal component such SMB and HML besides the market related returns from CAPM. These links have more detais ... 4 Following @silencer's comment, your formula for variance is wrong. I would suggest that instead of trying to re-invent the wheel, you just use the formula that everyone else uses. So I'd replace your first indented line with$$ w^{*}\equiv argmin\left\{ \frac{1}{2}w'\varSigma w-\lambda\left(w'\mathbf{1}-1\right)\right\} $$which will give you$$ w^{*}=\...