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### explanation of factor tilts that uses mathematical notation

Can anyone provide a definition of "factor tilt" that uses mathematical notation? Perhaps factor tilts are based on factor regression models. Let's say that our returns vector $\mathbf{y}_t$ can be ...
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I am currently conducting a performance analysis, where I use the 3-, 4-, and 5-factor models, hence $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}HML$ $R_{it}-R_{Ft}=\alpha+b_{i}RMRF+s_{i}SMB+h_{i}... 3 votes 2 answers 2k views ### Portfolio Weights to Maximize Information Ratio (Finding Alphas) In Finding Alphas, Chapter 1, Introduction to Alpha Design, the authors state: An alpha can be represented as a matrix of securities and positions indexed by time. The value of the matrix ... 1 vote 2 answers 2k views ### How do I control for a firm's “factor loadings” based on the Fama French model in a regression model? I asked this question before, but in the wrong community (sorry): I want to explain stock returns in a regression model. Besides regressing against my main explanatory variables, I want to control ... 2 votes 0 answers 481 views ### kalman filter for a multifactor model in R I am trying to set up a time varying factor model for the purpose of return decomposition via kalman filter. Following this example and slightly modifying it so as to accommodate for more than one ... 0 votes 1 answer 5k views ### How can I calculate Fama-French Beta, RMW and CMA factor for a particular stock? I already have a method of calculating Size: the natural logarithm of the market value of equity at the end of the fiscal year. But how to account for the Market Risk Premium, RMW, CMA and MOM ... 3 votes 1 answer 127 views ### How to Cross-Validate whether fund returns are due to static factor exposures? I'm currently dealing with the following problem. I'm using lasso regressions to model hedge fund returns and understand their exposures. The idea being, that if their returns are simply due to ... 2 votes 1 answer 272 views ### Help understanding factor modeling, solving for residuals I am trying to understand and implement a factor model, and I think I might be having some issues. I am trying to solve for the residuals in the equation: $$R_{i} = \sum_{A=1}^{K}\beta_{iA} f_{A} + ... 2 votes 0 answers 307 views ### Fama-French Factors for ETFs and MFs Is there a public source or a paid service that provides FF3 (or FF4 = "Carhart") factor loadings for US traded ETFs and Mutual Funds? Something that is regularly updated and that provides comparable ... 6 votes 0 answers 204 views ### Interplay of statistical factors (PCA) and market factors (value, momentum, low vol, ...) Is there any research done on the interplay between statistical factors (as a result of principle component analysis PCA) and the market factors (especially value, size, low vol, momentum, quality)? ... 3 votes 0 answers 165 views ### Estimating factor returns with linearly dependent loadings Given an n\times 1 vector of asset returns r, and a n\times k matrix of factor loadings X, we can express the asset returns in terms of as-yet-unknown factors f using$$ r = Xf + \epsilon $$... 0 votes 1 answer 266 views ### Factor model to Portfolio optimization By using the Fama and MacBeth methodology, I have identified the significant factors that explain the returns of my stocks. Now, I want to build a portfolio and backtest it. For that, I am trying ... 1 vote 1 answer 1k views ### how can I calculate the factor loading (beta)? I am writing my Thesis about hedge funds performance measurement and I want to use the seven factor model proposed by Fung & Hsieh (2004). Now, I am struggling to find out how to calculate the ... 7 votes 3 answers 5k views ### How to interpret the French-Fama SMB factor? I regressed ten portfolios on the Fama French factors and get significant loadings on the SMB factor. However, if I look at the actual average market cap of these portfolios, the portfolios with the ... 8 votes 1 answer 490 views ### Why is Weighted Least Squares necessary in fundamental factor model? Why is Weighted Least Squares necessary in fundamental factor model while it is not in a standard Macroeconomic factor model? I understand that \mathbb{E}[\epsilon^2_{it}]=\sigma_i^2 varies across ... 1 vote 0 answers 307 views ### Variable Selection with Kalman Filter I'm trying to estimate factor loadings on portfolios over time for portfolios that are traded pretty frequently. I have a sense that several portfolios are loading on the Fama-French HML factor ... 3 votes 1 answer 257 views ### After PCA on original factors, how to tell which original factors are dominant? When doing the PCA analysis, you end up with eigenvalues which are ordered by how much variance they explained for each eigenvector. Say, the eigenvectors since they are orthogonal, do not represent ... 1 vote 2 answers 9k views ### How can I calculate Fama-French betas for a particular stock? For a particular stock, what's the simplest way to calculate betas for the Fama-French factors SMB and HML? 7 votes 2 answers 2k views ### Non-negative matrix factorization for factor analysis of stocks I stumbled over the term Non-negative matrix factorization in presentations such as Application of Machine Learning to Finance and this Big Data in Asset Management. The basic idea is to decompose a ... 1 vote 1 answer 1k views ### Calculating Variance Explained from PCA Loadings I have a return history for a universe of risky assets and I've run a principal component algorithm and obtained a loadings matrix (num_factors by num_assets) for the first 5 factors. I have a ... 4 votes 4 answers 2k views ### Robust Returns-Based Style Analysis Sharpe's Return-Based Style Analysis is an interesting theory but flawed in practice when working with long-short funds or funds that are changing strategies over shorter periods of time due to the ... 1 vote 1 answer 457 views ### How to use financial ratios in a factor model? I am trying to understand how factor loadings in a general factor model are computed. For simplicity sake, lets assume a simple model:$$ R = B \times F + \epsilon  R = N \times 1  B = N \... 2 votes 1 answer 515 views ### Combining covariances? Consider an economy with assets with return processes$A$,$B$,$C$,$D$. Consider a weighted index with return process$I=aA + bB + cC + dD$where$a,b,c,d$are coefficients, and$a+b+c+d = 1\$. ... 11k views

### Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?

There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods: The time-series regression approach of Fama and French. Factors are ...