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Jennifer Bender of MSCI Barra has a paper from 2007 entitled: To Beta or Not to Beta: A Comparison of Historical Versus Fundamental Betas for Hedging Market Risk She deals specifically and exclusively with which method is superior for hedging long-only portfolios. Not surprisingly, she finds that Barra's approach is better. She tests long-only and long-...


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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 ...


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PCA gives you a decomposition of the covariance matrix of the form $$ \Sigma = V \Lambda V^T $$ where $\Lambda$ is diagonal with the eigenvalues in the diagonal. Your portfolio variance is $$ w^T \Sigma w = (V^T w )^T \Lambda (V^T w) $$ On the other hand if you take your return matrix $R$ and define $$ F = V^T R $$ then the covariance matrix of these so ...


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I think the way to see the real effect in a backtest is to produce the distribution achieved with zero skill. You can get one point from this distribution by starting with the same initial portfolio, then do random trading through the time period conditional on obeying the same set of constraints. Do that several times to get the approximate distribution. ...


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On the Expected Performance of Market Timing Strategies, a recent working paper by Hallerbach from Robeco Asset Management, attempts to construct a rigorous framework for evaluating market-timing strategies. We derive expressions for the Information Ratio (IR) that can be expected from market timing strategies in non-parametric and parametric settings. ...


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This question seems rather vague, but I believe what the question can be answered by identifying the portfolio with the largest difference in the portfolio's excess return and the FF3FM expected return after subtracting the risk free rate. If, for example, the model prices the portfolio near the portfolio's actual excess return then you know that the ...


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Not sure what the question is. As John points out: the method is linear regression. For the data you could look at Kenneth French's wegpage for US stocks. In the wikipedia article you find the links to factors for other countries (UK, Germny, Switzerland) - though I have not checked these links. Note however that the Fama-French model works better for ...


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If you are doing something cross-sectional (like Fama-Macbeth regressions) you can just use the ratios where you would put the factor loadings (i.e. betas from the time series regs). You probably want to do some kind of transformation on the ratio to make it well-behaved first though. If you want an actual factor based on the ratio, you can use "factor ...


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When I use PCA, I follow a few typical steps. First, I would apply PCA to the covariance matrix, I would then designate certain eigenvalues as dominant or significant (such as by those that contribute up to $x\%$ of variance or by RMT), and then I would identify the eigenvectors that match up with those significant eigenvalues. I think you're with me at ...


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It is not as simple as changing a value. You need to replace the current factor loadings by feasible values. Furthermore, factor loadings have dependencies between them, that means that when you change one of them, the other factors are affected by this change. In the CCruncher Technical Document there is a proposal to do so. It propose to estimate the ...


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In the chapter that deals with NMF of the book "Programming collective intelligence" , the author did NMF on several stock trading volumes and found some comovement. I googled a little. This did NMF on 40 chinese stock close prices. This developed A variant of nonnegative matrix factorization for Stock Trend Extraction. Another google found this also did ...


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Use monthly returns and follow Ken French's website. RMW, CMA, and MOM are all calculated in depth on a near daily basis. From his Dartmouth data library. MRP Rm-Rf, 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 or 11 at the ...


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Thanks for editing your original post to show that betas are in front of the factors. In factor models, $\beta$ are factor loadings (regression coefficients) while $X$ are factor exposures (independent variables/the data). The model in the paper uses $r_i-r_m$ as factor loadings (premia over some benchmark), while $b_i$ are standardized factor exposures (...


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Portfolio behaving like a small cap portfolio is not necessarily a small cap portfolio. Your regression shows the appearance, not the fundamentals.


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By assuming the procedure you followed in replicate the model is correct and there are not errors in data mining or quality, your findings could be affected and influenced by several reasons. I report as follows those that, according to me, could be the main ones: Data sample: the dataset you used to replicate the Fama-French model could be too little in ...


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There are two main reasons for using weights when estimating factor returns with cross-sectional regressions: a. The 'technical argument': To fix for heteroskedasticity as cross-sectional returns of small companies are more volatile than large ones, so you assign weights for correcting for this fact, hoping that it will be a good proxy for reciprocal of ...


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It sounds like something reasonable/standard to do would be. Sort your companies into five portfolios based upon quintiles of social responsibility. Also make a long-short portfolio of the top quintile portfolio minus the bottom quintile portfolio. (This long-short return will be an excess return so when you run the below regression, you would not subtract ...


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Both of the references below talk about specifically the problem you are looking at and discuss methodologies that might of interest. There has been a lot of work done on replicating hedge fund returns and studying whether they can be explained by common factors. The seminal paper on this topic was written by Andrew Lo Also Andrew Ang, when he was at ...


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You see $(Y,X)$, you want a relation ship between $X$ and $Y$. You will assume Linear regression I.e you assume it exists $\beta$ such that $Y=X\beta + \epsilon$ and you want to find $\beta$. Solution: $\hat{\beta}=(X'X)^{-1}X'Y$ and $\epsilon = Y-\hat{Y}=Y-X\hat{\beta}=(I-X(X'X)^{-1}X')Y$ So if you apply to your case : $X\to B$ $\beta \to f$ $Y\to R$ ...


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Statistically speaking you should not include the factor that aren't significant. Economically speaking you should take all the factors because intuitively they explain the returns of the assets, and if you don't do it will incur in specification bias by omit the factors and will cause the the estimates aren't efficient, unbiased and consistent


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The R function you have to use is the lm() function. On QuickR you can find a simple and clear tutorial on how to estimate a linear (multiple) regression model generally using the lm(). As further reference, I suggest you to read the Introducing R tutorial about linear model by G. Rodriguez. I did not read the paper you cited, but, anyway, you should ...


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There could be a number of reasons, let go over this. First, your sample (the 10 portfolios) might differ from the sample FF used to compute the SMB factor. May be you're using a smaller market or sector? To check this look at the average beta's of your regressions or regress your full sample on the SMB factor. If your market consists of smaller stocks ...


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Thanks for the answers and comments above. In particular to Eric Brady, who had me reading a lot of Bayesian papers. In the end, I think the answer to the question is that on the monthly time-frame robust factor algorithms aren't really necessary. On daily and lower time frames, large spikes in returns due to events (earnings ect.) can really mess with ...


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Whether or not it is flawed in practice depends on dynamic the risk exposures really are. Many factors or indices used for style analysis actually require dynamic trading to maintain - so you could potentially have a fund that trades a lot while still generating a return series that can be be modeled out of sample with static exposures. One relatively ...


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Wikipedia gives: $\sigma(x,y) = E[xy] - E[x]E[y]$ and $\sigma(ax+by,cz) = ac\, \sigma(x,z) + bc\, \sigma(y,z)$ (paraphrasing the $\sigma(ax+by,cW+dV)$ rule). So $\sigma(I,A) = \sigma([aA+bB+cC+dD],A)$ $\sigma(I,A) = a\,\sigma(A,A) + b\,\sigma(B,A) + c\,\sigma(C,A) + d\,\sigma(D,A)$ $\sigma(I,A) = a\,\sigma^2(A) + b\,\sigma(B,A) + c\,\sigma(C,A) + d\,\...


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The "factor loadings" are really the weights attributed to different variables that predict default. If you increase the value of these factor loadings, you increase the prediction of default, thereby making the model more conservative. Whether factor loadings are high enough ex ante is often defined by ex post events. If you had a sample of firms a certain ...


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