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6

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 ...


6

Glad people are reading. Simple with more history in terms of time and indexes is better in my book. I have spent 13 years reading over 200 research papers, incorporating complicated and advanced techniques, and studying very reputable buy side research with no improvement in results. Readers are on their own to extend to lots of markets including Nikkei ...


5

I don't think risk factors are that important here. This is a simple market timing strategy where you're either fully exposed to the market or not exposed at all. All he needs to show is that he's adding value above buy-and-hold by all of the in-and-out trading.


5

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 ...


4

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. ...


4

"Factor loading" is a somewhat ambiguous phrase -- it could refer to the factors in a linear model (e.g. the beta in CAPM or extended linear stock models), the factors of principal component analysis, etc. If you could provide a reference to the exact example/paper it would be clearer. In credit, however, a likely interpretation is the loadings of different ...


2

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 ...


2

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 ...


2

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 ...


1

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 ...


1

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. ...


1

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 ...


1

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 ...


1

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) + ...


1

In many popular copula models a factor driving a certain even (e.g. default) has the form $ Y_i = \sum_k a_{ik} X_k + b_i Z_i $ where $\lbrace X_k \rbrace, Z_i$ are independent random factors. Coefficients $a_{ik}$ and $b_i$ are commonly called "factor loadings".



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