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PCA for portfolio optimization (Markowitz)

Suppose that I've used the spectral theorem of linear algebra to completely decompose the covariance matrix. I now know the largest and smallest eigenvalue, which corresponds to the largest and ...
Marlon Brando's user avatar
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PCA 'unnormalize' weights

When computing a PCA on several prices, we usually normalize them first. Let's say I got the weights (eigenvectors) for the PC5. This weights are made from normalized prices. If I believe PC5 is too ...
Felipe Cancela's user avatar
6 votes
1 answer

Markowitz Eigenvalues & PCA

I came across this passage in a book about PCA and denoising of Markowitz: But eigenvalues that are important from risk perspective are least important ones from portfolio optimization perspective. ...
Markowitz's user avatar
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Why cant I use PCA to find all stock factors? [closed]

Why cant I run all the stocks in the stock market thru a PCA model, and use the resulting principal components to create a factor model to price stocks and then buy stocks under priced and short ...
Matthias Tom's user avatar
2 votes
1 answer

How to extract normalised portfolio weights from PCA, when the eigenvector has negative elements?

Most of the examples of using PCA of asset returns to construct an eigen portfolio seem to tend to focus on equities, which tend to all be positively correlated. As such I usually see normalised (such ...
rwb's user avatar
  • 123
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Terminology - are each of the eigenvectors of a PCA themselves called an "eigen portfolio"

Sorry, I suspect this is rather trivial but just want to confirm that, given a portfolio constructed of n assets, each of the n ...
rwb's user avatar
  • 123
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Choose the best combination of 5 stocks from 15 stocks using PCA

I am working on a project to choose the perfect combination of 5 stocks from a total of 15 stocks to get the "highest gains". Here's the approach I plan to use. Run a loop for all ...
atastix's user avatar
  • 85
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0 answers

Calculating the eigenvector centrality of a portfolio described by a minimum spanning tree

I am working with the eigenvector centrality of a minimum spanning tree, which can be calculated as: v(i) = lambda^-1 * sum[Omega(i,j)*v(j)] where: ...
Vitomir's user avatar
  • 821
4 votes
1 answer

Why the weight vector of 'global minimum variance' the 'eigenvector' with the minimum eigenvalue?

Question Why is it the case that the weight vector of the global minimum variance portfolio the eigenvector of the covariance matrix with the smallest eigenvalue? Question with more details I ...
Eiffelbear's user avatar
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1 answer

Why are my eigenvalues coming out negative for my positive definite covariance matrix?

I have a 51 x 51 covariance matrix that is derived from historic forward rates that is positive definite. I know it is because in Python np.cholesky returns a correct cholesky decomposition. However, ...
M Thomas's user avatar
3 votes
2 answers

Filtering smallest eigenvalues

In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
Hans-Peter Schrei's user avatar
4 votes
1 answer

Interpreting Eigenvalues of Co-variance Matrix

Im working on market reaction to events and I'm using the co-variance matrix to do this. In this paper the author writes It has been known for some time that the largest eigenvalue (λ1) contains ...
MosesA's user avatar
  • 143
2 votes
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What is PCA and how does it relate to eigenvectors and eigenvalues?

What are the principal components? How they are calculated? What is their relationship with eigenvalues and eigenvectors? This is a lead-in question to explain PCA basics. EDIT: PCA is implemented ...
user12348's user avatar
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11 votes
1 answer

What do eigenvalues/eigenvectors of the yield/forward rates covariance matrices mean?

I have 5 bonds (with maturities 1,2,3,4,5 years) which I calculated the yield curve for 10 days. I also calculated the forward rates from the yield rates. Now I've been told to calculate the ...
Louise's user avatar
  • 351
5 votes
0 answers

Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
Geraldine Bailey's user avatar