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11 votes

Markowitz Eigenvalues & PCA

The main problem stems from the case opposite of the one that you are focusing on: The inversion of the covariance matrix leads to a situation where the smallest eigenvalues of the covariance matrix (...
Hans-Peter Schrei's user avatar
8 votes
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What is the textbook answer to dealing with multicollinearity?

As one of the interviewers suggested, the expected answer starts with PCA and SVD. Before detailing it, let's take a paragraph about the way you seem to "misunderstand" the problem: ...
lehalle's user avatar
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6 votes
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Principal Components Analysis on overlapping contracts

I would do as follows: A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out ...
ZRH's user avatar
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6 votes
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Interpreting Eigenvalues of Co-variance Matrix

What you basically do here is a Principal Component Analysis (PCA). A good starting point in the financial sphere is Managing Diversification by Attilio Meucci (2010) Page 3: "The most natural ...
vonjd's user avatar
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6 votes
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Hedging a trade for PCA component neutrality

Simple Directionality Spread Trade Hedge If the sum of the risks of the trade $t$ are zero (as in the case of the 2Y5Y10Y spread trade) that immediately gives a starting point from which to make a ...
Attack68's user avatar
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5 votes
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Construct a butterfly interest rate portfolio to eliminate PCA exposures

Let $S$ be your risk sarray, expressed in pv01, for each of your (implied) 10 instruments. You restrict the array to all zeroes except those corresponding to the 5Y, 7Y and 10Y risks, e.g. if 1Y:10Y ...
Attack68's user avatar
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4 votes
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Applications of PCA to yield curve analysis

You can see my remark above for some more words on PCA for the yield curve and an interesting paper. About the question whether it helps us to creat a risk model: PCA on the yield curve changes (!) ...
Richi Wa's user avatar
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4 votes
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Principal component analysis on a yield curve

The first 3 PCs have clear geometric interpretations: PC 1 is “level” or “parallel shift”; PC 2 is “slope” or “tilt” or “flatness / steepness” or “twist”; and PC 3 is “curvature”, “bow”, or “butterfly”...
Dimitri Vulis's user avatar
3 votes

Do you use seasonally or non seasonally adjusted index in analysis

It depends on the intended end-use of your model, but generally-speaking, if you were solely trying to measure and forecast inflation levels or the GDP deflator over the course of a year (including ...
Emma Muhleman CFA CPA's user avatar
3 votes

PCA: How to select a smaller set of the original features that best represent first PC with minimal contribution to the other PCs

What you are describing is not mathematically plausible. Firstly, but less important, a PC is a normalised vector (an eigenvector) meaning if it has more than one non-zero element they will always be ...
Attack68's user avatar
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3 votes

PCA for Risk bucketing

So my question is how do I prove that the use of 2y, 5y, 10y and 30y is justified for risk bucketing and not other alternate buckets? Ok so just to pose a second viewpoint but why do you have to ...
Attack68's user avatar
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3 votes

PCA for Risk bucketing

To justify the use of tenors 2Y, 5Y, 10Y, 30Y for risk bucketing, you could analyse up to the first four principal components and examine which variables summarize better the information displayed on ...
Wane Mamadou's user avatar
3 votes

Reconstruct yield curve from principal components

The point of PCA is that your components are supposed to represent axes of principal variation. I.e. if you just use one principal component you can describe the most variation of true market ...
Attack68's user avatar
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3 votes

Interpretation of PCA for commodity futures

So, the interpretation here is fairly straightforward but I don't think it is likely what you are looking for. Looking at the factors above I notice the returns for each future matter, but the month ...
rhaskett's user avatar
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3 votes
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Portfolio Optimisation/Covariance Estimation on a large scale

Broadly speaking, as you probably already know, there are 2 approaches to estimating large covariance matrices: 1) Shrinkage Methods like Ledoit-Wolf that try to reduce the noise in a large matrix (N ...
Alex C's user avatar
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3 votes
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Calculating PCA hedge ratio for 3-leg spread

Let's use the following returns matrix, X ...
Chris Taylor's user avatar
  • 5,901
3 votes
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PCA FOR STOCK PICKING

The first observation I make is that the proportion of variance is not very high for the first PCs, with the implication that I would hypothesise that the PCs are not very stable, nor reliable. (You ...
Attack68's user avatar
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3 votes

PCA and risk bucketing

It is very simple to make a matrix transformation you simply have the structure: $$ \begin{bmatrix} m_{11} & m_{12} & m_{13} & m_{14} & m_{15} & m_{16} \\ m_{21} & m_{22} &...
Attack68's user avatar
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3 votes

Why is PCA/ML not used frequently in trading?

ML is a very broad term. Do you mean linear regression? To you mean random forests? People use all of these approaches with various degrees of success. Bloomberg will have a story every few ...
JoshK's user avatar
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3 votes
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PCA and K-means clustering on returns

A classic problem, been there, done that, didn't buy the T-shirt ;-) PCA and clustering (K-means, or hierarchical) are similar but different. They're both "unsupervised learning" methods; ...
demully's user avatar
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3 votes
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Principal Component Analysis for attributing yield curve changes

I added an update to answer your updated question below. The PCA pertains to the attribution of changes (i.e. returns) of your valuation factors (e.g. zero rates across tenors) to latent "...
Kermittfrog's user avatar
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3 votes

Can PCA be used to transform a ladder of interest rate risk?

PCA is a mathematical transformation from a certain basis representation, i.e. 1y,2y,3y,4y, into another representation PC1, PC2, PC3 and PC4. In its raw form it is not a dimension reduction procedure....
Attack68's user avatar
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3 votes
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PCA for portfolio optimization (Markowitz)

There is a rich body of knowledge about spectral decomposition of the covariance matrix. Gatheral and Cucuringu have very readable lectures on this topic. I also found a larger and more formal review ...
Adam N.'s user avatar
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2 votes

The danger of using Principal Component Analysis (PCA) in Robust Optimization problems

Possibly she is referring to the fact that classical PCA is not robust in the sense that its asymptotic properties depend on the distribution of the data. Large deviations from normality will result ...
Colin's user avatar
  • 21
2 votes

Low-rank approximation techniques for portfolio optimisation

I don't think that PCA works how you think it does. In coming up with orthogonal vectors (i.e. the eigenvectors of the covariance matrix), Principal Component Analysis generally ends up with each ...
David Kozak's user avatar
2 votes
Accepted

Yield curve PCA vs real life frequency

Re: does the ordering tell us something about the frequency with which they occur? No it doesn't. It's more about how much this component contributes to the final variance. Probably every bit of move ...
Will Gu's user avatar
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2 votes

Using PCA to predict Stock Prices

Without knowing everything about your procedure, your graph is most probably % cumulative variance explained against each principal component, sorted starting from the largest. See this SE post for a ...
madilyn's user avatar
  • 5,230
2 votes

PCA for Risk bucketing

On the technical side of things, make sure that your actual PCA analysis is correct. A reasonable check here is to plot the loadings of all tenors (not just the few you are interested in) for the ...
Bram's user avatar
  • 812
2 votes

statistical arbitrage using PCA

The estimation of the parameters by regression ensures that the mean of the residuals is 0. So, technically the residuals are not IID as if the number of observations is $n$, any $n-1$ residuals ...
Bob Jansen's user avatar
  • 8,543
2 votes

Principal component analysis for yield curve

Based on factor loadings you should be able to tell if the first component is a parallel shift (if you did everything correctly it's highly like that it is). The variance explained by the factor then ...
Bram's user avatar
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