# Tag Info

### 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 (...
• 1,779
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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 ...
• 11.1k
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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: ...
• 12.4k
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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 ...
• 1,671
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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 ...
• 11.1k
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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 ...
• 27.5k
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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 (!) ...
• 13.8k
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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”...
• 12.6k
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### Does PCA for yield curve has any tangible value?

My view on this is summarised in my book "Pricing and Trading Interest Rate Derivatives". In it I give a chapter on PCA calculation and demonstrate calculations and applications. But my ...
• 11.1k
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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 ...
• 11.1k

### 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 ...

### 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 ...
• 11.1k

### 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 ...
• 11.1k

### 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 ...
• 111

### 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 ...
• 11.1k

### 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 ...
• 1,641
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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 ...
• 9,382

### 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} &...
• 11.1k

### 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 ...
• 2,633
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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; ...
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### How to extract normalised portfolio weights from PCA, when the eigenvector has negative elements?

I'm not entirely sure what you are carrying out the PCA on, are you using a correlation matrix or covariance matrix? As for the negative eigenvalue issue, the sign associated with an eigenvalue is not ...
Accepted

### 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 "...
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### 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....
• 11.1k
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### PCA on a portfolio of spot and forward contracts

You have a portfolio, $P$, filled with many positions, which are specifically dependent upon various asset price movements, say $X,Y and Z$. These price movements are random variables, but they may ...
• 11.1k

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

To be honest I don't believe that what you are doing is particularly useful, and I think it may even be misleading for risk management purposes. But with that disclaimer out of the way, what about ...
• 11.1k

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