Questions tagged [pca]

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16
votes
1answer
1k views

Meta-view of different time-series similarity measures?

While I spend most of my StackExchange time on MathematicaSE, I'm in the business and follow the questions and answers on this site with great interest. Recently questions like the following (and ...
16
votes
2answers
1k views

Applicability of PCA to get historical volatilities to calibrate interest rates trees

My question in short is as follows: can I take main principal component of historical covariance matrix and use it as historical volatilities when fitting a binomial tree? Here's more detailed ...
15
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1answer
7k views

Why is the first principal component a proxy for the market portfolio, and what other proxies exist?

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
14
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4answers
5k views

Equity Risk Model Using PCA

I'm trying to build a simple risk model for stocks using PCA. I've noticed that when my dimensions are larger than the number of observations (for example 1000 stocks but only 250 days of returns), ...
13
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2answers
3k views

Cluster analysis vs PCA for risk models?

I built risk models using cluster analysis in a previous life. Years ago I learned about principal component analysis and I've often wondered whether that would have been more appropriate. What are ...
12
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5answers
3k views

Time series of PCA - Sign change in factor loadings

I have a time series of data that is 300 days long. I compute PCA factor loadings on a moving window of 30 days. There are 7 stocks in the universe. Thus factors F1 through F7 are calculated on each ...
12
votes
1answer
658 views

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

I have received a reviewer's comment on a paper which applies PCA to reduce the size of a problem and the application is in the robust optimization field. The reviewer implies that "In robust ...
10
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4answers
1k views

Hedge Fund risk management on a daily basis

Since Hedge Funds/Fund of Funds report on a monthly basis usually within 10 days after the month end, monitoring and managing (hedging) potential risks is quite a difficult task. Having done some ...
9
votes
2answers
18k views

How to use PCA for trading

Can anyone give me a few pointers of how to approach using PCA for trading? In particular, it seems to me, PCA is useful for selecting a subset of a portfolio of stocks(or other) rather than trading ...
8
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2answers
3k views

How to make the final Interpretation of PCA?

I have question regarding final loading of data back to original variables. So for example: I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10. ...
8
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2answers
804 views

Looking for Research Paper on Creation of Currency Baskets

I came across a paper, not sure it originated from academia or a blog or such, that reported on applying principal components to build currency baskets from a set of individual currency pairs and to ...
8
votes
1answer
475 views

Are there any other standard rates term structure decomposition than PCA?

PCA is sometimes used to estimate components in the rates term structure. Are there any other standard method discussed in the literature or used in practice, what are their advantages and ...
8
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0answers
3k views

Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
7
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2answers
3k views

Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo

Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...
7
votes
1answer
240 views

Principal Components Analysis on overlapping contracts

I am conducting several PCAs on the gas forward curves (months, quarters, seasons, calendars) for hedging purposes which give me some rather reasonable and stable results. However, these contracts ...
6
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2answers
1k views

Factor Model - Minimum Variance Portfolio [Complete Proof]

Can someone check my proof? I think there is something not quite right. I have found limited resources online for this as well so I think it might benefit others to get this on the internet. Assume ...
6
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2answers
2k views

Non-negative matrix factorization for factor analysis of stocks

I stumbled over the term Non-negative matrix factorization in presentations such as Application of Machine Learning to Finance and this Big Data in Asset Management. The basic idea is to decompose a ...
6
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2answers
525 views

PCA for stand alone equity VaR

I am trying to compute equity VaR, forex VaR and total VaR on an international portfolio (10 stocks x 4 countries). Since I am not interested in the risk disaggregation among diffrent countries I was ...
5
votes
3answers
229 views

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

I have performed PCA on a covariance matrix. I have 24 original features and subject to some constraints over which features are used i would like to chose the combination of features that best ...
5
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0answers
165 views

Interplay of statistical factors (PCA) and market factors (value, momentum, low vol, …)

Is there any research done on the interplay between statistical factors (as a result of principle component analysis PCA) and the market factors (especially value, size, low vol, momentum, quality)? ...
4
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2answers
447 views

Why use market capitalization weighted index over PCA?

Why is it so popular to use market capitalization weighted indices instead of taking the first principle component that explains the most variation of the constituents? I haven't yet seen an academic ...
4
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1answer
732 views

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 ...
4
votes
1answer
2k views

Statistical arbitrage using eigen portfolios

I was trying to understand below paper https://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf Page 20 explains about "Entering a trade". I wan't to know clearly what it means to ...
4
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2answers
1k views

Some clarifications on eigenvectors and eigenvalues from PCA

Could somebody tell me whether suggestions in bold true or not? Q # 1: http://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf ...
4
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0answers
168 views

VAR FPCA analysis paper replication

I've been trying to replicate the following publication: CONSISTENT FUNCTIONAL PCA FOR FINANCIAL TIME-SERIES, Sebastian Jaimungal, Eddie K. H. Ng, 2007 but I havent been able to get the same results ...
4
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0answers
456 views

How replicate data using PCA

I have a set of date covering petrol prices. My example has two columns where each row represents a sequential date. ...
4
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0answers
507 views

PCA Variances and Principal Portfolio Variances

In Meucci's paper called "Managing Diversification" he mentions that: "Indeed, the eigenvalues A correspond to the variances of these uncorrelated portfolios" I tried to replicate it but found they ...
4
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0answers
126 views

Estimating two normal random numbers with one equation

Subtitle: Estimating the correlation of the shocks driving two commodities in two multi-factor models I am fitting two 2-factor models to electricity and gas futures, respectively. In order to ...
3
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3answers
646 views

PCA for Risk bucketing

I'm working on a project to justify the use the certain tenors (2y, 5y, 10y, 30y) for risk bucketing. I'm a little stuck after calculating the principal components. Just to describe my approach- a) ...
3
votes
1answer
232 views

how to construct a diversified portfolio based on correlation

I have a porfolio of indexes and I built up a python model based on spearman correlation (I used a spearman and not a pearson because, after running some test on outliers and normality ...
3
votes
1answer
640 views

statistical arbitrage using PCA

While reading the paper Statistical Arbitrage in the U.S. Equities Market by Marco Avellaneda and Jeong-Hyun Lee on statistical arbitrage using PCA I realized that the author sums the residuals of ...
3
votes
1answer
623 views

Weights Blowing up in PCA

I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
3
votes
1answer
221 views

After PCA on original factors, how to tell which original factors are dominant?

When doing the PCA analysis, you end up with eigenvalues which are ordered by how much variance they explained for each eigenvector. Say, the eigenvectors since they are orthogonal, do not represent ...
3
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0answers
85 views

What is special about covariance estimation from statistical factor models?

If you were to compare the usual sample covariance estimate to a robust covariance estimate (such as MCD), you can say that the robust estimate is more tolerant to outliers in the data and will not be ...
3
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0answers
184 views

Which kind of normalization to prefer before PCA (generic solution for any factor analysis)

I have financial assets with totally different volatilities, thus I must standardize them before PCA, otherwise, assets with high variance may be considered as principle components, which is wrong. ...
2
votes
1answer
1k views

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 ...
2
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2answers
485 views

Reproducing levels when PCA has been done on changes

I want to use PCA for rich/cheap analysis of interest rates. For this I did the PCA on the time series of daily difference in interest rates, which is stationary. I cant do pca on levels, as they are ...
2
votes
1answer
643 views

Hedging a trade for PCA component neutrality

Suppose I am given a set of financial instruments, e.g. {1Y, 2Y, ..., 30Y} interest rate swaps or {Barclays, Lloyds, .. } FTSE100 companies. It doesn't matter which so let's go with IRS. I have ...
2
votes
2answers
470 views

PCA and risk bucketing

I have a portfolio of bonds and I have calculated their PV01 per risk bucket. The relevant buckets are 1m,2m,...,1y,2y,...30y; a total of 40 buckets. I also run a PCA and have identified the three ...
2
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2answers
400 views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
2
votes
2answers
606 views

Reconstruct yield curve from principal components

I am currently building a model which aim is to model shocks to the yield curve (i.e. 25bps hike in the short rate). Currently I am looking at a swap curve from which I derive the PCs. Assessing the ...
2
votes
1answer
223 views

PCA on a portfolio of spot and forward contracts

I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l. ...
2
votes
1answer
681 views

Using PCA to predict Stock Prices

I would like to model an index e.g. FTSE 100. I have a list of all companies that make up the index and their stock values (daily high, low, volume, close values). In total, this time series data has ...
2
votes
1answer
700 views

Constructing a stock market index using PCA

Let's say that I've got a final component and its score derived from n number of stock returns (time-series data). I want to construct a stock market index using this component (having negative and ...
2
votes
1answer
351 views

Orthogonal Regression/PCA

I am doing orthogonal regression. My X matrix consists of returns on a broad market index, value index, growth index, a few sectors,.....(my Y is the returns on an equity fund) I am regressing the Y ...
2
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0answers
172 views

Bond Hedging: PCA and regression based hedge ratios

This is my first question and I would very much appreciate any help. For a project I am trying to compare different hedging techniques for hedging a long portfolio of bonds. I have a history of ...
2
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0answers
68 views

machine-learning method to predict PCA weights

I have been using certain linear-regression to extract the PCA (top 3) weights relating to a certain data-set. I was wondering, instead of using linear-regression to generate the weights, I can use ...
2
votes
0answers
302 views

How to interpret DV01 in terms of PCA equivalent?

I have computed the PCs for daily changes in the UST yield curve over the last 5 years using the covariance matrix and can explain 94% of the variance using the first two components, which is good ...
2
votes
0answers
194 views

Using PCA to identify proxies for highly illiquid assets?

Was wondering if anyone had any literature to share on the use of PCA to identify proxies for highly illiquid assets? Say for example I have sold an option on stock A, an index constituent, and would ...
2
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0answers
60 views

Covariance Matrix: Calculating Error [duplicate]

I have a sample covariance matrix that is non positive-semi definite (due to missing data points). I am looking at a number of techniques to 'fix' my covariance matrix and make it positive semi-...