Questions tagged [pca]
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132 questions
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Suggestions for using implied variance covariance matrix of rates for PCA
Looking to feed PCA an implied variance covariance matrix of swap rates instead of historical one.
Taking advantage of available swaption and capfloor implied volatility surfaces, any suggestions on ...
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Volatility surface PCA and SABR explanation gap
I am wondering how would the results of PCA on a volatility surface would be used differently than the SABR parameters. Given the first three components of a PCA are related to level, smile and skew, ...
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When you have negative weights in the context of portfolio construction, what is the correct way normalize them?
For context, I am building an eigenportfolio following the conventions of Avellaneda and Lee Statistical Arbitrage in the U.S. Equities Market (2008), and I get negative weights for eigenportfolios 2,...
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Estimating various outputs using PCA from various features
I have a situation where I am trying to come up with a function to predict different max altitude (in meters) of 5 seconds of various balls thrown by various players with different features such as ...
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Empirical factors vs PCA factors representation
I have performed a Principal Component Analysis on Matlab on a time series of US Treasury yields from 1990 to the present, which determines a $n \times m$ matrix $Y$, where $n = 8577$ are the ...
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Computing statistical risk factors with SVD/PCA - do you center daily returns?
Imagine you have a matrix of returns (n assets, t days) and want to compute c statistical risk factors using PCA/SVD, so that you get (n, c) matrix of factor loadings and (c, t) matrix of factor ...
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PCA on yield curve - Matlab
Consider that I have a dataset of 8964 daily observation of US yields from 1990 to May 2024. These yields are related to each maturity from 3 months, every 3 months, to 30 years, for a total of 120 ...
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How to estimate the diffusion matrix $\Sigma_0$ in Li and Papanicolaou, Applied Mathematics & Optimization (2022)?
In Li and Papanicolaou, Applied Mathematics & Optimization 86, 12 (2022), a key step is the determination of the diffusion matrix $\Sigma_0 = \Psi_0\Psi_0^T$ with $\Psi_0\in \mathbb{R}^{m\times (d+...
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PCA risk modelling
Been doing loads of reading about PCA, FA and SVD but still fail to understand the fundamentals of how PCA links with factor analysis in the context of risk modelling. Here is where I'm stuck:
Given a ...
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Conducting PCA on features of dataset
To preface, I am very new to quantitative finance and nowhere near the point of actually trading so forgive me if this question is trivial to most of you.
I am making a basic k-means clustering ...
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Does PCA for yield curve has any tangible value?
I am aware of an abundant literature on Principal Component Analysis (PCA) application for yield curves. All of these papers to me look merely a statistics-oriented results. Most of the papers argue ...
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Price display of weighted spreads via PCA and value changed
Using PCA I have the below PC1, first component weights, for 4 quarterly expiries of short term interest rate future. These are hypothetical values used to help my question.
March: 0.005542604,
June: ...
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PCA factors not uncorrelated
I ran into an interesting case recently. I am trying to construct a set of uncorrelated factors for a statistical factor model. I have started with picking a certain amount of assets (indices) which I ...
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Scaling returns to use PCA?
Many machine learning techniques perform better, if the data is preprocessed - either by normalization (MaxMin Scaler) or standardization (Standard Scaler). But that comes with a lack of ...
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PCA and OLS regression to transform to interest rate risk? [duplicate]
I’ve been working on different interest rate risk transformation methods for swaps and was interested in implementing PCA & OLS regression. I’m looking to bucket my exposure in all tenors to ...
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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 ...
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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 ...
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PCA analysis within Private Credit
A very broad question but nevertheless a important and difficult one.
Within private markets (Private Equity funds, infrastructure funds and private credit funds) how should one do a risk-based PCA ...
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Dimension reduction of par risk strips
I saw some threads about reducing dimensionality of IR risk strips, e.g. PCA and risk bucketing.
However, I did not find a satisfying answer to that yet. Therefore, I decided to formulate a similar ...
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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 ...
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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.
...
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Can PCA be used to transform a ladder of interest rate risk?
The context
For traders/market makers on interest rate swaps desks, it is essential to have a model that transforms risk from its most complex representation (i.e. a ladder of every tenor) into a less ...
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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 ...
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What is the textbook answer to dealing with multicollinearity?
I have recently struggled in interviews, for two quantitative trading positions, by producing weak answers to effectively the same (fairly basic) question. I would like to understand, from a quant ...
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PCA on levels or returns, and standardized or not?
When you run PCA on some financial assets, let’s say stocks, do you calculate covariance on levels, standardized levels, returns or standardized returns?
I’ve seen several papers and posts that ...
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Yield curve PCA: levels or daily moves?
I have tried using both yield curve levels as well as daily moves (absolute change) while doing PCA. Using both types of input/dataset gives me roughly the same shape in terms of principal components ...
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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 ...
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FX weights and P&L
How to correctly express basket of currencies in and index, such that P&L would align?
Assume our index is 20% EURUSD and 80% GBPUSD and rates are 1.10 and 1.31 for T1 and 1.05 and 1.35 for T2. On ...
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Principal component analysis on a yield curve
When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?
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PCA on portfolio depending on multiple time series
There is extensive documentation about PCA on specific time series (for example the UK yield curve). When you have a portfolio which only depends on the change of the UK yield curve then a PCA on the ...
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How to reduce fx currency pairs ? PCA or other tools?
I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like AUD.CAD, EUR.AUD,EUR.CAD etc.
When I look to their graphs, most look similar, so I want to reduce number of pair ...
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Attribute P&L to PCA vectors (swaps)
I have a daily US swaps data here for 2020 https://easyupload.io/yh4rnd . I have run PCA on standardized data and got PCA matrix (and basic statistics):
I also have such hypothetical portfolio that ...
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Principal Component Analysis for attributing yield curve changes
I have calculated the Principal components using daily yield curve changes. After calculating these components, i noticed that 98% of the return can be attributed to the first 3 components.
How do i ...
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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 ...
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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 ...
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factor hedging erodes portfolio alpha
I am hedging a long-short equity portfolio for statistical factors, and finding an improvement in sharpe but not surprisingly an erosion of portfolio alpha (ex ante and ex post). No one factor is ...
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Implementing Hierarchical PCA for financial time series in R
I would like to implement the method "Hierarchical PCA", as described in the following paper and compare it to a "standard" PCA. I like to do this in R
AVELLANEDA, Marco. ...
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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 ...
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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 ...
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How to extract informative value from correlations of assets? Subadditivity of correlation calculation an issue
I was reading Nassim Taleb's Paper: Fooled by Correlation and found it very informative. I had always struggled with finding value in correlation in Finance, especially seeing a lot of bad ...
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How to use PCA to find best portfolio replication
I have an exposure to 3 products. I have another 12 tradable products that I can use for hedging myself. I have the correlation matrix between the 15 (12+3) products.
How can I use PCA to find the ...
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Pca on multidimensional data
My data has stock returns over n periods for x stocks and m factor exposures for each stock ( ex: value, momentum) for n periods(output of regressions ) . Can I club this data together and then ...
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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 ...
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PCA on returns gives negative loadings on market short
I have run a PCA on some returns to get a set of factors. All is good except that the first PC seems to be the short of the market, it has a correlation of -0.9 with the S&P500 but all the ...
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PCA and K-means clustering on returns
I am running a PCA on a set of returns and I would like to cluster the results of the output to group stocks that have similar factor exposures.
However when I run the PCA on the covariance of the ...
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First Principal Component Large Volatility
I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the ...
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PCA on covariance matrix with weights on the columns?
I'm reading two papers by Mark Kritzman on two indicators (turbulence proxied by the Mahalanobis distance and absorption ratio which is basically the ratio of the variance captured by the top 20% PCA ...
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Factor investing and PCA
I'm struggling to understand how Principal Component Analysis (PCA) is used in Factor Models of returns. For example, in the JPMorgan paper (p.19) the authors write:
In a multi asset portfolio, factor ...
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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.
...
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Why is PCA/ML not used frequently in trading?
I'm curious why things like PCA/ML aren't use frequently in trading? Is there an underlying philosophy that prevent this? What I was thinking, was that if PCA worked for making money, then everyone ...
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