Questions tagged [correlation-matrix]
The correlation-matrix tag has no usage guidance.
60 questions
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Estimate swap rates correlation in absence of spread options
Any suggestions / pointers on how to estimate swap rates correlation in absence of spread options? Is it feasible to work it out with the correlation of forwards coming from the intersection of ...
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Average correlations of stock returns
Say I had a pool of companies (specifically the Latin American Countries). The task was to work out the 'Correlation coefficient between the returns of any 2 companies selected from "different ...
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Calculation of break-even correlation for diversification effect in N-assets case?
I'm thinking about a generalization of the following case: for 2 assets, there is a diversification effect as soon as i obtain a positive weight for the minimum-variance portfolio in the asset with ...
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N asset covariance matrix vs N-1 asset covariance matrix
so I have been using a M-V framework to form M-V efficient portfolios. I have noticed that every time I make my investment universe smaller the minimum variance frontier moves to the right. This ...
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How to properly calculate the average across multiple correlations?
I'm trying to obtain an average across 3 correlations.
Using Python, I obtain these correlations with:
corr = df.apply(lambda s: df.corrwith(s))
which outputs:
<...
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Correlation between brownian motions and Cholesky decomposition [closed]
I know it is a pretty basic question (I'm new at Quantitative Finance), but what's the logic behind the Brownian Motions correlation?
The expression is:
Where is this formula coming from?
On the ...
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Select top $n$ most correlated assets in universe
I know this questions is a bit ambiguous, but I guess that's natural. To put it simply: I have a universe of around 600 stocks. How do I find the top $n$ "most correlated" assets?
At the ...
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Sub-portfolio correlation
I am trying to reduce correlation matrices into sub portfolios.
For example, I have a covariance matrix $\Sigma$ and weight-vector $w$ of two line items which I blend together into a sub-portfolio $\...
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Interpreting factor coefficients when correlation flips
I am looking at mainly value and growth factor coefficients of a fund during the recent Covid market “crisis”.
I have found that said fund had a negative coefficient to value at the start of 2020 (let’...
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Odd Result from Computing Correlation Matrix from Kalman Filter Posteriori Covariance Estimate
I am using a Kalman Filter to estimate the return dynamics of a forwards curve on a particular commodity. My state space is the initial forwards values, and an initial guess of the drift functions for ...
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Correlation Matrix - NaN Values
I am trying to create a Correlation Matrix of one particular industry (in the consumer goods sector) with around 15 securities across multiple stock exchanges for the year 2020.
However, I have a lot ...
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Can the covariance matrix be represented as a scalar or something similarly small, instead of a large pair-wise grid?
The covariance matrix tabulates pair-wise interactions between variables (assets) one-at-a-time into a grid, which can quickly become large as the number of assets included in a portfolio, for example,...
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Should portfolios have zero or negative correlation between assets? [closed]
Is it more optimal to have a portfolio whose assets are negatively
correlated? (I am not requiring all assets to be negatively correlated in this case, nor (-1) perfectly negative correlation either. ...
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462
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Which portfolio is more "diversified": the $\frac{1}{N}$, the MDP or the max decorrelation?
Equally-weighted portfolio: weights each asset the same $w_i = 1/N$
Maximum diversification portfolio: maximizes the ratio, $\frac{w' \sigma}{\sqrt{w' \Sigma w}}$
Maximum decorrelation portfolio: ...
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How to annualize the correlation matrix?
If asset returns are daily, and the asset return covariance matrix, $\Sigma$, is annualized by $\Sigma \times 252$, do I also multiply the correlation matrix by 252 to annualize it?
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Double objective in portfolio optimization
Is there anything infeasible or ethically wrong about optimizing portfolios like this?
$$\min_w \enspace w' \Sigma w + w' C w$$
where $\Sigma$ is the asset return covariance matrix, and $C$ is the ...
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Which is more ill-conditioned, the asset correlation matrix or covariance matrix?
If i have a matrix of multivariate asset returns for $N$ stocks, and i compute from it the covariance matrix and then the correlation matrix, can I always know which of the two will have the higher ...
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Covariance of Individual Return and Portfolio Return
Hi guys,
Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix?
I know how to get ...
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Computing covariance matrix with historical data
I have been reading Active Portfolio Management by Grinold and Khan. In the chapter about risk, they mention,
"The third elementary model relies on historical variances and covariances. This ...
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727
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Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R
I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
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368
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How to stress test a correlation matrix
As part of a mean variance portfolio task, I am calculating portfolio risk and optimal allocations between assets given required level of return. Input: expected returns, volatility and correlation ...
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Correlations between different baskets of assets
Struggling to see the answer to the following problem - Assume you have $N$ different assets, and all pair-correlation coefficients $\rho_{ij}$ between them are known. If you now form two arithmetic ...
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Averaging Correlation Matrices based on different Periodicity
Averaging correlation matrices based on different models, but the same data, is commonly done. If the correlation matrices are derived from return series, is it proper/common to also average the ...
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Barra covariance matrix construction
I am trying to replicate the covariance matrix used by Barra risk models.
All Barra models have half life parameters for volatilities and correlations (e.g. if the half life for volatlity is 90 days, ...
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Parametric VaR assumption question
Why do you have to make a correlation matrix when calculating the parametric value at risk, if one of the assumptions for this method to work is that the assets of the portfolio must be independently ...
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How to do QE scheme for n correlated assets?
I'm trying to simulate correlated assets under Heston model.
I coded the QE scheme for a single asset but i dont understand the next step:
How should i set the correlation matrix given my n-asset ...
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3
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266
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generating a correlated RV which has the same correlation to existing samples
Suppose I have generated a collection of correlated sequences of samples $(S_i)_{i=1}^{n}$ from random variables $\mathbf{\underline{x}} = x_i$.
Let's fix a sequence of reals $(\sigma_i)_{i=0}^{n}$. ...
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Didier Sornette's Strategy to Exploit Return Correlations
In his book, "Why Stock Markets Crash", Didier Sornette discusses a trading strategy that exploits return correlations.
Consider a return $r$ that occurred at time $t$ and a return $r'$ that
...
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Cleaning correlation matrix, Bun Bouchaud Potters (2016) method
Stock returns correlation matrices are notoriously hard to estimate, especially when the number of assets $N$ is large with respect to the size of the readily available historical returns $T$. Many ...
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How to calculate ex Ante Tracking Error
I'm looking to find the correct way to calculate the ex ante tracking error of a portfolio.
If say I have 10 funds, and their historical returns series (used to calculate mean return, standard ...
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Minimum Subset within Correlation Matrix
I have a correlation matrix that I produced in Excel using the monthly returns from 200 different trading systems over a X year period. So, the correlation matrix is 200 rows by 200 columns. How do ...
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Average Correlation
We're given a spreadsheet with a correlation matrix for four stocks.
Then there is a calculation for average correlation, but I don't know how it's derived.
$$=\left(\operatorname{Average}(C14:F17)-\...
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Isolating single assets standard deviation in a portfolio accounting for correlation
I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio ...
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Correlation Between 2 Portfolios
I have a set of assets, n. I'm trying to find the correlation between 2 portfolios, say x and y, where x is nested in, or, a sub-set of y. That is, x is a portfolio based on a sub-set of n, while y is ...
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How to create a basket of currency pairs with the lowest correlation in R?
My strategy is designed to buy and sell all assets of a universe and rebalance periodically. It goes either long or short. To limit risk exposure to a single currency I would like the assets in the ...
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How to infer correlation?
Let's say a have a correlation matrix $\Omega$ for 25 assets which I use to generate a Monte-Carlo simulation. Let's assume that $\Omega$ is valid (i.e positive-semi-definite, etc...) and estimated ...
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modeling regime switching for Correlation matrix
I am trying to estimate covariance in multiple time series. However, I want to do this using a regime-switching framework. So, I start with fitting a GARCH(1,1) model and then de-volatalize the series....
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Interpretation of Correlation Matrix
I have past data which is in vector form. The information shows the probabilities of a AAA rated company to migrate to another credit rating. So for example, (x1, x2, x3) has the probabilities of ...
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PCA on term structure of interest rates
Interest rate time series seems to be non-stationary whenever test is performed
But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA ...
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Does the correlation of matrices have explanatory power when building a pattern recognition model?
I'm using 8 different variables (with daily observations) with the purpose to compare different months across the historical data. For that purpose I calculate the correlation between each month and ...
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Stock Correlation Matrix, Multiple Currencies
If i have a portfolio of stocks from different currencies and i want to generate a correlation matrix from the stocks, how is the correct procedure ?
Imagine a portfolio which the base currency is ...
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Sample size and historical correlation matrices
I was wondering whether any literatures existed on how to properly
estimate correlation matrices from historical data.
Obviously the entire procedures allows a lot of leeway. The frequency of the ...
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Effect of kernel smoothing on correlation
Instead of deriving correlation matrix on standardized returns (z scores) would it not be more accurate to kernel smooth the cdf and then norminv the cdf values for the return z score and then ...
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Given a correlation martrix, calculate portfolio's correlation with its assets
Find correlation vector like $[ d e f ]$ where d, e and f represent correlation of P(portfolio) with its assets A, B and C respectively. The assets A, B, C can be another portfolio.
In order for that,...
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ex ante tracking error correlation between funds
I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...
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Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples
Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why?
Thanks in advance.
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How to treat large (5K-10K) non-positive-definite (particularly near-singular) covariance matrices for Cholesky decomposition?
I have a very large covariance matrix (around 10000x10000) of returns, which is constructed using a sample size of 1000 for 10000 variables. My goal is to perform a (good-looking) Cholesky ...
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Interpretation of cross-correlation matrix when one sample distribution is not normal
I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
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How to simulate correlated Geometric brownian motion for n assets?
So I'm trying to simulate currency movements for several currencies with a given correlation matrix. I have the initial price, drift and volatility for each of the separate currencies, and I want to ...
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Stress testing covariance
Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure ...
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