Questions tagged [covariance-matrix]
The covariance-matrix tag has no usage guidance.
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Calculating Portfolios Covariance via Bilinearity with Log or Simple Returns
I'm wanting to calculate the covariance between two portfolios $A$ and $B$ which are allocated to assets $X_i$ (where $i \in \left[1, 2, \cdots, N \right]$) with weights $\vec{w_A}$ and $\vec{w_B}$, ...
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negative portfolio variance? Creating a positive semi definite matrix in excel
I am attempting a portfolio optimization model and ended up generating negative portfolio variance using 2WaWbσaσbcorrel(a,b) or 2WaWb*Cov(a,b)
From reading the linked article where other users had an ...
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How to implement computation of a certain covariance matrix?
The screenshot below from the paper "Short-Term Variations and Long-Term Dynamics in Commodity Prices" by Schwartz and Smith (2000) shows the formula for the covariance matrix $V_n$ based on ...
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How can one quantify the incremental value of better covariance matrix modeling in portfolio optimization?
Let's say we have two estimators of the covariance matrix, $\hat{C}_1$ and $\hat{C}_2$, and the latter is an improvement on the former.
Is there any measure of the improvement that can be sensibly ...
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Estimating covariance with intraday data
I have intraday (30 min) data for a number of stocks, and I would like to calculate the covariance matrix of returns.
For the purpose of calculating the covariance matrix, is it better/more correct to ...
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Clustered vs. GMM-based standard errors: which ones to use in asset pricing?
Consider estimating an asset pricing model such as the CAPM or a multifactor model using monthly data. Petersen (2009) section "Asset pricing application" suggests use of standard errors ...
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Imposing diagonality of error covariance matrix when the CAPM holds
Assuming that the CAPM holds, the total risk of an asset can be partitioned into systematic risk (associated with the market factor) and idiosyncratic risk. Idiosyncratic risk is asset specific. Does ...
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Calculating variance of long/short portfolio
Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions:
stock A: long 100 USD
stock B: long 50 USD
stock C: short 200 USD
How do I calculate the portfolio variance ...
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finding the monthly covariance matrix given daily covariance matrix
consider the following problem i am trying to find the monthly covariance matrix given daily data. i have the following codeimport datetime
...
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What does a non-stochastic limiting shrinkage function mean?
I'm reading the paper "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation" by Ledoit and Wolf (2020). When a function that is used to transform the ...
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How do I annualise a covariance matrix?
It is very difficult to source a rigorous answer to the above question.
I know the answer is:
Ann. Covariance = covariance * frequency
Can anyone explain the ...
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How to incorporate "correlation neglect" in a M-V-Framework?
at the risk of boring you with another behavioral finance question, i found a bunch of papers on a phenomenon dubbed correlation neglect, where economic agents misperceive the correlation structure of ...
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Calculate Exponentially-Weighted Covariance Matrix over Finite Window
I have an (n,m) array (specifically containing asset returns over n days for m assets). I'm ...
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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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Variance covariance matrix for a portfolio of credit derivatives
If the var-covar matrix for equities takes the return on equity prices, what should the var-covar matrix for credit derivatives (like a CDS) take?
Should it be the probability of default, since that ...
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Sample Variance of Portfolio
Let $w$ denote a vector of portfolio weights, $r_i$ denote the $i$th return vector, $\Sigma$ denote the Covariance matrix of $r_i$ and let $\hat{\Sigma}$ denote the sample covariance matrix of $r_i$.
...
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Why does Hierarchical Risk Parity ignore the clusters generated?
I am currently working through the Hierarchical Risk Parity algorithm (Lopez de Prado (2016) link ) and trying to understand each of the steps.
I have completed the step of creating the clusters, and ...
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Express the covariance in terms of the standard deviations and correlations
I really need help on this problem. Any suggestion is greatly appreciated!
Suppose there are $n$ assets with $n\times n $ covariance matrix $C=SRS$, where $S$ is a matrix with standard deviations $\...
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Number of Observations for Non-Singular Covariance Matrix Estimation
Marcos López de Prado writes the following in his book Advances in Financial Machine Learning:
In general, we need at least \frac{1}{2} N (N+1) independent and ...
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Optimise the Sharpe ratio of a portfolio of uncorrelated assets
Given a portfolio of $n$ assets, mean returns vector $\mu$, covariance matrix $K$, one can calculate the portfolio weights $w^*$ that maximise the portfolio Sharpe ratio, by solving:
$$w^*=\text{...
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Ledoit & Wolf (2003) shrinkage approach
http://www.ledoit.net/honey.pdf
In the case where you have one sample covariance matrix S and an optimal shrinkage parameter and you want to estimate the covariance matrix resulting from the Ledoit ...
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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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Covariance Matrix for asset returns [closed]
Hey guys I'm pretty new here, not sure how to code my question so I'll include a picture reference instead. I'm a bit confused on how the standard deviation of F (commodity price) would affect the ...
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What is the difference between np.cov(array) and array.cov()?
I'm trying to find a covariance matrix, so when i use returns.cov() on my returns variable, I get a good result. Unfortunately, when i want to use ...
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Is there a way using matrix algebra to add portfolios to a covariance matrix of assets?
What I want to do is the following:
Let's say I have two assets 1 and 2, and have a 2x2 covariance matrix.
Then I have two portfolios A and B made of weights from assets 1 and 2.
What I would like to ...
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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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For portfolio variance, why doesn't $Var(X w) = w^\top \Sigma w$? [closed]
From multivariate asset returns $X$, we can calculate the sample covariance matrix $\Sigma$.
The definition of (any) portfolio variance is $w^\top \Sigma w$, where $w$ are portfolio weights.
If $X w$ ...
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Covariance matrix for multiple assets - Second attempt
Ok, on the advice of administration I open a new question, hoping that in this way it becomes clearer.
Like I said before, I am trying to understand how the authors of this (page 76) and this (page ...
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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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Mathematical proof that the covariance between two portfolios is $w_A^\top\Sigma w_B$
How to prove in a line-by-line derivation that the covariance between two mean-variance efficient portfolios is equal to
$$w_A^\top\Sigma w_B$$
where $w_i$ is a unique portfolio weight vector, and $\...
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Covariance matrix for historical series w/ different start and end dates
I am trying to compute the variance-covariance matrix of my portfolio composed by some shares of different companies. I would select a time horizon of two years but for some shares of one company I ...
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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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Inverse Covariance Matrix Transformation from CAPM
Beginning with the CAPM model we have (with a risk free rate of 0%):
$r_i=\beta_i (r_m)+\varepsilon_i$
with $\varepsilon_i$ the diversifiable risks per assets
The variance matrix:
$\Omega = \beta'\...
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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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Covariance matrix using world stocks [closed]
What is the best way to compute a covariance matrix of daily stock returns made up of international stocks. Knowing that the world markets are not trading simultaneously.
This matrix could then be ...
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Covariance/correlation matrix from data with missing data points
I have a data set with index fund quotes, and I'm trying to compute the efficient portfolio frontier for it.
But some data points are missing. In some cases there are few funds that trading even on ...
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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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Interpretation and units of a covariance element in portfolio risk
Given portfolio risk is $\mathbf{w}\boldsymbol{\Sigma}\mathbf{w}$ where $\boldsymbol{\Sigma}$ is the covariance matrix whose diagonal elements $\sigma^2_{n}$ are individual asset return variances and ...
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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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Meaning of an identity matrix for the covariance in portfolio optimization
Instead of using a sample covariance matrix for portfolio optimization, Ledoit and Wolf use an estimator that is the weighted average of the sample covariance matrix and the identity matrix, $I$. This ...
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Why does portfolio optimization require a positive-definite covariance matrix?
Why does the portfolio optimization mean-variance model require the covariance matrix to be positive-definite? Does this requirement have to do with the need to be able to invert the matrix during ...
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Simulating covariance matrices with nonzero correlation
How would you simulate a covariance matrix of 1,000 stocks where each pair has nonzero correlation?
I have literally no idea how to start with this.
Any suggestions?
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Variance-Covariance Matrix under $\mathbb{P}$ and $\mathbb{Q}$
I'd like to understand why $\Sigma$ is the same under both measures $\mathbb{P}$ and $\mathbb{Q}$.
Is it an assumption or a general fact based on theoretical concepts?
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Effective Time Length of Exponentially Weighted Covariance Matrix Estimate
In [1] Pafka, Potters and Kondor mention the following in section 2:
In contrast, if this covariance matrix estimate is used for portfolio optimization (i.e.
for selecting the portfolio in a ...
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Variance attribution calculation from a covariance matrix
Say I have a portfolio with two assets with weights $(x, y)$, and the covariance matrix of the two asset is $((a, r)(r, b))$. Then the total portfolio variance would be $x^2a+2xyr+y^2b$. It is easy to ...
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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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is it possible to get minimum variance line having only covariance matrix?
Hey I have covariance matrix:
$$C=\begin{pmatrix} 0,01 & 0.01 & 0\\ \\ 0.01 & 0,02 & -0.01 \\ \\ 0 & -0.01 & 0,03 \end{pmatrix}$$
So the variance of porfolio is:
$$\...
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Calculating covariance from three variances
I have been asked to look to refactor some code.
There is a line shown below:
$\text{implied covariance} = -\frac{(\text{var}_1 - \text{var}_2 - \text{var}_3)} {2}$,
where $\text{var}_1$ is the ...
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Estimate covariance matrix using prices
We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case?
I can think of two possible reasons and would appreciate comments/feedback regarding ...
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