Questions tagged [covariance-matrix]
The covariance-matrix tag has no usage guidance.
99
questions
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How to create three variable system + test the hypothesis that the VAR residuals from two variables' equations can be treated as "structural" errors
I am currently doing an econometrics assignment and am completely stumped on a question. I have screenshotted the question and pasted below.
Both questions are to be answered on EViews; having looked ...
2
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1answer
68 views
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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1answer
119 views
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 ...
0
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1answer
75 views
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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2answers
117 views
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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0answers
38 views
Generate a Fractional Gaussian Noise
I am trying to simulate a Fractional Gaussian Noise using Fast Fourrier algorithm.However,I couldn't even if I could retrieve my original covariance matrix such :
$E\left[ X(t)X(s) \right] = \frac{1}{...
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0answers
38 views
How to use Partial Correlations in Portfolio Construction
In learning more about precision matrices and partial correlations, I've begun wondering (very generally) how these statistical measurements could be used in portfolio construction. More broadly, can ...
1
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1answer
185 views
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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1answer
116 views
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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0answers
58 views
Covariance matrix for risk factors of a FX Forward contract
Does it make sense to calculate log-returns of interest rates from a zero curve?
Context: I'm trying to build a variance-covariance matrix for the risk factors of a USDBRL FX Forward maturing in 1 ...
0
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1answer
59 views
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 $\...
-1
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1answer
73 views
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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161 views
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 ...
1
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1answer
291 views
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 ...
0
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1answer
61 views
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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1answer
207 views
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$ ...
2
votes
1answer
131 views
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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0answers
63 views
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 ...
0
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1answer
274 views
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 $\...
0
votes
1answer
168 views
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 ...
1
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0answers
36 views
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,...
3
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1answer
238 views
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'\...
-2
votes
1answer
128 views
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. ...
-1
votes
1answer
59 views
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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0answers
75 views
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 ...
0
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1answer
100 views
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 ...
2
votes
3answers
184 views
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 ...
1
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2answers
150 views
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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0answers
38 views
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 ...
1
vote
2answers
220 views
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 ...
-1
votes
2answers
558 views
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 ...
1
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3answers
356 views
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?
2
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1answer
117 views
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?
0
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1answer
113 views
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 ...
2
votes
1answer
713 views
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 ...
0
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1answer
448 views
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 ...
0
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1answer
207 views
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}$$
So the variance of porfolio is:
$$\...
2
votes
1answer
77 views
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 ...
2
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2answers
215 views
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 ...
2
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2answers
1k views
Creating a Covariance Matrix
Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
0
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1answer
132 views
Demonstration of the Schweinler-Wigner Orthogonalization procedure
Can anyone give me a practical demonstration of the Schweinler-Wigner Orthogonalization procedure? The steps of performing it or possibly a code snippet.
The Schweinler-Wigner Orthogonalization ...
4
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6answers
392 views
Is a more robust Covariance estimation possible?
I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
2
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2answers
693 views
Volatility and weights of a portfolio whose value is negative
How do you calculate the one day standard deviation (in dollars) for a portfolio that is short $30,000? How do you calculate the weightings to use? I already have the necessary covariance matrix.
2
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2answers
1k views
Why annualizing sampled covariance matrix changes stock weight vector?
Question
While optimizing a portfolio using 'Global Minimum Variance' (GMV) method, I found that annualizing a sampled covariance matrix makes a difference in stock weight vector.
Q1. Why ...
0
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1answer
94 views
Covariance matrix from GJR-GARCH?
I am implementing a AR(1)-GJR-GARCH(1,1) model to some asset returns, and I would need to have a covariance matrix but I struggle to see how I can compute one from the model I used?
I know I can have ...
4
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2answers
1k views
Widely accepted methods for coming up with the co-variance matrix of assets?
Question
What are the widely accepted ways for coming up with co-variance matrix of assets
after the Markowitz's modern portfolio theory?
Question explained in more detail
After Modern portfolio ...
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0answers
2k views
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, ...
0
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1answer
471 views
Variance-Covariance VaR: how to get the volatility?
Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the ...
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0answers
141 views
Black Litterman - numerical instability
I am trying to work out the formula for the posterior mean in Black Litterman's model assuming 100% confidence :
Ref: https://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/...
0
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1answer
740 views
beginner portfolio statistics - annualized volatility of multi-asset portfolio
Sorry for the dumb question, but I wanted to make sure my understanding of what I read and compiled was correct! I am trying to calculate the variance-covariance matrix, and annualized volatility of a ...
