# Tag Info

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### Shrinkage of the Sample Covariance matrix, theory

Yes. It comes from a core theorem of statics, Stein's Lemma. It shook the foundations of the field of statistics when it came out. It blew up an entire way of viewing mathematical statistics. ...
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### Ledoit/Wolf covariance shrinkage in risk-parity optimisation

The Risk Parity portfolio will be equal weighted if the assets have uniform correlation and equal variance. This would be the case for the shrunk covariance matrix if the shrinkage coefficient used ...
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### Creating a Covariance Matrix

here is how to get covariance matrix from correlations:
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### Meaning of an identity matrix for the covariance in portfolio optimization

OK, so think of it this way... Your standard (Markowitz) covariance matrix is a sample observation. That may or not be close to the population sigmas and correlations of your sampled markets. Even if ...

### Meaning of an identity matrix for the covariance in portfolio optimization

You can think of it in Bayesian terms. To start with, knowing nothing at all about stocks, you might assume that stock returns are i.i.d with unit variance. This would be your prior. It is very simple ...

### Number of Observations for Non-Singular Covariance Matrix Estimation

Let $f(N) = \frac{1}{2} N (N + 1)$ then $f(50) = 1275$. A year has approximately 255 trading days. So you need at least 1275 / 255 = 5 years. I believe the rule above is used in practice but I think ...
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### Multivariate GARCH in Python

PYTHON I have found this class from the statsmodels library for calculating Garch models. Unfortunately, I have not seen MGARCH class/library. Below you can see the basic information about the garch ...
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### Portfolio Optimisation/Covariance Estimation on a large scale

Broadly speaking, as you probably already know, there are 2 approaches to estimating large covariance matrices: 1) Shrinkage Methods like Ledoit-Wolf that try to reduce the noise in a large matrix (N ...
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### Implementation of Ledoit Wolf shrinkage estimator within R package tawny

The question you asked can be explained by these two lines of the code ...

### Covariance estimation: shrinkage, random matrix theory, what else?

I thought I would answer the question of "what am I using." All shrinkage estimators map to a Bayesian estimator that differs only in the prior distributions. In other words, you get a point ...

### Is a more robust Covariance estimation possible?

As an addition to the already rich answers, I would suggest you to read the following paper by Marcos L. De Prado on the computation of Forward-Looking Correlation Matrices. Estimation of Theory-...

### Is a more robust Covariance estimation possible?

The Ledoit-Wolf estimate cited by @develarist can be quite good, but as you say you already knew about "shrinking". It takes the population of correlations observed as an effective Bayesian prior for ...

### Is a more robust Covariance estimation possible?

Quantile regression is considered a robust procedure but lacks the quality of being fully differentiable. There are also regularized regression models like ridge regression, lasso regression and ...

### Shrink covariance or correlation matrix

Generally it is better to shrink the covariance matrix—since the variances of your data probably vary a lot, and the correlation matrix treats them all as essentially equal variance, you throw out the ...
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### Sample Variance of Portfolio

Yes, indeed. It's a simple Linear Algebra and Expectation result: Given: $Var(w'r) = \mathbb{E}[(w'r)^2] = \mathbb{E}[(w'rr'w)]$ With $w$ and $r$ the vectors of weights and returns. As $w$ is constant,...
The relationship between covariance, standard deviation and correlation is: $$corr(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}$$ So to construct your matrix you will have the variances in the ...