# Tag Info

Accepted

### 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. ...
• 4,105
Accepted

### 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 ...
• 496
Accepted

### Creating a Covariance Matrix

here is how to get covariance matrix from correlations:
Accepted

### 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 ...
• 4,936

### 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 ...
• 9,617

### 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 ...
• 7,702
Accepted

### 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 ...
Accepted

### 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 ...
• 9,117
Accepted

### Implementation of Ledoit Wolf shrinkage estimator within R package tawny

The question you asked can be explained by these two lines of the code ...
• 1,688

### 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 ...
• 4,105

### 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-...
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### 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 ...
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### 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 ...
• 2,835

### 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 ...
Accepted

### 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,...

### Creating a Covariance Matrix

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 ...
• 5,345
1 vote
Accepted

The covariance matrix of $N$ stocks (or whatever) consists of $N(N+1)/2$ distinct elements, so, to statistically measure these elements reasonably well, your number of independent observations $ND$ ($... 1 vote ### Odd Result from Computing Correlation Matrix from Kalman Filter Posteriori Covariance Estimate Let your linear system be defined by the latent multivariate state variable$x_t$, progressing in an AR(1) fashion, and let your observation at time step$t$be linear in the latent state: $$\begin{... • 5,853 1 vote ### Update sample covariance matrix Hi: Exponential smoothing weights observations by taking a weighted combination of the old estimate and the new. So, if you denote your original matrix ( or current covariance matrix ) as R_t and ... • 1,017 1 vote Accepted ### Covariance Shrinkage in Black-Litterman Framework Yes all you have to do is estimate the Black Litterman covariance matrix that includes investor views using a shrinkage estimator. Covariance shrinkage like Ledoit Wolf is an old technique, however, ... • 2,835 1 vote Accepted ### Effective Time Length of Exponentially Weighted Covariance Matrix Estimate Usually, when one talks about exponential smoothing, they talk about it's halflife. So, for example, suppose we exponentially smooth some quantity ( argument carries over to covariance matrix but I'd ... • 1,017 1 vote ### Is a more robust Covariance estimation possible? I have actually considered the problem that you are working on, though configured somewhat differently. There isn't going to be a universal answer to your question. See, in particular, Holland, ... • 4,105 1 vote ### Is a more robust Covariance estimation possible? This is not a complete answer, more a different perspective to the answers already given. If you have some a-priori knowledge about the covariance structure and about the factors influencing it, you ... • 1,933 1 vote ### Misunderstanding of time series autocovariance this answer is on hold first it used the fact that your function y is symmetric around 0 (proof) can be found here, so i don't need to type everything. then just expanding the summation$$lim_{n \... • 609 1 vote ### Multivariate GARCH in Python mgarch is a python package for predicting volatility of daily returns in financial markets. DCC-GARCH(1,1) for multivariate normal and student t. distribution. 1 vote ### Multivariate GARCH in Python I recently met the same problem and found a way to achieve it using R in Python. ... 1 vote ### Multivariate GARCH in Python Slight correction: the package in R is called rmgarch, not mgarch. It works well with rugarch... 1 vote Accepted ### Bayes Stein Porfolio Implementation The implementation is explained in more detail in the Horse - Race of DeMiguel: see here • 1,436 1 vote ### How to get Multivariate Betas from an Estimated EWMA co variance Matrix? Say that you did the calculations in the classic regression way. If you stick the returns of your 4 asset returns in a$(T\times 4)$matrix$Y$, and your 3 factor returns in a$(T\times 3)$matrix$X$,... • 4,227 1 vote ### How to get Multivariate Betas from an Estimated EWMA co variance Matrix? With this solution you have to split your covariance matrix somewhat, but it should give you a vector with betas based on you conditional covariances. Example with two indexes,$x1$and$x2\$, and ...
• 153

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