6
votes
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
6
votes
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
5
votes
Accepted
3
votes
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
3
votes
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
3
votes
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
3
votes
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 ...
3
votes
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
3
votes
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
3
votes
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
2
votes
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-...
- 119
2
votes
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 ...
- 14.4k
2
votes
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
2
votes
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 ...
- 21
2
votes
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,...
2
votes
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
Number of Observations for Non-Singular Covariance Matrix Estimation
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.
- 11
1
vote
Multivariate GARCH in Python
I recently met the same problem and found a way to achieve it using R in Python.
...
- 11
1
vote
Multivariate GARCH in Python
Slight correction: the package in R is called rmgarch, not mgarch. It works well with rugarch...
- 239
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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