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8 votes
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Creating a Covariance Matrix

here is how to get covariance matrix from correlations:
Valometrics.com's user avatar
6 votes
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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. ...
Dave Harris's user avatar
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6 votes
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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 ...
MGL's user avatar
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4 votes
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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 ...
demully's user avatar
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4 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 ...
nbbo2's user avatar
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4 votes
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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,...
André Bittencourt's user avatar
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 ...
Bob Jansen's user avatar
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3 votes

Multivariate GARCH in Python

I recently met the same problem and found a way to achieve it using R in Python. ...
Bowen Cao's user avatar
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 ...
Dave Harris's user avatar
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3 votes
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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 ...
Alex C's user avatar
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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-...
Davide L.'s user avatar
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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 ...
Brian B's user avatar
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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 ...
develarist's user avatar
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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 ...
David Duarte's user avatar
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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 ...
Python31241's user avatar
2 votes

Excess Return Covariance Matrix is Singular - Cash return and risk free rate are the same

I believe this answers your question? "Adding" risk-free asset to covariance matrix after the fact but the answer is replacing cash with the riskless asset. The key message is either - ...
KaiSqDist's user avatar
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2 votes
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Covariance matrix of Gaussian EM output

If you replace missing returns (and indeed if you replace anything that can be used as an input of an investment strategy), it is strongly recommended to never use future information (it means: to ...
lehalle's user avatar
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2 votes
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Return forecasting for portfolio optimization

I want to understand why factor models such as FF- 3-factor model are not used in practice for estimating the expected returns and covariance matrix (or different estimates given the inputs required ...
Richard Hardy's user avatar
2 votes

Reliability of R Package on Covariance Matrix Shrinkage

You can use the code provided from the authors directly. Michael Wolf has a whole library of examples here in different programming languages. For the "Honey, I Shrunk the Covariance Matrix" ...
oronimbus's user avatar
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1 vote

Calculating Portfolios Covariance via Bilinearity with Log or Simple Returns

Suppose we start with two stocks $A$ and $B$, and we assume they are lognormally distributed. Specifically, let's assume: $$\log(A_t) - \log(A_{t-1}) = X \sim N(\mu_A, \sigma^2_A)$$ $$\log(B_t) - \log(...
Rylan's user avatar
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1 vote
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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 $ND$ ($...
Michael Isichenko's user avatar
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{...
Kermittfrog's user avatar
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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 ...
mark leeds's user avatar
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1 vote
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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, ...
develarist's user avatar
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1 vote
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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 ...
mark leeds's user avatar
  • 1,140
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, ...
Dave Harris's user avatar
  • 4,299
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 ...
g g's user avatar
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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 \...
numerairX's user avatar
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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.
Faisal Nawaz's user avatar

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