# Questions tagged [covariance-estimation]

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### 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 ...
66 views

### Covariance Shrinkage in Black-Litterman Framework

Good evening guys I am looking into the effects of covariance shrinkage on the diversification of asset weights for different portfolio optimisations. Initially, I was interested to see how it affects ...
98 views

### Ledoit/Wolf covariance shrinkage in risk-parity optimisation

This is more of a theoretical question. I have been working on some mean-variance / Black-Litterman models and played around with Ledoit/Wolf's covariance shrinkage method (sklearn function in Python)....
45 views

### Effective Time Length of Exponentially Weighted Covariance Matrix Estimate

In  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 ...
51 views

6k views

### Multivariate GARCH in Python

Is there a package to run simplified multivariate GARCH models in Python? I found the Arch package but that seems to work on only univariate models. I'd like to test out some of the more simple ...
131 views

### MLE estimate of normal distribution

Probably a naive question. I am quoting this from Greene's econometrics book: "The occasional statement that the properties of the MLE are only optimal in large samples is not true, however. It can ...
120 views

### Bayes Stein Porfolio Implementation

From this paper from Jorion. Has anyone implemented this? How is the Covariance matrix estimated? It needs to estimate also the conditional distribution of the returns? Best
611 views

### How to get Multivariate Betas from an Estimated EWMA co variance Matrix?

I have a portfolio of 4 assets. I also have returns for 3 indices. I want to get the multivariate betas for these 4 assets-based on these assets. I only have the 7 x 7 covariance matrix estimated by a ...
3k views

### Portfolio Optimization : Shrinkage of Covariance Matrix when data is available

It seems that shrinking the covariance matrix is especially useful if the number of individual stocks is greater than the number of data points. However is there any special gain if you're not ...
2k views

### Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
1k views

### Step-by-Step PCA algorithm (checking correctness without math packages)

I would appreciate if someone could correct me if i am wrong in my suggestion. I am using PCA to : find measure of cointegration between selected assets find the eigenvector and its portfolio with ...
I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$\Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right),$$ where $\Sigma(i)$ is the lag ...