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2
votes
1answer
22 views

“Adding” risk-free asset to covariance matrix after the fact

Given a covariance matrix that was calculated from the returns of a number of risky assets. Is there a way to "add" a risk-free asset to the covariance matrix without calculating its covariance with ...
3
votes
1answer
81 views

Portfolio Optimization - n risky assets

I'm currently implementing a CAPM model in Excel: A portfolio of n risky assets when n=6 (in this case) A riskless borrowing rate of 8% and riskless lending rate of 3% I'm given the expected return ...
2
votes
1answer
323 views

Does one use the covariance or correlation matrix in cholesky decomposition to generate correlated samples

Can we interchangeably use Cholesky decomposition of covariance and correlation matrix to generate simulations? If not, in which situations do we use one or the other and why? Thanks in advance.
3
votes
0answers
217 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 ...
4
votes
0answers
213 views

Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow Min $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
6
votes
4answers
327 views

Large (5K-10K) non positive definite (particularly near singular) covariance matrices and treatments for Cholesky decomposition

I have a very large covariance matrix (around 10000x10000) of returns, which is constructed using a sample size of 1000 for 10000 variables. My goal is to perform a (good-looking) Cholesky ...
1
vote
1answer
323 views

VaR Calculation - Covariance matrix is not positive semidefinite

This is a basic question. I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like - ...
5
votes
0answers
149 views

Covariance estimation

Shrinkage was much en-vogue before RMT took everybody's attention, however the latter also showed its limits. A plethora of other estimators has been presented, but I could not yet spot a golden ...