# Questions tagged [covariance-matrix]

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### How can we simulate daily return based on multi-factor model?

This is an interesting question for simulation. The question is a bit lengthy but I'm trying my best to make it super clear here. Now I have some multi-factor model, say some US barra risk model from ...
37 views

### Reliability of R Package on Covariance Matrix Shrinkage

I recently used a R package CovTools in R with the command CovEst.2003LW(X), where X is your sample covariance matrix as an input, to compute the shrunk covariance matrix (an estimate that is closest ...
1 vote
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### Robust estimates of variance covariance matrix

I am looking for help from other people with experience creating variance covariance matrix that have enough predictive power to actually lower portfolio volatility out of sample. Using real world ...
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### Evaluating estimate of covariance matrix

I am testing out different methods / shrinkages to estimate a covariance matrix and I am wondering what is the best method of comparing the estimated covariance matrix to the true covariance matrix (...
110 views

### Calculating Portfolios Covariance via Bilinearity with Log or Simple Returns

I'm wanting to calculate the covariance between two portfolios $A$ and $B$ which are allocated to assets $X_i$ (where $i \in \left[1, 2, \cdots, N \right]$) with weights $\vec{w_A}$ and $\vec{w_B}$, ...
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### negative portfolio variance? Creating a positive semi definite matrix in excel

I am attempting a portfolio optimization model and ended up generating negative portfolio variance using 2WaWbσaσbcorrel(a,b) or 2WaWb*Cov(a,b) From reading the linked article where other users had an ...
1 vote
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### How to implement computation of a certain covariance matrix?

The screenshot below from the paper "Short-Term Variations and Long-Term Dynamics in Commodity Prices" by Schwartz and Smith (2000) shows the formula for the covariance matrix $V_n$ based on ...
139 views

### How can one quantify the incremental value of better covariance matrix modeling in portfolio optimization?

Let's say we have two estimators of the covariance matrix, $\hat{C}_1$ and $\hat{C}_2$, and the latter is an improvement on the former. Is there any measure of the improvement that can be sensibly ...
106 views

### Estimating covariance with intraday data

I have intraday (30 min) data for a number of stocks, and I would like to calculate the covariance matrix of returns. For the purpose of calculating the covariance matrix, is it better/more correct to ...
129 views

### Clustered vs. GMM-based standard errors: which ones to use in asset pricing?

Consider estimating an asset pricing model such as the CAPM or a multifactor model using monthly data. Petersen (2009) section "Asset pricing application" suggests use of standard errors ...
1 vote
111 views

### Imposing diagonality of error covariance matrix when the CAPM holds

Assuming that the CAPM holds, the total risk of an asset can be partitioned into systematic risk (associated with the market factor) and idiosyncratic risk. Idiosyncratic risk is asset specific. Does ...
1 vote
380 views

### Calculating variance of long/short portfolio

Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions: stock A: long 100 USD stock B: long 50 USD stock C: short 200 USD How do I calculate the portfolio variance ...
2k views

### Practical implementation of Libor Market Model

I am trying to implement a project about the BGM model, suggested in the book "The Concepts and Practice of mathematical finance" by Mark Joshi. My question is related to the forward volatility ...
123 views

### finding the monthly covariance matrix given daily covariance matrix

consider the following problem i am trying to find the monthly covariance matrix given daily data. i have the following codeimport datetime ...
39 views

### What does a non-stochastic limiting shrinkage function mean?

I'm reading the paper "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation" by Ledoit and Wolf (2020). When a function that is used to transform the ...
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### Semi-variance/Downside Risk, what about the rest of the covariance matrix?

I just bumped into a rather interesting article from wikipedia : http://en.wikipedia.org/wiki/Downside_risk where they define the semi-variance also called Downside risk, which bascially only ...
1k views

### Ledoit & Wolf (2003) shrinkage approach

http://www.ledoit.net/honey.pdf In the case where you have one sample covariance matrix S and an optimal shrinkage parameter and you want to estimate the covariance matrix resulting from the Ledoit ...
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### Odd Result from Computing Correlation Matrix from Kalman Filter Posteriori Covariance Estimate

I am using a Kalman Filter to estimate the return dynamics of a forwards curve on a particular commodity. My state space is the initial forwards values, and an initial guess of the drift functions for ...
460 views

### What is the difference between np.cov(array) and array.cov()?

I'm trying to find a covariance matrix, so when i use returns.cov() on my returns variable, I get a good result. Unfortunately, when i want to use ...
359 views

### Is there a way using matrix algebra to add portfolios to a covariance matrix of assets?

What I want to do is the following: Let's say I have two assets 1 and 2, and have a 2x2 covariance matrix. Then I have two portfolios A and B made of weights from assets 1 and 2. What I would like to ...
282 views

### For portfolio variance, why doesn't $Var(X w) = w^\top \Sigma w$? [closed]

From multivariate asset returns $X$, we can calculate the sample covariance matrix $\Sigma$. The definition of (any) portfolio variance is $w^\top \Sigma w$, where $w$ are portfolio weights. If $X w$ ...
224 views

### Covariance matrix for multiple assets - Second attempt

Ok, on the advice of administration I open a new question, hoping that in this way it becomes clearer. Like I said before, I am trying to understand how the authors of this (page 76) and this (page ...
1 vote
88 views

### PCA on covariance matrix with weights on the columns?

I'm reading two papers by Mark Kritzman on two indicators (turbulence proxied by the Mahalanobis distance and absorption ratio which is basically the ratio of the variance captured by the top 20% PCA ...
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### Should portfolios have zero or negative correlation between assets? [closed]

Is it more optimal to have a portfolio whose assets are negatively correlated? (I am not requiring all assets to be negatively correlated in this case, nor (-1) perfectly negative correlation either. ...
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### Covariance matrix using world stocks [closed]

What is the best way to compute a covariance matrix of daily stock returns made up of international stocks. Knowing that the world markets are not trading simultaneously. This matrix could then be ...
165 views

### Covariance/correlation matrix from data with missing data points

I have a data set with index fund quotes, and I'm trying to compute the efficient portfolio frontier for it. But some data points are missing. In some cases there are few funds that trading even on ...
314 views

### Interpretation and units of a covariance element in portfolio risk

Given portfolio risk is $\mathbf{w}\boldsymbol{\Sigma}\mathbf{w}$ where $\boldsymbol{\Sigma}$ is the covariance matrix whose diagonal elements $\sigma^2_{n}$ are individual asset return variances and ...
127 views

### Double objective in portfolio optimization

Is there anything infeasible or ethically wrong about optimizing portfolios like this? $$\min_w \enspace w' \Sigma w + w' C w$$ where $\Sigma$ is the asset return covariance matrix, and $C$ is the ...
1 vote
264 views

### Which is more ill-conditioned, the asset correlation matrix or covariance matrix?

If i have a matrix of multivariate asset returns for $N$ stocks, and i compute from it the covariance matrix and then the correlation matrix, can I always know which of the two will have the higher ...
1 vote
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 ...