Questions tagged [covariance-matrix]
The covariance-matrix tag has no usage guidance.
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Computing covariance matrix with historical data
I have been reading Active Portfolio Management by Grinold and Khan. In the chapter about risk, they mention,
"The third elementary model relies on historical variances and covariances. This ...
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is it possible to get minimum variance line having only covariance matrix?
Hey I have covariance matrix:
$$C=\begin{pmatrix} 0,01 & 0.01 & 0\\ \\ 0.01 & 0,02 & -0.01 \\ \\ 0 & -0.01 & 0,03 \end{pmatrix}$$
So the variance of porfolio is:
$$\...
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Calculating covariance from three variances
I have been asked to look to refactor some code.
There is a line shown below:
$\text{implied covariance} = -\frac{(\text{var}_1 - \text{var}_2 - \text{var}_3)} {2}$,
where $\text{var}_1$ is the ...
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Estimate covariance matrix using prices
We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case?
I can think of two possible reasons and would appreciate comments/feedback regarding ...
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Creating a Covariance Matrix
Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
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Demonstration of the Schweinler-Wigner Orthogonalization procedure
Can anyone give me a practical demonstration of the Schweinler-Wigner Orthogonalization procedure? The steps of performing it or possibly a code snippet.
The Schweinler-Wigner Orthogonalization ...
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Is a more robust Covariance estimation possible?
I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
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Volatility and weights of a portfolio whose value is negative
How do you calculate the one day standard deviation (in dollars) for a portfolio that is short $30,000? How do you calculate the weightings to use? I already have the necessary covariance matrix.
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Why annualizing sampled covariance matrix changes stock weight vector?
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While optimizing a portfolio using 'Global Minimum Variance' (GMV) method, I found that annualizing a sampled covariance matrix makes a difference in stock weight vector.
Q1. Why ...
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Covariance matrix from GJR-GARCH?
I am implementing a AR(1)-GJR-GARCH(1,1) model to some asset returns, and I would need to have a covariance matrix but I struggle to see how I can compute one from the model I used?
I know I can have ...
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Widely accepted methods for coming up with the co-variance matrix of assets?
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What are the widely accepted ways for coming up with co-variance matrix of assets
after the Markowitz's modern portfolio theory?
Question explained in more detail
After Modern portfolio ...
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Barra covariance matrix construction
I am trying to replicate the covariance matrix used by Barra risk models.
All Barra models have half life parameters for volatilities and correlations (e.g. if the half life for volatlity is 90 days, ...
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Variance-Covariance VaR: how to get the volatility?
Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the ...
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Black Litterman - numerical instability
I am trying to work out the formula for the posterior mean in Black Litterman's model assuming 100% confidence :
Ref: https://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/...
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beginner portfolio statistics - annualized volatility of multi-asset portfolio
Sorry for the dumb question, but I wanted to make sure my understanding of what I read and compiled was correct! I am trying to calculate the variance-covariance matrix, and annualized volatility of a ...
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How to compute the portfolio risk when weights are negative?
In QMiF (p. 239) , the variance of a portfolio is defined as:
V(R) = w'Vw = w'DCDw = x'Cx
Does this formula hold if the weights are negative (i.e., short)?
For example, if I have a 5x5 covariance ...
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Why is my Covariance matrix not positive definite?
I'm trying to do PCA on historic forward rates. I'm using forward rates from the Bank of England going from Jan 2015 through end of May 2018. I calculate the differences in the rates from one day to ...
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Filtering smallest eigenvalues
In Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors [1], which introduces minimum torsion bets, Meucci gives an example involving the computation of covariance matrices on ...
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Variance covariance matrix - number of periods required
Hi I am reviewing the example of Barra risk model in the following document page 23 there is the statement:
"Estimating a covariance matrix for, say, 3,000 stocks requires data
for at least 3,...
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Which program for a DCC-MIDAS model?
for a thesis research, I plan to use a DCC-MIDAS model. The program I was working with (STATA) is not able to run this.
Do you have any suggestions as to which program is best for this analysis?
...
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Hierarchical Risk Parity with allocation constraints?
In the really interesting paper by Marcos Lopez de Prado a variation of risk parity is applied whereby the underlying assets of the portfolio are first split in 'correlation clusters' and the ...
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Solving a system of two equations with non-convex matrix multiplication for MV optimization
Scenario: I am trying to do a variation of the MV optimization for a portfolio. In this instance, I already have a vector of mean returns ($\mu$), a vector of ones, a covariance matrix ($\Sigma$), and ...
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Covariance Interest Rate Risk Time Series
Apologies in advance if this question has been asked already.
I am estimating basis risk for different term points in the curve. Imagine i have three time series (1-month, 3-month, 1-year). I ...
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principal component analysis on non stationary data
I read that since stock prices are non-stationary it does not make sense to take their covariance. So I took the log returns of stocks, computed covariance matrix, took the top few eigen vectors that ...
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Covariance Matrix: Calculating Error [duplicate]
I have a sample covariance matrix that is non positive-semi definite (due to missing data points). I am looking at a number of techniques to 'fix' my covariance matrix and make it positive semi-...
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Portfolio Optimisation/Covariance Estimation on a large scale
When using Markowitz Portfolio Theory, e.g. for finding an optimal portfolio composition, one needs to have estimates of the returns, but most importantly of the covariance matrix. If our universe of ...
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Reduced rank / matrix factorisation techniques and their uses in portfolio optimisation?
I am interested in reduced rank / matrix factorisation techniques and their uses across finance and portfolio optimisation. For example, PCA might be used to reduce the number of components you are ...
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Variance Matrix with 'nan' values
I am trying to optimize a simple portfolio using several random weights and choosing the best. When the number of assets is large I get a covariance matrix with 'nan' values because some asset pairs ...
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How can I use a more efficient volatility estimator to improve the co-variance matrix?
Using mean-variance, I need to estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio.
However, there are other ways to compute the volatility $\sigma$ than historical ...
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What is the difference between the Single Index Model and Multi-Index Models in computing the variance-covariance matrix of stock returns?
Would be very grateful for some help in comparing the single index model with other multi-index models in computing the variance-covariance matrix.
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Why does the Markowitz mean-variance model require the assumption of normality?
Given $N$ assets, the Markowitz mean-variance model requires expected returns, expected variances and a $N \times N$ covariance matrix. The joint distribution is fully defined by these measures.
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What is the total correlation between assets in a portfolio?
Suppose I have portfolio with 10 assets, each one of them with a weight of 10% from the total portfolio (equally weighted).
It's well known how to measure from historical prices->returns a variance-...
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Explanations regarding Minimum Variance Portfolio
I am sorry in advance if this question seems a bit stupid but during my class my lecturer said that:
"The traditional estimator of the variance-covariance matrix is the sample covariance. However ...
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Prove that a determinant in markowitz method derivation is greater than zero
I want to prove that the following determinant, that appears in the markowitz method of portfolio allocation is greater than zero.
($\mu$ is the vector of returns and $\sum$ is the covariance matrix)
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How to compute the variance of a Long-Short Equity Portfolio?
I am calculating the historical portfolio variance of various long-short equity portfolios. For simplicity, assume the portfolio is long stock A with weight 1.0 and short stock B with weight -0.5. ...
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Transform raw forecasts into orthogonal forecasts
I am trying to combine multiple forecasts on each of N assets in line with Grinold and Kahn's methodology, taken from Active Portfolio Management, 2nd ed. On p.311, they suggest transforming the raw ...
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Generating a random covariance matrix with variances in range
I would like to generate a random covariance matrix with variances in certain range.
How can it be done? (In R if possible)
I tried to generate a lower triangular matrix $L$ where the diagonal $D = ...
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Annualize a covariance matrix?
I am attempting to find the annualized covariance between assets in a portfolio but I only have daily data. So how do I annualize the covariance matrix between these assets?
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How to adjust corporate actions for VaR
I am using variance co variance matrix for calculating the VaR. Now if the some corporate action comes in between like stock split, resulting a huge VaR number on that particular day as the volatility ...
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Average Correlation
We're given a spreadsheet with a correlation matrix for four stocks.
Then there is a calculation for average correlation, but I don't know how it's derived.
$$=\left(\operatorname{Average}(C14:F17)-\...
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Interpreting Eigenvalues of Co-variance Matrix
Im working on market reaction to events and I'm using the co-variance matrix to do this. In this paper the author writes
It has been known for some time that the largest eigenvalue (λ1) contains ...
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PCA for stand alone equity VaR
I am trying to compute equity VaR, forex VaR and total VaR on an international portfolio (10 stocks x 4 countries). Since I am not interested in the risk disaggregation among diffrent countries I was ...
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Variance of a portfolio based on log-returns
Modern Portfolio Theory Optimization Problem is based on expected linear returns and covariances of linear returns.
That's said, variance and expected return of a portfolio based on linear returns r ...
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Historical Scenario analysis for stress testing
I am doing historical scenario analysis in order to calculate stressed VAR for which I have taken 2007-2008 US crisis. I have two question in this regard:-
1) As we have to take prices for stocks ...
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Variance covariance matrix for a portfolio containing bonds also with other asset classes
What should we take for a bond or a zero coupon bond in order to make a variance covariance matrix?
For example:-
Equities - we take the market price
Cash - we take the spot rates
Bonds - Do we take ...
user18663
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Portfolio with lots of subportfolios
An account manager has $N$ distinct, equally-sized pots of money, which will be used to make $N$ distinct subportfolios, each of which is drawn from a slightly different (but potentially overlapping) ...
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Ledoit-Wolf Shrinkage estimator not giving positive definite covariance matrix
I used ten year daily data for 407 stocks and computed the daily and monthly covariance matrices. Since I have more variables than observations for the monthly matrix, I wasn't surprised to find the ...
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Correlation Between 2 Portfolios
I have a set of assets, n. I'm trying to find the correlation between 2 portfolios, say x and y, where x is nested in, or, a sub-set of y. That is, x is a portfolio based on a sub-set of n, while y is ...
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Residual Covariance Matrix, and MVO for Residual Variance and Alpha
My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$.
We know the equation for residual variance ...
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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 ...
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