Questions tagged [covariance-matrix]
The covariance-matrix tag has no usage guidance.
58
questions
3
votes
6answers
162 views
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 ...
1
vote
1answer
58 views
Covariance - Negative Portfolio
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.
1
vote
2answers
94 views
Why annualizing sampled covariance matrix changes stock weight vector?
Question
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 ...
0
votes
1answer
51 views
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 ...
3
votes
2answers
130 views
Widely accepted methods for coming up with the co-variance matrix of assets?
Question
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 ...
0
votes
0answers
496 views
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, ...
0
votes
1answer
316 views
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 ...
1
vote
0answers
103 views
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/...
0
votes
1answer
267 views
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 ...
0
votes
0answers
231 views
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 ...
-1
votes
2answers
846 views
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 ...
3
votes
2answers
323 views
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 ...
-2
votes
1answer
147 views
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,...
0
votes
1answer
322 views
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?
...
8
votes
2answers
1k views
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 ...
1
vote
1answer
155 views
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 ...
-1
votes
1answer
93 views
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 ...
1
vote
1answer
703 views
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 ...
2
votes
0answers
56 views
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-...
0
votes
1answer
374 views
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 ...
2
votes
0answers
65 views
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 ...
2
votes
2answers
1k views
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 ...
6
votes
1answer
313 views
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 ...
1
vote
1answer
1k views
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.
8
votes
2answers
3k views
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.
...
9
votes
2answers
2k views
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-...
1
vote
2answers
105 views
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 ...
0
votes
1answer
167 views
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)
3
votes
1answer
1k views
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. ...
2
votes
1answer
86 views
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 ...
1
vote
3answers
503 views
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 = ...
1
vote
0answers
3k views
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?
1
vote
1answer
114 views
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 ...
0
votes
1answer
370 views
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)-\...
4
votes
1answer
347 views
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 ...
5
votes
2answers
461 views
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 ...
4
votes
0answers
740 views
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 ...
1
vote
1answer
477 views
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 ...
0
votes
1answer
912 views
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 ...
3
votes
1answer
276 views
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) ...
1
vote
3answers
1k views
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 ...
0
votes
2answers
1k views
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 ...
3
votes
0answers
247 views
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 ...
2
votes
3answers
1k views
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 ...
2
votes
1answer
110 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
4
votes
2answers
729 views
Black-Litterman: Why should the views be independent of each other?
This question relates to this question.
In the Black-Litterman framework views of inverstors on the market are modelled.
These views have a covariance-matrix $\Omega$.
I always found it quite ...
3
votes
2answers
565 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 ...
6
votes
2answers
739 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 ...
2
votes
1answer
1k views
short-sale constraint with nonpositive-definite matrix in portfolio optimization
I need help about portfolio optimization in R. I have inverted matrix and I want to use it as an input in portfolio optimization. It was non-positive definite before I have handled it. In portfolio ...
0
votes
1answer
994 views
PCA on term structure of interest rates
Interest rate time series seems to be non-stationary whenever test is performed
But covariance or correlation matrix is derived from term structure time series which are non stationary and later PCA ...
