# Questions tagged [correlation-matrix]

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38 questions
76 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, ...
34 views

### Parametric VaR assumption question

Why do you have to make a correlation matrix when calculating the parametric value at risk, if one of the assumptions for this method to work is that the assets of the portfolio must be independently ...
35 views

### VECM Correlation Matrix

I am trying to implement the modified information share price discovery method desribed by Lien. They start by estimating a VECM of the form where and and it's Vector Moving Average ...
129 views

### How to do QE scheme for n correlated assets?

I'm trying to simulate correlated assets under Heston model. I coded the QE scheme for a single asset but i dont understand the next step: How should i set the correlation matrix given my n-asset ...
166 views

### generating a correlated RV which has the same correlation to existing samples

Suppose I have generated a collection of correlated sequences of samples $(S_i)_{i=1}^{n}$ from random variables $\mathbf{\underline{x}} = x_i$. Let's fix a sequence of reals $(\sigma_i)_{i=0}^{n}$. ...
785 views

### Didier Sornette's Strategy to Exploit Return Correlations

In his book, "Why Stock Markets Crash", Didier Sornette discusses a trading strategy that exploits return correlations. Consider a return $r$ that occurred at time $t$ and a return $r'$ that ...
243 views

### Cleaning correlation matrix, Bun Bouchaud Potters (2016) method

Stock returns correlation matrices are notoriously hard to estimate, especially when the number of assets $N$ is large with respect to the size of the readily available historical returns $T$. Many ...
4k views

### How to calculate ex Ante Tracking Error

I'm looking to find the correct way to calculate the ex ante tracking error of a portfolio. If say I have 10 funds, and their historical returns series (used to calculate mean return, standard ...
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### Minimum Subset within Correlation Matrix

I have a correlation matrix that I produced in Excel using the monthly returns from 200 different trading systems over a X year period. So, the correlation matrix is 200 rows by 200 columns. How do ...
295 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)-\...
68 views

### Isolating single assets standard deviation in a portfolio accounting for correlation

I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio ...
738 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 ...
1k views

### How to create a basket of currency pairs with the lowest correlation in R?

My strategy is designed to buy and sell all assets of a universe and rebalance periodically. It goes either long or short. To limit risk exposure to a single currency I would like the assets in the ...
136 views

### How to infer correlation?

Let's say a have a correlation matrix $\Omega$ for 25 assets which I use to generate a Monte-Carlo simulation. Let's assume that $\Omega$ is valid (i.e positive-semi-definite, etc...) and estimated ...
216 views

### modeling regime switching for Correlation matrix

I am trying to estimate covariance in multiple time series. However, I want to do this using a regime-switching framework. So, I start with fitting a GARCH(1,1) model and then de-volatalize the series....
111 views

### Interpretation of Correlation Matrix

I have past data which is in vector form. The information shows the probabilities of a AAA rated company to migrate to another credit rating. So for example, (x1, x2, x3) has the probabilities of ...
780 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 ...
126 views

### Does the correlation of matrices have explanatory power when building a pattern recognition model?

I'm using 8 different variables (with daily observations) with the purpose to compare different months across the historical data. For that purpose I calculate the correlation between each month and ...
285 views

### Stock Correlation Matrix, Multiple Currencies

If i have a portfolio of stocks from different currencies and i want to generate a correlation matrix from the stocks, how is the correct procedure ? Imagine a portfolio which the base currency is ...
138 views

### Sample size and historical correlation matrices

I was wondering whether any literatures existed on how to properly estimate correlation matrices from historical data. Obviously the entire procedures allows a lot of leeway. The frequency of the ...
81 views

### Effect of kernel smoothing on correlation

Instead of deriving correlation matrix on standardized returns (z scores) would it not be more accurate to kernel smooth the cdf and then norminv the cdf values for the return z score and then ...
2k views

### Given a correlation martrix, calculate portfolio's correlation with its assets

Find correlation vector like $[ d e f ]$ where d, e and f represent correlation of P(portfolio) with its assets A, B and C respectively. The assets A, B, C can be another portfolio. In order for that,...
2k views

### ex ante tracking error correlation between funds

I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...
4k 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.
685 views

### How to treat large (5K-10K) non-positive-definite (particularly near-singular) covariance matrices 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 ...
450 views

### Interpretation of cross-correlation matrix when one sample distribution is not normal

I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
12k views

### How to simulate correlated Geometric brownian motion for n assets?

So I'm trying to simulate currency movements for several currencies with a given correlation matrix. I have the initial price, drift and volatility for each of the separate currencies, and I want to ...
350 views

### Stress testing covariance

Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure ...
362 views

### Obtaining a consistent covariance matrix for stochastic volatility processes

What is the condition for underlying stochastic volatility processes to give a consistent covariance matrix? I read in Hull that in order to have a consistent covariance matrix, volatility parameters ...
254 views

### Is Optimization ignoring correlation valid?

I have a fairly pedestrian optimization problem: Max sharpe, subject to a x% vol target. I have a set of expected returns, asset vols and a correlation matrix. I am finding that when i set the off-...
202 views

### How to see if a set of asset returns corresponds to a known correlation matrix?

Let's say I have an arbitrary set of $n$ period returns for $k$ assets, and a given $k \times k$ correlation matrix (of asset returns), which is known a priori. Does it makes sense, or is it even ...
1k views

### Searching for pairs-trading in sub O(n^2 t) time

Let there be $n$ stock symbols. Let each stock symbol have exactly $t$ ticks (with all ticks miraculously aligned.) We are now searching for potential pairs for pair trading. A brute-force solution ...
210 views

### Rolling window Kendall's tau against APARCH(1,1) correlation

Assume you want to forecast the correlation matrix of a stocks' basket (say 15 ~ 20 stocks from different sectors); assume you need to forecast at $T$ days because you will use the forecast ouput with ...
98 views

### Neglect the positive values in negative interest rates modelling?

The magnitude of the negative interested rate should vary correlated with the increase in fixed assets prices and with cross-currency basis spreads. Could their volatility / correlation coefficients,...
264 views

### Does the correlation amongst stocks rise when stock values decline?

Is there any research on whether the correlations among stocks rise when stock indices decline? Which model could account and test for that effect ? Maybe GARCH-BEKK, or some models using copulas?
2k views

### Analytical relationship between a covariance matrix and cross-sectional dispersion

Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average cross-sectional variation as the standard deviation across returns for a particular joint ...