Questions tagged [correlation]
A measure of the degree of linear association between a pair of random variables.
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How are correlation and cointegration related?
In what ways (and under what circumstances) are correlation and cointegration related, if at all? One difference is that one usually thinks of correlation in terms of returns and cointegration in ...
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Time-series similarity measures
Suppose I have two time series $X$ and $Y$ of stock prices. How do I measure the "similarity" of $X$ and $Y$?
(I'm being deliberately vague as I don't have a particular application, and I'm curious ...
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How do I graphically represent the evolution of a covariance matrix over time?
I am working with a set of covariance matrices evaluated at various points in time over some history. Each covariance matrix is $N\times N$ for $N$ financial time-series over $T$ periods. I would ...
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What is the best way to "fix" a covariance matrix that is not positive semi-definite?
I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix).
I am ...
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How to quickly estimate a lower bound on correlation for a large number of stocks?
I would like to find stock pairs that exhibit low correlation. If the correlation between A and B is 0.9 and the correlation between A and C is 0.9 is there a minimum possible correlation for B and C? ...
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Correlation between prices or returns?
If you are interested in determining whether there is a correlation between the Federal Reserve Balance Sheet and PPI, would you calculate the correlation between values (prices) or period-to-period ...
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Cleansing covariance matrices via Random matrix theory
I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
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Why does the VIX index have *any* correlation to the market?
It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of e.g. the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to ...
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What is the most stable, non-trivial dependence structure in finance?
The highest rated answer to the question on What concepts are the most dangerous ones in quantitative finance work? is this one:
Correlation
Correlations are notoriously unstable in ...
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How do I find the most diversified portfolio, or least correlated subset, of stocks?
I have a trading system that chooses top 10 stocks in Nasdaq 100 ranked on relative strength and some other factors. However, I'd like to take positions in only 5 of these 10 stocks based on how ...
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How to detect regime change when estimating asset correlation from historical time series?
Suppose I have two asset time series, $X_t$ and $Y_t$, and I'm estimating their correlation from historical data. I'd like to apply some systematic criterion to estimate what time window I should use ...
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How to generate a random price series with a specified range and correlation with an actual price?
I want to generate a mock price series. I want it to be within a certain range and have a defined correlation with the original price series.
If I choose, say, oil, I want as many time series which ...
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Approximately what proportion of a stock’s volatility is explained by market movement?
Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market ...
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Meta-view of different time-series similarity measures?
While I spend most of my StackExchange time on MathematicaSE, I'm in the business and follow the questions and answers on this site with great interest.
Recently questions like the following (and ...
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Simulating Returns
I'll start this off with a rather broad question: I am trying to simulate returns of a large number of assets within a portfolio of different classes - equity and fixed income in a first step, say 100 ...
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How would you test the hypothesis "There are no idiosyncratic returns available in the market"?
A commentary attributed to Matt Rothman had recently (in the past six months) been making the rounds of the internet echo chamber claimed "There are no idiosyncratic returns available in the market". ...
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Estimate Beta of CAPM from Implied Volatility?
In the CAPM theory Beta of asset $i$ are estimated in this way:
$ \beta_i = \frac{\sigma_{im}}{\sigma^2_m} $
where $\sigma_{im} = \rho_{im} \sigma_i \sigma_m$
But all these data are historical data. ...
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How to estimate the covariance of an index with a basket of stocks?
What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?
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Alternative ways to understand time-varying comovement between two time-series?
I have been looking into ways to better understand how the dependencies/correlations/etc between two time series can vary over time.
I first thought about using a Kalman/particle filter over a ...
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Two correlated brownian motions
Is it true (see here, footnote 2, p.22 / p.14, without proof) that we can obtain two discretized brownian motions $W_t^1, W_t^2$ with correlation $\rho$ by doing
$$d W_t^1 \sim \mathcal N(0,\sqrt{dt}...
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Why do volatility and correlation increase in times of crisis?
can somebody please explain to me why volatility and correlation increase in times of crisis? It is connected somehow to the herding effect. But I cannot really explain it.
And also why are negative ...
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What weights should be used when adjusting a correlation matrix to be positive definite?
I have a correlation matrix $A$ for an equity market that is not positive definite. Higham (2002) proposes the Alternating Projections Method, minimising the weighted Frobenius norm $||A-X||_W$ where $...
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How do I estimate the joint probability of stock B moving, if stock A moves?
I have two stocks, A and B, that are correlated in some way.
If I know (hypothetically) that stock A has a 60% chance of rising tomorrow, and I know the joint probability between stocks A and B, how ...
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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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How can I select the least correlated portfolio of assets?
Can anyone explain the process and the calculations needed to select a portfolio of liquid futures assets with the least correlation? Given a set of returns for a series of assets, how do I select the ...
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If stock A has a 60% chance of rising, and stocks A and B have 80% correlation, what is the chance of stock B rising?
As in the subject, I'm interested in a math puzzle of sorts:
If stock A has a 60% chance of rising, and stocks A and B have an 80% correlation, what is the chance of stock B rising?
Would it be ...
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What are the advantages / disadvantages of the ANTICOR algorithm?
The algorithm is introduced in the paper, Can We Learn to Beat the Best Stock.
The obvious advantage is superior risk-adjusted returns (if you can actually achieve them). Transaction costs and ...
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Does random matrix theory (RMT) for returns' correlation matrices apply if there are high correlations?
Steps to replicate:
Take the correlation matrix of a sample of stocks in the SP500, or a set of ETF's that are include some that are highly correlated (0.7 and above).
Problem observed:
I observe ...
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Why isn't it appropriate to use correlation between prices in a pairs trade strategy?
I've already seen this question and read through all the answers, but I'm still confused about why you shouldn't use price correlation in a pairs trade strategy.
For example, if I'm looking at the ...
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age-sensitive correlation measurements in finances
When it comes to comparing returns or prices of instruments like stocks/ETFs, are there any well-established formulas, or ones in common use, that place stronger emphasis on recent correlations more ...
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The T+H Problem in Factor model forecasts
Suppose we train on M individuals consisting of T observations (i.e. TxM design matrix). The dependent variable is one-year return for each security (H = horizon of one year). In a factor model ...
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When does the Epps effect start?
Wikipedia defines the Epps effect as follows:
In econometrics and time series analysis, the Epps effect, named after T. W. Epps, is the phenomenon that the empirical correlation between the returns ...
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Most natural generalization of covariance/correlation to model dependence of extreme events
One of the most serious shortcomings of covariance/correlation are the assumptions of linearity and normality.
What is the most natural generalization of these measures of dependence when you want to ...
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What is the preferred GARCH method in practice?
My advance apologies, if this question is too naive or basic. Please be patient with my first experiences with SE; ask for clarification, if needed.
I recognize there are many (often-criticized) ...
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Principle Component Analysis vs. Cholesky Decomposition for MonteCarlo
Let's assume we have a portfolio containing large number (~500) of risk factors. We want to simulate the portfolio dynamics. PCA based simulation would be faster as we can reduce the dimensionality. ...
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Correlation decay in lognormal distribution
I noticed that if you use two correlated geometric brownian motions, the correlation structure decays in time pretty fast even for really high correlation values.
I think that is not replicating ...
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How to simulate correlated assets for illustrating portfolio diversification?
I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
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cointegration applied to Portfolio Construction & Risk management
There are all sorts of applications of cointegration to generating alpha on mean-reverting timeseries: comparing spot vs. futures, bond spreads, identifying mean-reverting residuals, etc.
But there ...
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Average correlation of index/portfolio
We try to analyze the average correlation of a portfolio as it can be found here in section 2 b), the same formula which is also used by the CBOE to calculate implied correlations:
$$
\rho_{av(2)} = ...
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When the Inverse Correlation between the SPX and VIX breaks down
As we all know the S&P and its implied vol, the VIX, generally move in opposite direction. To a large extent, the correlations makes sense. IV is one of the main drivers of the price of options, ...
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Measuring co-movement at non-constant intervals
Correlation measures how much two series move together over a fixed interval. Are there any techniques that measure co-movement over a variable time frame? One technique I am aware of is concordance.
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Applications of distance correlation
This question mentions distance correlation.
Where has this concept been applied to financial data and provided new insight?
Do you know any examples or references?
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Is there a copula that can estimate negative tail dependence?
I have encountered numerous copula estimators that can estimate time-invariant and time-varying linear and non-linear correlations on the interval $[-1,1]$, and these estimators are fully consistent ...
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Stability of correlations and volatility
I had a discussion recently about the stability of volatilities and correlations. If we take for example stocks and bonds (think of DAX and Bund) then I have seen changing volatilities (something like ...
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Control for non-synchronous trading in correlations
I am trying to replicate some results from the Betting Against Beta paper by Frazzini & Pedersen.
In section 3.1, Estimating Ex Ante Betas, they illustrate their approach to correlations:
[we ...
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Regime Switching for Dynamic Correlations
I would like to implement a Regime Switching for Dynamic Correlations in an out-of-sample analysis using MATLAB.
After looking at the literature on the subject, they all refer to an article by Denis ...
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Two correlated time series - driver and follower
Say that there are two time series of highly correlated stocks one of which is the driver and the second one follows the first one.
What mathematical measure or formula would you use to identify ...
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Co-integration constraints of coint(X,Z) given coint(X,Y) and coint(Y,Z)?
The Augmented Dickey-Fuller Test can be used to measure how well ranked certain pairs are against others for co-integration.
So then say we have a known co-integration between ...
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FX Forward pricing with correlation between FX and Zero-Cupon
I would like to extend my question about about FX Forward rates in stochastic interest rate setup: FX forward with stochastic interest rates pricing
We consider a FX process $X_t = X_0 \exp( \int_0^t(...
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How to deal with zeroes in returns?
Suppose there are two time series that I want to analyze and compare. However, many, or most, of the data are zeroes for some reason. For example, consider a pair of intraday trading returns time ...