A measure of the degree of linear association between a pair of random variables.

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2
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1answer
393 views

Need overlapping sample autocorrelation correction for calculating asset return correlations

I want to measure the covariance structure of various asset returns based on varying investment periods. Campbell and Viceira (2005) do this, using known return predictors (i.e. dividend yield, ...
6
votes
2answers
228 views

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 ...
2
votes
0answers
132 views

Correlation between idiosyncratic residuals and forward returns

The classic mean-reversion strategy is to calculate an "expected return" (alpha) by computing the raw return for each security and then remove the part which you think is market driven. Statistically ...
4
votes
2answers
219 views

Multifractal Model, Generating Sample Paths with Correlations between Assets

I have studied option pricing using Geometric Brownian Motion to generate sample paths. Because of the normal distribution, it is easy to create a covariance matrix and get correlated asset returns. ...
1
vote
1answer
293 views

Help with understanding a normal distribution/probability question

Could someone please help me translate what this is saying on page P15, section 4.2: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf Specifically: When the ...
2
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0answers
173 views

Potential pitfalls in the use of correlation

Background: The red line is an index, which goes from 0 to 100, measuring uncertainty in the markets. The dark blue line is a price index, which has a lower bound at 0, and virtually no upper bound. ...
2
votes
2answers
274 views

Correlated Wiener processes of different factors

I'm relatively new in this field, so I have a couple of points that I need to clarify. I would like to know how I can estimate the correlation matrix necessary to implement a Cholesky decomposition ...
0
votes
1answer
381 views

Non-intuitive correlation between S&P sector indexes and economic indicators

I am trying to understand how changes in economic indicators like Unemployment Rate, Inflation Rate, and Consumer Sentiment affect the portfolio values. For that I want to measure the correlation ...
4
votes
1answer
104 views

tail correlation during crisis

I am seeking a recommendation for an empirical paper on increased correlations of returns during the 2008 financial crisis, or 'tail correlation' during the crisis, if that is different, or whatever ...
5
votes
1answer
378 views

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 ...
4
votes
2answers
240 views

Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE and the Mass/Material Balance PDE have similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive the ...
2
votes
2answers
1k views

Are two stocks with the same beta have a correlation of 1?

If two stocks have the same beta over same time period, does it mean they are 100% correlated over that time period? In a CAPM framework, a stock's beta is defined as $$\beta_1={\rm Cov} (R_1, M) / ...
5
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0answers
118 views

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?
4
votes
2answers
451 views

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)} = ...
22
votes
6answers
5k views

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 ...
8
votes
4answers
1k views

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 ...
0
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0answers
287 views

Time-varying correlation via state-space representation and Kalman filter

Let a linear time-varying mode like this one: $y_{t}=\alpha_{t}+\beta_{t}x_{t}+\epsilon_{t}$. You can also suppress the constant term to simplify this example: $y_{t}=\beta_{t}x_{t}+\epsilon_{t}$. ...
2
votes
1answer
908 views

Counterintuitive time varying Beta with Kalman filter

If you're used to play with R, you'll enjoy the following reproducible code: ...
6
votes
2answers
270 views

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 ...
5
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0answers
212 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 ...
6
votes
2answers
978 views

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. ...
4
votes
1answer
3k views

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, ...
1
vote
1answer
410 views

Testing Significance of Correlation

Lets say I have the returns of two stocks(stock1 and stock2). Now without running a regression, I lag one of the variables, calculate the correlation between the two stocks and repeat this process as ...
0
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0answers
264 views

Correlation Sensitivity

Suppose I have 2 stocks $S_{1}$ and $S_{2}$: \begin{align} & dS_{1}=rS_{1}dt+\sigma_{1}S_{1}dB_{1}\\ & dS_{2}=rS_{2}dt+\sigma_{2}S_{2}dB_{2}\\ & dB_{1}dB_{2}=\rho dt \end{align} Then I ...
5
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2answers
434 views

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 ...
4
votes
1answer
543 views

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 ...
3
votes
1answer
103 views

How can I evaluate how poor a fit a parametric VaR result would be for a given holding?

I'm currently working on an application that, among other things, computes a one-day parametric VaR for security positions. I understand that the parametric method of computing VaR is a poor fit for ...
3
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3answers
603 views

portfolio diversification tester

Are there any online tools (optionally with developer API, to spare me the scraping) that given an existing portfolio, calculate how well a new candidate position would score to increase combined ...
0
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2answers
342 views

What stock market indicators to model based on twitter feed? [closed]

We are developing an algorithm that models twitter users and groups of words that may indicate real world events. One application is modelling elections, i.e which party is likely going to win. ...
11
votes
3answers
1k views

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 ...
5
votes
2answers
312 views

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 ...
3
votes
1answer
310 views

Rank Correlation Based Prediction

Are there any methods of prediction (machine learning, regression, etc.) which are designed to maximize the rank correlation (spearman correlation, kendall's tau, etc.) of your prediction with your ...
4
votes
0answers
153 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 ...
2
votes
1answer
221 views

Combining covariances?

Consider an economy with assets with return processes $A$, $B$, $C$, $D$. Consider a weighted index with return process $I=aA + bB + cC + dD$ where $a,b,c,d$ are coefficients, and $a+b+c+d = 1$. ...
3
votes
1answer
240 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?
5
votes
2answers
325 views

Correlation: Test for linear dependence

Setting the scene: Assume a multivariate GBM with correlation matrix $\Sigma$. Further, one want to estimate the correlation between two of the assets. Assume one has a suitable estimator of the ...
11
votes
1answer
580 views

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 ...
29
votes
6answers
11k views

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 ...
18
votes
2answers
1k views

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? ...
6
votes
1answer
318 views

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.
7
votes
3answers
715 views

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 ...
32
votes
5answers
4k views

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 ...
7
votes
3answers
303 views

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 ...
1
vote
0answers
89 views

how to identify similar assets based only on a few price samples

Using quantitative finances techniques on limited information, how might one go about finding similar(highly correlated) assets whose public information is available? The only data offered on a list ...
2
votes
2answers
506 views

How to calculate cumulative loss from two factors that have negative correlation?

I went through the most advanced books on statistics and still can't find an answer. There is a well known formula for combining volatility of two correlating variables, but what about adding the ...
5
votes
1answer
996 views

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. ...
5
votes
1answer
261 views

RMT (Random Matrix Theory) issue with callibrating MP distribution -

I am seeing an issue when callibrating an MP distribution. Assume a log return series for the SP500 with the following dimensions dim(xts.sp500.ret.stocksonly) ==> [1] 1133 478 ...
10
votes
6answers
2k views

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 ...
1
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2answers
138 views

Buying one company or index against another, is this readily possible with options, with an accurate return (also Alpha Indexes)

There's a relatively new product in the market / on the Nasdaq called Alpha Indexes. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the ...
10
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1answer
404 views

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 ...