Questions tagged [correlation]

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

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87 views

If I have 2 uncorrelated currencies, why is the volatility of their product higher than either of the volatilities? (better explanation inside)

Let's say we have 3 currencies: EUR/USD USD/GBP EUR/GBP For a minute let's assume that we calculated the EUR/USD-USD/GBP correlation for the last N days and the result was 0.0 (I know this is not ...
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Should negatively correlated stocks avoided while trading on small intervals?

I understand that negatively correlated stocks can be useful for diversification of portfolio while investing. But can it any good for trading?
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101 views

Correlation Matrix - NaN Values

I am trying to create a Correlation Matrix of one particular industry (in the consumer goods sector) with around 15 securities across multiple stock exchanges for the year 2020. However, I have a lot ...
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133 views

Bug found in Optimal Number of Clusters algorithm - from de Prado and Lewis (2018)

I believe I have found a bug in Optimal Number of Clusters (ONC) from the paper "Detection of False Investment Strategies Using Unsupervised Learning Methods". ...
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71 views

Correlation between assets used for valuing multi-asset options (Rainbow options, basket options etc.)

Is there an equivalent to implied volatility used when it comes to modelling correlation in option valuation for multi asset options such as rainbow options (best-of/worst-of calls/put), or is the ...
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Is “Information Coefficient” correlation or rank correlation?

From the textbook, information coefficient (IC) is a measure of the depth of an active manager’s skill. On a more formal basis, IC measures the “correlation” between actual returns and those predicted ...
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29 views

Value the claim $(X-K)1_{X>K}1_{L<Y<U}$

Consider two correlated assets $X$ and $Y$ with marginals $f_X$ and $f_Y$ and linear correlation coefficient $\rho$. Assume a Gaussian copula, $C_{X,Y}(x,y,\rho)$, can approximate the joint CDF well ...
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64 views

Simulating correlated Geometric Brownian Motion with lag

I know that it is possible to simulate two correlated GBM in e.g. Matlab (Generating Correlated Asset Paths in MATLAB) based on cholesky decomposition. However, they take as input the correlation ...
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Credit VaR for this portfolio assuming no default correlation and no recovery?

I am trying to estimate the Credit VaR for a portfolio of two risky bonds. The Credit VaR is defined as the maximum unexpected loss at a confidence level of 99.9% over a one-month horizon. Assuming ...
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Correlation of financial returns: how to account for different frequencies?

If you had to calculate a correlation between two financial return time-series, on what frequency would it make sense to do so? Yearly returns? Monthly? Weekly? Daily? What is the norm here? The issue ...
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Correlation of two strategy's returns, is it a good standard to select strategies?

Let say I have two strategies, A and B. Historically, when the portfolio value of strategy A moves up, then that of portfolio B moves up. Same in the down case. Then, we can say both strategies are ...
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How do you adapt Marcenko-Pastur for EWMA correlation matrix

Hi to denoise the correlation matrix you can use the marcenko pastur distribution. Even without getting into its detail,. its easy, you just use t/n to get the lambda value under which you will ...
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Hierarchical copula vs. vine copula

Vine copulas are a sequential cascade of bivariate copulas meant to capture the hierarchical structure in the dependence structure of random variables. How does this relate or differ from the concept ...
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Correlation between mean-variance efficient portfolios

If the covariance solution between the returns series of the minimum-variance portfolio ($A$) and any other portfolio along the efficient frontier ($B$) is $$Cov_{A, B} = \frac{1}{\mathbf{1}^T\mathbf{\...
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Simulating correlated Geometric Brownian Motion in Python

I want to simulate two correlated Geometric Brownian Motion processes in Python. I found an implementation from Matlab (https://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html) and ...
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Simulating two correlated time series using GBM [duplicate]

My situation is the following: I have two time series TS1 and TS2, whereas TS1 is a stock price. According to literature, TS2 is positively correlated to TS1. Furthermore, since TS1 is a stock price, ...
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Does the $t$-copula or Clayton copula capture the dependence structure of empirical returns better?

Which copula captures the dependence structure of empirical asset returns better? the $t$-copula, which has symmetric tail dependence, or the Clayton copula, which has asymmetric tail dependence, and ...
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Correlation vs. dependence in finance

I found an example that shows how two uncorrelated random variables can be dependent: a normally distributed variable $X$ is not correlated with its square $Y=X^2$. What can be $X$ and what can be $Y$ ...
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143 views

Monte Carlo simulations of correlated stocks by Geometric Brownian motion

I am trying to simulate using a Geometric Brownian Motion process three autocorrelated stocks. In particular, I need to simulate three different matrices with 1000 scenarios each using a Monte Carlo ...
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1answer
83 views

Correlation sensitivity in multivariate $t$-copula for portfolio VaR of electricity futures using Kendall's tau-$b$ correlation matrix

My t-copula model captures the daily dollar returns of a portfolio of approximately 400 assets. I am curious if there's a generally accepted way to quantify the sensitivity of portfolio movements with ...
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1answer
120 views

Covariance of mean-reverting Vasicek process?

I am dealing with a mean-reverting Vasicek process defined as: \begin{equation} S_t = S_0 e^{-at} + b(1-e^{(-at)}) + \sigma e^{(-at)} \int_{0}^{t} e^{(-as)} \ W_t \end{equation} I want to ...
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What is the appropriate transform before calculating the correlation between two assets?

When calculating the correlation between two assets, what is the appropriate transform before taking the correlation? PChg = (P2/P1) - 1.0 LChg = Log(P2) - Log(P1) x = Log(P2) where P2 is the newest ...
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Nasdaq and HML factor positive coefficient

I am using the HML factor from Fama French’s website and have always assumed that a negative coefficient indicates that the portfolio has a tilt towards growth stocks. When I however perform a simple ...
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Are the correlations of multivariate stock prices preserved when converted to multivariate returns?

If data for multiple stock prices has a specific correlation matrix, is the correlation matrix preserved when those prices are converted to multivariate log-differenced returns?
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Should portfolios have zero or negative correlation between assets? [closed]

Is it more optimal to have a portfolio whose assets are negatively correlated? (I am not requiring all assets to be negatively correlated in this case, nor (-1) perfectly negative correlation either. ...
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1answer
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Why does the likelihood of corner solutions in portfolios increase as the number of assets grows?

A three- asset portfolio doesn't seem prone to generating corner solutions, which are very high allocations to one of the assets and $0$ to the others. Instead, when the number of assets is low, these ...
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117 views

Which portfolio is more “diversified”: the $\frac{1}{N}$, the MDP or the max decorrelation?

Equally-weighted portfolio: weights each asset the same $w_i = 1/N$ Maximum diversification portfolio: maximizes the ratio, $\frac{w' \sigma}{\sqrt{w' \Sigma w}}$ Maximum decorrelation portfolio: ...
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1answer
117 views

Non-linear correlation (co-dependence) and the efficient frontier

The graph below shows how the efficient frontier for 2 assets bends into a sharp bisection as correlation decreases from $1$ to $-1$, with $\rho=-1$ being the most diversified, and highly unattainable ...
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comparing volatility and correlation over time

I'm trying to figure out if some emerging markets change over time. First of all I am going to check for changes in volatility. What would be a good method to do this. And do you suggest comparing ...
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454 views

How to annualize the correlation matrix?

If asset returns are daily, and the asset return covariance matrix, $\Sigma$, is annualized by $\Sigma \times 252$, do I also multiply the correlation matrix by 252 to annualize it?
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292 views

How can beta be negative? [closed]

I've been reading about the security market line and the definition of beta as $$\beta_i = \frac{Cov(R_i, R_m)}{Var(R_m)} $$ for any asset (doesn't have to be an efficient portfolio), and have read ...
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References for deep understanding of correlation matrices

Can anyone suggest some references for learning as much as possible (and in detail!) about correlation matrixes? In particular, would be great to have (among others) covered: algebraic and ...
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44 views

Modelling dependance between the two uncorrelated variables using copulas

Are copulas good tool to model the dependence between the two uncorrelated variables. I have X and Y datasets with 260 data points each with Pearson's correlation=-0.06 and Kendall rank correlation=0....
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Sharpe from signal to daily return correlation

A few years back in an interview I remember being asked to derive the Sharpe ratio from the correlation between a pre-open daily signal and the open-close returns. I think you had to make some ...
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Ranking assets by covariance vs correlation

After every change in portfolio (i.e. every trade), I need to calculate a price for each asset in my portfolio. But the calculator is slow. So I want to order the sequence of price updates, from the ...
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1answer
43 views

Pearson correlation significance : Issue with $t$-statistic increasing with $N$

I have two assets which seem not correlated (correlation coefficient = 6.3% using monthly frequency and 48 data points). I want to test the significance of the correlation. Null hypothesis is that ...
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By how much do specific asset correlations increase during a market downturn?

It is well-known that asset return correlations of stocks increase during market downturns. But are there any general properties derived from empirical observation or evidence regarding by how much ...
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Hedging or Relative Value Strategies with Rho or Tau Correlations?

I understand that the Pearson correlation indicates the strength of linear relationship between two data sets. The applicability of this to hedging strategies is intuitive: If I can establish a linear ...
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Covariance of Individual Return and Portfolio Return

Hi guys, Is it possible to get the covariance between the individual return and portfolio return given the correlation matrix, volatility matrix, weights matrix and return matrix? I know how to get ...
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1answer
110 views

Pairs Trading: Normalized price series (co-integrated and correlated) always end up diverging

Need some expert advice and suggestions: I am trying out pairs trading or statistical arbitrage (as traders say). But even if two price series are co-integrated (ADF test, Hurst exponent, Ornstein–...
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27 views

Do asset return correlations have strong non-linear interactions? [duplicate]

If I compute the correlation matrix for $N$ stocks or indices, are there always expected to be strong non-linear dependencies between each asset pair-wise? Or are there only linear dependencies in ...
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65 views

Wrong way risk exotic option

I've priced an exotic option with Monte Carlo method under the Heston model. Then I want to estimate Wrong way risk. In a paper I've found this method to calculate WWR: WWR can be modeled by means of ...
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1answer
113 views

Is non-linear correlation an issue in portfolio optimization?

Portfolio weights are linear combinations of assets. How can it be true then for there to be, and how can someone prove that there is any, non-linear correlation issues in portfolio optimization? Is ...
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105 views

Instantaneous correlation in the 2 factor Hull White model

I'm trying to understand which parameter controls the instantaneous correlation in the 2 F HW model. As in, correlation b/w 2 rates observed at the same time. My thinking is as follows: $$Rate(1)=P(t,...
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218 views

Simulating covariance matrices with nonzero correlation

How would you simulate a covariance matrix of 1,000 stocks where each pair has nonzero correlation? I have literally no idea how to start with this. Any suggestions?
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Joint Distribution of Correlated Variables with Markov Switching

I am modeling a portfolio of correlated assets whose lack of liquidity can be reasonably described by a Markov-switching model. That is, not only is movement size among assets correlated, but so is ...
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1answer
64 views

does oversampling affect the correlation?

I have a dataset of monthly data. One column is my target variable and all the other are my feature. I have computed correlation between my target and all the other feature and then I made linear ...
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Choice of factor model based on correlation

I have a portfolio of assets. Each assets have been discretionally (based on investment manager experience) related to economic factors like (like exchange rate inflation spread etc). Now for each ...
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177 views

Effect of correlation on a best-of rainbow option

EDIT 2: I found the problem(s) and the prices seem to behave as expected now. For anyone interested there was a bug when normalizing the dependant ranom normal variates used in the simulation, so ...
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Cumulative returns are more correlated than non-cumulative

I was just comparing two daily returns series and noted that the correlation between them is a lot higher if they are cumulated (about .95 for cumulative returns, vs .15 for non-cumulative). I feel ...

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