Questions tagged [correlation]

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

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48 views

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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154 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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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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117 views

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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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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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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209 views

Questions about beta, correlation, and covariance

Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in ...
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626 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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782 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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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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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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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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1answer
264 views

how to construct a diversified portfolio based on correlation

I have a porfolio of indexes and I built up a python model based on spearman correlation (I used a spearman and not a pearson because, after running some test on outliers and normality ...
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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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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,...
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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
121 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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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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2answers
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Spot variance drift consequently to style drift

I am looking for some information on how to spot variance drift for a portfolio in accordance to its benchmarks, Let's say that we have returns of the portfolio $\textbf{P}=(P_1,...,P_t,...,P_n)$ and ...
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274 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
277 views

Cega - Correlation Delta from multi-asset derivative

I want to calculate the Cega, i.e. correlation delta, for a multi-asset derivative numerically (the difference of the price from a tiny move in correlation). However, I found it is difficult to follow ...
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mixing fractional Brownian motions

Given two Brownian motions $W_t^1, W_t^2$, we can have them correlated by $$W_t^1 = \rho W_t^2+\sqrt{1-\rho^2}Z_t$$ where $W_t^{2}$ and $Z_t$ are independent of each other. My question then: is there ...
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1answer
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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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59 views

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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227 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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105 views

Conditional and unconditional variance, autocovariance and autocorrelation of an ARMA process

Given an ARMA(1,1) process $x_t = a + bx_{t-1} + \varepsilon_t + \theta\varepsilon_{t-1}$, how can we find the conditional variance, i.e. $Var_{t-1}(x_t)$, find the unconditional variance, i.e. $Var(...
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Is non-linear correlation problematic in financial time series prediction?

Many traditional finance models assume linear relationships between variables and features. Aren't linear correlations/covariances unable to capture financial processes empirically since they actually ...
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1answer
75 views

Covariation of Ito semimartingales

If we have two Ito semimartingales over $[0,T]$: $$d X_t^i=a^i_tdt+\sigma_t^idW_t^i,\quad i=1,2$$ What is the relationship between $$\langle X^1,X^2 \rangle_t \quad \text{and} \quad \langle W^1,W^2 \...
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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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110 views

Hedge Ratio Calculation

My question is if I have a spot position of a commodity e.g Naturals Gas I want to hedge, how would I determine, which futures e.g. quarterly, yearly I should pick. Should I just take the one it is ...
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realized correlation estimation

I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
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391 views

Correlation between stock prices given correlation between returns

assume I have two stocks with known volatilities and a known correlation coefficient of returns - does anyone know how to determine the correlation between the prices and NOT THE RETURNS
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56 views

Proving an Identity between a pair of correlated Wiener processes

Suppose we have the following subordinated stochastic differential equations: $dR(t)=\mu dt+\sigma (Y(t))dW_{1}(t)$ $dY(t)=f(Y)dt+g(Y)dW_{2}(t)$, where $W_i$'s are standard Wiener process such that ...
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Trading Ranges for Tactical Asset Allocation

Do methods exist to determine trading ranges around benchmark weights/strategic asset allocation weights for a tactical asset allocation from the correlation structure between the individual asset ...
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1answer
178 views

question about spot/vol correlation

In this paper The Interplay between Stochastic Volatility and Correlations in Equity Autocallables by Alvise De Col, Patrick Kuppinger (2017) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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Exact solution stock price with Vasicek interest rate model

Define two correlated stock price- and interest rate (Vasicek) processes, governed by the Wiener processes $W^{S}(t)$ and $W^{r}(t)$ $$dS(t)=r(t)S(t)dt+\sigma S(t)dW^{S}(t)$$ $$dr(t)=\kappa(\theta-r(...
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Simulate correlated Brownian motions conditioned on future state(s)

Consider a model defined by 2 geometric Brownian motions $$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$ $$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$ with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(...
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What are non-variance (non Markowitz) based theories of capital allocation between non-correlated assets?

A large amount of literature in finance accepts the standard deviation in return as if it were an accurate measure of "risk." What are some other financial theories for how to allocate capital ...
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Literature and Intro to Dispersion Trading

I am familiar with the basic idea of the dispersion trade i.e. index vol vs constituent vol and implied correlation. I am wondering if there are any standard resources (pdfs, books, presentations) ...
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94 views

Average portfolio correlation vs. external metric

I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it! I have a portfolio of assets, with data on historical ...
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183 views

Estimate covariance matrix using prices

We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case? I can think of two possible reasons and would appreciate comments/feedback regarding ...
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2answers
849 views

Creating a Covariance Matrix

Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
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1answer
357 views

target market correlation for long / short equity portfolio

Given a long / short equity portfolio, I want to have some net long market exposure. My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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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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80 views

Two commodities which are normal distributed and perfectly correlated

The daily price change in commodity 1 is distributed $N(0,0.15^2)$ and the daily price change in commodity 2 is distributed $N(0,0.3^2)$. The two commodities are 100% correlated. 1) Does the relative ...

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