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Questions tagged [correlation]

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

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Admissible values for non diagonal elements of correlation matrix

Preparing for possible job market interview questions I was reading some questions on the site. Regarding this question with its solution interview questions Question Let $\mathbf{C}$ be a $n\times n$...
XY0's user avatar
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How to construct a delta-neutral portfolio containing stocks using correlations?

I’m aware of the mean-variance framework where we construct a portfolio such that we attempt to minimise the variance and maximise returns. What if instead we’re in a scenario where the main goal is ...
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PCA factors not uncorrelated

I ran into an interesting case recently. I am trying to construct a set of uncorrelated factors for a statistical factor model. I have started with picking a certain amount of assets (indices) which I ...
Georgi B's user avatar
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short-term statistical factor models for equities with different trading hours

I wonder if there are existing theory/literature about estimating a short-term statistical factor models for equities with different trading hours. For example if we are estimating a universe with US ...
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Why didn't LMT stock spike and NOC dip in 1990 due to the F-22 raptor competition?

Disclaimer, I am a newbie at finance! I have been tracking the NOC and LMT stock prices and I have a few questions. Both companies seem to be moving together in terms of stock prices. I would expect ...
George Fanaras's user avatar
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Correlation between a stock and the index without the stock

The weight of stock i in index m is w. The returns are, respectively, r(i) and r(m). I know the volatility s(i) of i, the volatility s(m) of m and the correlation rho(i, m) between i and m. The index ...
makpalan's user avatar
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How do I measure the "dispersions" of a group of stock returns

I have $n$ stock return time series $X_1, X_2, ... X_n$. I want to measure how much they have "dispersed" over time. i.e. are they moving "more together" in 2023, comparing to 2022....
Matt Frank's user avatar
2 votes
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How to design a strategy whose PnL is proportion to correlation?

I'm reading about this correlation breakout strategy, whose pnl is proportional to $$E[PnL] \sim (\rho_{1D} - \rho_{2D})\sigma_1 \sigma_2$$ where $\rho_{1D}$ is the correlation of daily returns, and $\...
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Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1

An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$. Discuss how you would ...
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Analytic Hull White model with correlated stochastic processes

I am trying to price a path dependent option which uses two underlyings (a stock index and an interest rate index). I am using Hull White model for interest rate modelling and local vol for stock ...
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Calculation of break-even correlation for diversification effect in N-assets case?

I'm thinking about a generalization of the following case: for 2 assets, there is a diversification effect as soon as i obtain a positive weight for the minimum-variance portfolio in the asset with ...
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A term to compare 2 stocks based on simultaneous trending and ranging characteristics

There a 2 stocks called A and B. We take a look at the daily chart of both stocks over the last 1 year. On 90% of the days A and B both trended or at least one of A or B trended. On 10% of days both ...
FawaMop's user avatar
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Correlation risk between protection (seller) and reference entity

I am learning about central clearing. In my understanding, CDS are usually cleared via central clearing. But at the same time I heard that in case of too much correlation such as US bank selling ...
neko's user avatar
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LMM (Libor market Model) Correlation Calibration

I use a LMM model from a well known vendor, using a SOFR swap curve and SOFR swaptions. The calibration set include many/all of the ATM swaptions from 1m-1y to 30y-30y and I get a very good fit for ...
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How can this problem be defined formally?

Let's consider a straightforward example in which I possess a portfolio consisting of two stocks: $ R(t) = S_{1}(t) \cdot x_1 + S_{2}(t) \cdot x_2, $ Here, $t$ represents the time index, $R(t)$ ...
Barbab's user avatar
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Covariance Matrix of Correlated Random Variable

Suppose I know or have estimated the covariance matrix for one random variable (for example an asset) and have: $$ \begin{bmatrix} <\text{spot, spot}> & <\text{atmv, spot}> \\ <\...
roz's user avatar
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Stochastic process for modelling correlation?

This question relates to Financial Machine Learning, and more specifically to competitions like Numerai. In this competition we have a dataset X and a target y (return over a given horizon). The ...
Lucas Morin's user avatar
3 votes
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79 views

Monte-Carlo method for multi-asset pricing

As I was working on this paper https://hal.science/hal-00319947/document by Emmanuel Gobet, I came across this paragraph that says to price a barrier option on (for example) two correlated assets, you ...
SVIJW's user avatar
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How do your solve for trader's optimal demand in market similar to Kyle's model?

Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a standard probability space and $Z_t=(Z_t^1,Z_t^2)$ is a two dimensional Brownian motion with the filtration $\mathcal{F}^Z_{t}$ and $Z_t^1$, $Z_t^2$ ...
Oliver Queen's user avatar
1 vote
1 answer
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How to hedge a dual digital option

Let us assume we have two FX rates: $ 1 EUR = S_t^{(1)} USD$ and $ 1 GBP=S_t^{(2)} USD $. Let $K_1>0, K_2>0$ be strictly positive values and a payoff at some time $ T>0 $ (called maturity) ...
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Maximum likelihood estimation of system of correlated SDEs

I have the following system of SDEs (which you can think of as 3 different stocks) $$dX_t^1 = \mu_t X_t^1 dt + \sigma_t X_t^1 dW_t^1$$ $$dX_t^2 = \mu_2 dt + \sigma_2 dW_t^2$$ $$dX_t^3 = \mu_3 dt + \...
Spandaver's user avatar
4 votes
1 answer
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If returns are correlated, are Sharpe ratios correlated?

Suppose we have two correlated return series: $$a \sim N(\mu_a,\sigma_a^2)$$ $$b \sim N(\mu_b,\sigma_b^2)$$ $$correl(a,b)=\rho$$ The sample Sharpe ratios of the two series, after $t$ samples for $t \...
elemolotiv's user avatar
1 vote
1 answer
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RiskMetrics Half-Life and Decay Factor Settings

I have been reading about the RiskMetrics methodology. I read that RiskMetrics recommend a lambda of 0.94 for daily data and 0.97 for monthly data. I would like to convert these numbers to half-lives. ...
The User's user avatar
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1 answer
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correlation of 1/X [closed]

My question is the following. If the correlation between the log-returns of X and Y is rho, what would be the correlation between the log returns of 1/X and Y ? Thanks for your answers.
user64747's user avatar
1 vote
2 answers
172 views

hedging out of cross-ccy vol risk using direct ccy options [closed]

Lets suppose a G10 FX vol market-maker starts out with a flat book. During the day, the market-maker bought a EURUSD 1 week ATM straddle from one client while sold USDJPY 1 week ATM straddle from ...
bng's user avatar
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Alternative To Granger Causality?

Are there any other mathematical tests besides Granger that quants use to determine casual relations between two time series? If so what are they? How about convergent cross mapping? Thanks
Daniel Berkowitz's user avatar
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2 answers
95 views

Correlation with Differ Units of Measurement [closed]

I was wondering how to accurately get the correlation between a variable of percent change return and a variable of dollar change or basis points. Should I standardize both variables or will that lose ...
Deepankar Joshi's user avatar
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1 answer
122 views

Correlation between CDS return relevance

I see that there is much literature that uses the correlation notion in the equity returns to construct a graph or look into how they are related to one another. If we want to extend this to Credit ...
statwoman's user avatar
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1 answer
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Mean-variance framework with endogenous correlations

In most mean-variance frameworks I have seen, once we clear markets in the model, it determines asset prices (and returns). However, all of these frameworks assume that the correlation matrix of the ...
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2 votes
1 answer
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Cholesky decomposition reduces volatility of simulated Wiener Process / Brownian Motions

I am trying to simulate $n$ correlated geometric brownian motions (GBM) given a specified correlation matrix $\Sigma$ by following this procedure which uses Cholesky decomposition. However, when I ...
Landscape's user avatar
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1 vote
0 answers
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Techniques for proxying time series / stock prices

What are some good techniques for proxying time series? My purpose is for risk management / modelling and I would like proxy to missing series. Given that I also have to account for volatility, ...
Landscape's user avatar
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0 answers
511 views

Local volatility implied spot vol correlation

I have a question about local volatility models. In a lot of articles it is stated that the implied spot vol correlation of this model is -1 and we usually compare this with stochastic volatility ...
Habib Anoma's user avatar
2 votes
1 answer
113 views

Simulating Correlation (but sample correlation is always too low)

I am trying to simulate correlation in order to price a correlation swap (via Monte-Carlo). For simplicity, let's assume we have 2 assets, and everything is correlated with $\rho$, and there is no ...
Phil-ZXX's user avatar
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How to optimize two highly correlated risky assets?

Suppose you have two highly correlated risky assets. Correlation coefficient: 0.9 Volatility: Asset 1 price varies 2.5% /day Asset 2 price varies 5% / day What can be done to do reduce the risk and ...
Andrew Richmond's user avatar
1 vote
1 answer
578 views

What's the right autocorrelation formula?

I'm trying to see the influence of autocorrelation in my processes and to do so I have to compute it, however it seems to be hard to find a coherent formula over the web. I found pretty much two ...
Fiatpanda2000's user avatar
1 vote
0 answers
106 views

Correlation between fundamental and market data

I got hold of a data set which contains fundamental data like analyst recommendations/revisions (consensus only) and I am trying to come up with an idea of how this could be used as a trading signal ...
ThatQuantDude's user avatar
1 vote
0 answers
53 views

Correlation Size

If I want to make an argument that two stocks are reasonably correlated: Q1. What is the most credible source (most cited) of correlation size for stock return pairs? What is a reasonable small, ...
user1016491's user avatar
1 vote
0 answers
104 views

Adjusting a correlation matrix based on one changed correlation

I have a correlation matrix that is created by historical asset returns, but I want to see how changing one of those correlations would affect the rest of the correlation matrix. How would I go ...
RandyF's user avatar
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1 vote
4 answers
710 views

Does correlation of stocks represent magnitude?

When calculating the correlation between two stocks I get an 85% correlation. Does this indicate anything about the amount the stocks are going up (so if one goes up 10% so does the other) or just ...
user1234's user avatar
2 votes
2 answers
957 views

On moving Linear Correlation (rolling correlation)

Let's say I have two random variables $X$ and $Y$ which each represents the daily returns of two given stocks. I can easy calculate their (total) correlation by finding their covariance matrix $\Sigma[...
Mr. N's user avatar
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1 answer
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Two sound waves in phase at different lags with varying signs?

I have two interest rate time series but want to think of this as sound signals for thought purposes. Imagine you have two time series of audio signals. You run a time lagged cross correlation ...
Jason008's user avatar
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3 votes
1 answer
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Interpreting the average correlation figure in Pozzi et al. (2013) paper

Has anyone read the paper "Spread of risk across financial markets:better to invest in the peripheries" by F. Pozzi, T. Di Matteo & T. Aste? If so, how do you interpret equation (1) in ...
user60352's user avatar
1 vote
0 answers
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Estimation of copula for discrete random variable

I'm interested in the estimation of parameter of copula for discrete random variables. The problem is described as follow: I have 30 discrete random variables $X_1,.., X_{30}$, each random variable is ...
InTheSearchForKnowledge's user avatar
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1 answer
102 views

Lemma (maybe) to imply the sign of the sensitivity to correlation

Can anybody please help me to understaind if this result is true ? Let $\pi=\mathbb{E}\left(f(X_{T})g(Y_{T})\right)$ where $f$ and $g$ are increasing functions. Hence, $\pi$ is increasing with respect ...
DeepInTheQF's user avatar
1 vote
1 answer
581 views

Simulating Correlated Stock Returns in Python (SciPy)

I'm looking to generate stock returns with inter-stock correlation in Python. However, the output is not behaving properly and may have accidental temporal correlation causing issues. This code is ...
rhaskett's user avatar
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2 votes
1 answer
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Kelly Criterion for Multiple Simultaneous Correlated Bets [closed]

I am looking for an equation for the optimal fractional bet sizing for N number of simultaneous correlated bets. I am looking specifically for an equation for binary bets, but an equation for bets ...
GotTheTrumpCard's user avatar
1 vote
1 answer
326 views

How to simulate correlated stock prices (not returns)

Suppose we have two stocks following GBMs. Drift and volatility are calculated based on historical data. Furthermore the stocks are assumed to be correlated (i.e. they move together, if stock 1 goes ...
Willart's user avatar
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1 answer
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GBM drift when simulating correlation betwenn GBM with Cholesky Decomposition

I am currently trying to simulate correlated GBM paths and I found the Cholesky Composition for it. From my understanding, the Cholesky Decomposition can be used to create correlated random variables ...
Merwin's user avatar
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2 votes
0 answers
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Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility

Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar ...
s5s's user avatar
  • 442
5 votes
1 answer
2k views

Information Coefficient (IC) Formulae Differences

I am learning about Fundamental Law of Active Management, and there seems to be two different Information Coefficient (IC) formulae presented. Though I myself am not a CFA candidate, these appear to ...
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