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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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48 votes
4 answers
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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 ...
Ram Ahluwalia's user avatar
18 votes
6 answers
3k 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 ...
Suminda Sirinath S. Dharmasena's user avatar
7 votes
2 answers
2k 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)} = ...
Richi Wa's user avatar
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63 votes
6 answers
31k 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 ...
Joshua Ulrich's user avatar
12 votes
2 answers
27k views

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}...
Basj's user avatar
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53 votes
8 answers
28k 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 ...
user672's user avatar
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22 votes
3 answers
39k views

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 ...
Milktrader's user avatar
22 votes
3 answers
4k views

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 ...
Ram Ahluwalia's user avatar
18 votes
3 answers
6k views

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 ...
user1232's user avatar
  • 181
6 votes
1 answer
1k views

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(...
Joe's user avatar
  • 301
3 votes
2 answers
613 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 ...
Amrit Prasad's user avatar
3 votes
1 answer
672 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 ...
ontic's user avatar
  • 85
2 votes
3 answers
656 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?
Trajan's user avatar
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49 votes
5 answers
10k 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 ...
Tal Fishman's user avatar
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25 votes
2 answers
3k 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? ...
Joshua Chance's user avatar
20 votes
1 answer
2k views

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 ...
vonjd's user avatar
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17 votes
3 answers
2k views

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 ...
Owe Jessen's user avatar
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11 votes
2 answers
5k views

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-...
michael's user avatar
  • 257
7 votes
2 answers
4k 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. ...
Alexey Kalmykov's user avatar
7 votes
1 answer
3k 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. ...
Belmont's user avatar
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5 votes
2 answers
917 views

Difference between Local Vol and Copula

Let's assume we have ATM European call on a basket of two stocks and price it with: 1) Multivariate Local Vol with constant correlation 2) Gaussian copula Assuming we use the same correlation ...
NullSpace's user avatar
4 votes
1 answer
776 views

Correlation sensitivity of Rainbow options

I read from various sources (eg. Exotic Options and Hybrids, M. Bouzoubaa) that the correlation sensitivity of Rainbow options (say a call price on a basket made of 50% of the best stock, 20% of the ...
Alex's user avatar
  • 225
4 votes
1 answer
603 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
ZRH's user avatar
  • 1,671
4 votes
1 answer
2k views

What is the covariance of two correlated Ornstein-Uhlenbeck processes?

What is the covariance of two correlated Ornstein-Uhlenbeck processes? I was trying correlation(1,2)*Var1^(1/2)*Var2^(1/2), but I am not sure! I took Var1=(sigma1^2/(2*speedofmeanreversion1))*(1-exp(-...
LenaH's user avatar
  • 133
3 votes
1 answer
363 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 ...
develarist's user avatar
  • 3,030
3 votes
2 answers
781 views

Find k of n assets that "minimize" the correlation matrix

I'm trying to find an efficient way to select $k$ from $n$ risky assets that are the least correlated with each other. I know that I can perform a brute-force search of all $k$-sized combinations of ...
geofflittle's user avatar
3 votes
1 answer
488 views

Pricing and Hedging an Option through a Currency Triangle

How is the option price of an plain vanilla option (in a Black Scholes setting) derived, which is written on, say XAGGBP but practically hedged with XAGUSD and GBPUSD (because these are more liquid)? ...
Tim's user avatar
  • 163
3 votes
1 answer
5k views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
Egodym's user avatar
  • 698
3 votes
1 answer
5k views

What is Base- vs. Implied Correlation of a CDO tranche?

What is the difference between Base Correlation and Implied Correlation for a CDO tranche?
emcor's user avatar
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2 votes
1 answer
3k views

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,...
user12348's user avatar
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2 votes
2 answers
6k views

Do 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) / {...
nonbaryonic13's user avatar
1 vote
1 answer
602 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
  • 1,641
1 vote
3 answers
257 views

generating a correlated RV which has the same correlation to existing samples

Suppose I have generated a collection of correlated sequences of samples $(S_i)_{i=1}^{n}$ from random variables $\mathbf{\underline{x}} = x_i$. Let's fix a sequence of reals $(\sigma_i)_{i=0}^{n}$. ...
Djoker's user avatar
  • 13
1 vote
1 answer
324 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 ...
Oscar's user avatar
  • 902
1 vote
2 answers
3k views

Correlation between S&P500 returns and 10y US Treasuries yields

I'd like to investigate the comovement of stock index returns with bond yields but I don't know which return's duration to use (1-year, 1-month or anything else) to get a better view of the ...
Alberto M's user avatar