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bariaji
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Joined: September 11th, 2018, 12:13 pm

Correlation & Volatility - what returns period to use ?

September 11th, 2018, 12:45 pm

Hi, 

I am trying to calculate the correlation between two indexes using closing prices that have significant time zone difference. Say, S&P 500 and Nikkei . For calculation of correlation over a rolling 3 month period is it prudent to use daily returns or are weekly returns better to allow time for information to have flowed across geographies ? Or is there any other better way to handle this ?
Also, if I were to compare the realized volatility of these two indexes, should I use daily returns or weekly return or anything else to compute the volatility ?

Thanks    
 
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Alan
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Joined: December 19th, 2001, 4:01 am
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Re: Correlation & Volatility - what returns period to use ?

September 11th, 2018, 4:33 pm

I'd use daily returns for everything. You might have to shift the Nikkei back one day to get maximum correlation. If so, just report that you are calculating the correlation associated to the shifted cross-covariance [$]Cov(X_t,Y_{t+1})[$], where X is the SPX return and Y is the Nikkei return.
 
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amike
Posts: 76
Joined: October 21st, 2005, 12:57 am

Re: Correlation & Volatility - what returns period to use ?

September 11th, 2018, 11:00 pm

In the absence of any real autoregressive effects, if you sum the direct and lagged covariance, you end up with an (almost) unbiased estimate of the covariance between then two processes.  Then just divide by the 1-day standard deviations.  My estimate is that roughly 75-80% of the dependence is in the lagged return, so it's still a bit of an underestimate if you just use it.

This is not the most efficient correlation estimator, but avoid longer horizon/overlapping returns unless you correct for overlap effects since the estimators are even noisier...  you may want to consider using a longer window though, 3M has a ~6.5% standard error [$]\sim (1-\rho^2)/\sqrt{N-1}[$] on the estimate even without the overlap effects -- the current correlation is ~65% I believe, so this is about 10% uncertainty.

my experience anyway.
 
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bearish
Posts: 3773
Joined: February 3rd, 2011, 2:19 pm

Re: Correlation & Volatility - what returns period to use ?

September 11th, 2018, 11:04 pm

In the absence of any real autoregressive effects, if you sum the direct and lagged covariance, you end up with an (almost) unbiased estimate of the covariance between then two processes.  Then just divide by the 1-day standard deviations.  My estimate is that roughly 75-80% of the dependence is in the lagged return, so it's still a bit of an underestimate if you just use it.

This is not the most efficient correlation estimator, but avoid longer horizon/overlapping returns unless you correct for overlap effects since the estimators are even noisier...  you may want to consider using a longer window though, 3M has a ~6.5% standard error [$]\sim (1-\rho^2)/\sqrt{N-1}[$] on the estimate even without the overlap effects -- the current correlation is ~65% I believe, so this is about 10% uncertainty.

my experience anyway.
+1
 
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figaro
Posts: 147
Joined: October 3rd, 2005, 5:49 pm

Re: Correlation & Volatility - what returns period to use ?

September 12th, 2018, 12:53 pm

Well it is not the same thing, is it?
Say these two time series.
[img]data:image/png;base64,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[/img]
They have negative correlation of daily returns, and positive correlation of weekly returns. And it is not difficult to find examples.
You should use which ever is relevant to the question you are trying to answer.
Having said that, in three months there aren't that many weekly returns, so you probably have to stick with daily.
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