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Topic Title: Correlation: price series or log(returns) ?
Created On Tue Feb 06, 07 09:35 AM
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Maikel
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Tue Feb 06, 07 09:35 AM
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For computation of VaR of stocks and indices, what are the advantages and disadvantages of finding the Pearson coefficient of either the price series or the returns series? (read, in the latter, log(returns) if you wish).

My early data suggest that closer-to-zero coefficient figures appear when using corr(log(returns)) or corr(returns), whereas corr(series) lead to higher correlation...

Regards,

Michael.


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Rez
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Tue Feb 06, 07 10:18 AM
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corr(series) is spurious since they are non-stationary.

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Traden4Alpha
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Tue Feb 06, 07 01:03 PM
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I'd consider three issues in making the decision:

1) Ask yourself which is more important to predict or understand: 1) the change in price that generates profits and losses in a trade or position (the returns) or 2) the absolute price level? Price series correlations may be much higher, but they don't explain the variance that you really want to explain.

2) Look at the pattern of the residuals for the two types of correlation. Price series correlation will probably show large and consistent residuals for long periods of time, suggesting that price correlation is missing crucial bits of structure (nonstationary)

3) If you look at price correlation in terms of each price being a sum of price returns, you'll find that early price returns have a much bigger influence on the corr(series) than more recent price returns -- the oldest price return of an N-data point series will have N times the influence as the most recent price return.

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Maikel
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Tue Feb 06, 07 01:13 PM
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Understood. Found a paper dealing (and referencing) with this kind of issues (The Effect of Mis-Estimating Correlation on Value-at-Risk - Vasiliki D. Skintzia, George Skiadopoulosb, Apostolos-Paul N. Refenesa) which is helping enormously.

Thanks to all.

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bogaso
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Fri Mar 07, 08 10:52 AM
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Can Traden4Alpha please explain me what you mean by residuals in correlation " Look at the pattern of the residuals for the two types of correlation"? And also if u detail abt the 3rd point, especially the phase "....each price being a sum of price returns" it wud be fine.
 
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Traden4Alpha
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Fri Mar 07, 08 12:01 PM
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The residuals of the correlation are what you have when you subtract the predicted value of dependent variable from the measured value of the dependent variable. This forms a dataset that one can plot or analyze. Standard approaches to correlation assume that the residuals are i.i.d. with zero mean and constant variance and we can perform various tests. If the residuals contain structure (e.g., time series of them contains significant runs of the same sign) then we might wonder if our correlation is really valid.

Regarding "....each price being a sum of price returns" the issue here is to express the price series algebraically as an initial price P0 and the sum of returns, Rn. Thus the price series [P1, P2, P3,..., Pn] becomes [P0+R1, P0+R1+R2, P0+R1+R2+R3, ...., P0+SUM[R1,R2,R3,....,Rn] ]. Notice that the value of R1 (the OLDEST value in the return series) contributes to every value of the price series and that Rn (the most recent value of the return series) only contributes to a single value of the price series. Thus, with a price series, the older data has more influence than the newer data which seems rather counterintuitive in most models of market action.

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