I've just begun to trade pairs using a mean reversion system and am looking for a mathematically sound way of judging the correlation of prospective pairs without getting, at this stage, pulled too deep into rocket science (no doubt that'll come later). Which is more reliable -- correlation of historic prices or of historic price changes? The tests I have carried out produce very different results. All help welcome.
Hotch
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Well...PMCC? That's simple correlation.
Pearson product-moment correlation coefficient - Wikipedia, the free encyclopedia
Should give you everything you could possibly want to calculate it.
Your second question doesnt really make sense IMO.
Surely the most reliable would be the one with the best correlation?
Pearson product-moment correlation coefficient - Wikipedia, the free encyclopedia
Should give you everything you could possibly want to calculate it.
Your second question doesnt really make sense IMO.
Surely the most reliable would be the one with the best correlation?
Thanks, Hotch. I shall check out that link straightaway. Perhaps I didn't phrase the earlier posting clearly enough. What I meant was whether a correlation of the daily percentage change of two securities over a set period was a more reliable indicator of their suitability than a correlation of the historic prices during that same period. Again, thanks for the help.
Overnight, I tested a range of securities on data going back over various time-frames using the CORREL and PEARSON functions in Excel. Deploying each on a variable that was the daily price produced two "top fives" (of highly correlated pairs) that were identical. But when I altered the variable so that it was the daily price change, the effect was significant. The most highly correlated pair was the same, but of the remaining four only one was the same. So the issue of whether to use price or price change (simple or log???) is crucial. But which? And why? Anybody else got ideas?
never traded pairs, but maybe the MV hedge ratio would be useful, which you can then add a weighting to??
Correl(A, B) * (sd(A)/sd(B)) = minimum variance hedge ratio
I guess you can use this, then just move some capital from stock A to B if you are Bullish on the spread, vice versa if you are bearish. Also make sure you use Log returns.
Correl(A, B) * (sd(A)/sd(B)) = minimum variance hedge ratio
I guess you can use this, then just move some capital from stock A to B if you are Bullish on the spread, vice versa if you are bearish. Also make sure you use Log returns.
Thanks, Mr Gecko. Just to be absolutely clear, you mean the natural log of, say, Friday's close, less the natural log of Thursday's?
yeah, but I'd think about it as Ln(Friday/Thursday); mathematically Identical, but it seems to make more sense, if you think about it.
so the two types of return you could have are simple:
geometric return = (Friday - Thursday) / Thursday
or
Log return = Ln(Friday/Thursday)
using the log change means we are now talking about continuously compounded returns, rather than simple geometric returns.
then the minimum variance hedge ratio (h*) is;
Correltation of (A and B log returns) * (standard deviation of A log returns / Standard deviation of B log returns).
FWIW, you can then do some more sums to find out how effective this hedge is going to to be:
[(h*)^2 ] * (variance log returns A / variance log returns B) ; that is, the proportion of the variance that eliminated by hedging. I guess you could vary the ratio h* to suit your own propensity for risk - I mean, you don't want a perfect hedge or you will wipe out your profits, so find out what h* is for the perfect hedge, then go above or below depending on which stock you thought would outperform the other - then find out the hedge effectiveness with this new ratio to see how far you can move away the ideal ratio without taking on too much risk (where hardly any of the variance in the "long stock" is hedged by the "short stock").
Also, be careful about the time series you use to compare data series; it might be a better idea, say, if you have 100 days of daily returns, to do the regression etc... 5 times with periods of 20 days data each, and average the results. It depends on how long you are looking to play the trade for I guess (in this case, you would be looking to run the trade for 20 days).
Have to say though, don't trade equities, so take all this with a pinch of salt.
EDIT: Just had a thought; maybe you should be thinking about Beta etc... instead of / as well as above
so the two types of return you could have are simple:
geometric return = (Friday - Thursday) / Thursday
or
Log return = Ln(Friday/Thursday)
using the log change means we are now talking about continuously compounded returns, rather than simple geometric returns.
then the minimum variance hedge ratio (h*) is;
Correltation of (A and B log returns) * (standard deviation of A log returns / Standard deviation of B log returns).
FWIW, you can then do some more sums to find out how effective this hedge is going to to be:
[(h*)^2 ] * (variance log returns A / variance log returns B) ; that is, the proportion of the variance that eliminated by hedging. I guess you could vary the ratio h* to suit your own propensity for risk - I mean, you don't want a perfect hedge or you will wipe out your profits, so find out what h* is for the perfect hedge, then go above or below depending on which stock you thought would outperform the other - then find out the hedge effectiveness with this new ratio to see how far you can move away the ideal ratio without taking on too much risk (where hardly any of the variance in the "long stock" is hedged by the "short stock").
Also, be careful about the time series you use to compare data series; it might be a better idea, say, if you have 100 days of daily returns, to do the regression etc... 5 times with periods of 20 days data each, and average the results. It depends on how long you are looking to play the trade for I guess (in this case, you would be looking to run the trade for 20 days).
Have to say though, don't trade equities, so take all this with a pinch of salt.
EDIT: Just had a thought; maybe you should be thinking about Beta etc... instead of / as well as above
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