This maybe an absurd question. However I ran some correlations on volatility instead of log returns for WTI and heating oil and Ethanol...to my surprise they were highly similar. Is this just coincidental or is there a mathamatical reason that this is almost the same. IF the same, do you see why this relationship would break down?thanks for your thoughts!Latigo

I will guess that it is because of 3 things:(i) the returns of say WTI & heating oil almost always have the same sign on a given day.(ii) the absolute returns can serve as a volatility proxy.(iii) certain cross-covariances are relatively smallTake A = WTI and B = heating oil.Assuming (i), E[r(A)_t, r(B)_t] = E[|r(A)_t|, |r(B)_t|]Simple model: the returns each day are drawn from a normal distribution with a mean zero and volatility (for that day) Sigma_tThen, E|r(A)_t | = C Sigma(A)_t, where Sigma(A)_t is the daily volatility. This is (ii)(The constant C involves a factor of Sqrt[Pi]). So, we could write (*) |r(A)_t | = C [ Sigma(A)_t + u(A)_t],where u(A)_t is a series with zero mean.Then (**) E[r(A)_t, r(B)_t] = E[|r(A)_t|, |r(B)_t|] = C^2 { E[Sigma(A)_t, Sigma(B)_t] + E[u(A)_t, Sigma(B)_t] + E[u(B)_t, Sigma(A)_t] + E[u(A)_t, u(B)_t] }So, if the last 3 cross-covariance terms are small compared to the first (this is (iii)) then E[r(A)_t, r(B)_t] = E[|r(A)_t|, |r(B)_t|] ~ C^2 E[Sigma(A)_t, Sigma(B)_t],which seems to be what you are seeing: The proportionality constant C will cancel when you compute the correlation. If this is what is going on, you can test it by estimating (*) from a regression,and then calculating each of the 4 terms on the rhs of (**) separately to see their relative magnitudes.The relation would fail when either of (i), (ii), or (iii) begin to fail.regards,

Thanks so very much for your input Alan. Is it possible to see a quick numerical example? Also, I have read some journals where there is some sort of movement to begin to test the correlation of VOLS given that when VOLS increase dramatically, most security types correlations revert to one. Now, these journals were mainly for the financial side and I have yet to read anything regarding commodities. but given so many products are a derivative or use crude in their creation, i would think in my layman's mind...these too would move toward one.Any thoughts?Latigo

Well, perhaps you should explain exactly what data you have, and what the results were for the various correlations of your question.Then, I might be able to suggest how you can use your data to test my explanation.

Oil is by far the biggest driver of heating oil, so how could the volatilities NOT be positively correlated? Not a rhetorical question--I can't think of a counter-example. Seems like refiners can pass on their cost increases pretty easily.

Hello Alan,Well i was trying to incorporate Hull's formula for exponentially weighted correlations. So I feel i bastardized his great work by exponentially weighting the VOLS and then using the excel function "Correl" to see the correlations of commodities like WTI, WTS, HO, NG and many more products.At the moment, it seems that there isnt much difference between my results and that of my coworker who did a simple regression analysis on Ethanol and WTI. (the relationship between these two is the main purpose of this project...but has grown to much bigger). However I have another coworker who has deployed the 'right' way of Hull's exponential correlation and she gets negative correlations. which i feel is totally wrong as well.So it appears that the regression analayis concurs with my 'method' of correlation and a simple correlation also gives similar results but what does similar really mean? Is there that massive of a difference between a correlation of 92 vs. 87? OK, I am just rambling and thinking out loud now. I look forward to your opinions Alan or anyone.Thanks!Latigo

What exactly are the VOLS? Implied volatilitys? (if so, exactly what contracts?) or historical volatilities (if so, computed how?)

Ok, i need to be a little better at my explanation. Yes, i use historical volsI pull the data from our internal database and I pull the historical prices from last COB (close of business) up to the last 75 trading days.I then take the log return from these prices to derive the VOLS. It is here where I deployed Hulls formula incorrectly. This is what the formula looks like in excel. Looks at yesterday's vol and todays log return.WHere: Lambda = .94P: Column equals VolsO: Column equals Log returnsP12=(SQRT(LAMBDA*(P11^2)+((1-LAMBDA)*(O12^2))))P13=SQRT(LAMBDA*(P12^2)+((1-LAMBDA)*(O13^2))))Once I have the monthly buckets for the curve, I then use the Excel 'correl' function to derive the correlation,Ok...so...I hope this all helps.

Sorry, I really don't follow what you are doing (I am not much of an Excel user).In any event, my analysis was based on the idea that you have a daily realized volatility, computed let'ssay from 5 min data, using only each day's data. This avoids overlap problems.Then, for each of WTI, heating oil, etc, you have two daily time series: Returns(t), and Volatility(t), fort = 1, 2, ... where t counts the days. You can compute cross-correlations of these various series andcompare them. Obviously, we expect most of these correlations to be positive and reatively large as theseries are all closely related.Beyond that, you might try to relate the Return(t) and Volatility(t) series for each underlying by the models I suggested.

Ok, Alan...thanks I believe i will try to build your model. A couple of questions for better understanding. Why would i want to use Sqrt[Pi])And why do we need to pull from a series with zero mean? Is this because we are assuming normal distribution. If so, I am using log returns...will this have an impact?thanks!

QuoteOriginally posted by: hlatigoOk, Alan...thanks I believe i will try to build your model. A couple of questions for better understanding. Why would i want to use Sqrt[Pi])... Once you have the two series, you can run the regression|r(A)_t | = C [ Sigma(A)_t + u(A)_t]This will generate an estimates for C. Then, you can compare with the value from the conditional normality assumption.The latter involves Sqrt[Pi]. And why do we need to pull from a series with zero mean? Is this because we are assuming normal distribution. If so, I am using log returns...will this have an impact?... Put in a mean if you want; usually they are negligible; do whatever is convenient.thanks!