Hi,I have noticed in general that the correlation of the daily returns is used when analysing more than one underlying. Is there a reason this is done rather than using the correlation of the underlying prices?Say the correlation of returns over the last three years for BP and Shell is 84.7% however the correlation of the prices of the two underlyings is 94.5%. As you would expect these stocks general trend in the same direction. BP Shell14-Aug-00 589p 558.5p12-Aug-03 442.75p 410.75pSimply - what's the reason to use the daily returns?

I used to think long and hard on what the correlation between the price series might imply (if anything...) and have decided that correlation of price series will only tell you that the price have been on the "same side" of its period average compared with the other price more than vice versa. This information is not usable for anything I know of. Calculating the correlation of the returns however will tell you if the two price series move in the same direction at the same time, which has (some) relevance to risk calculations for instance.Mess with some sample data and you will find the same.../Rutger

johndcb, Correlation is a dependency measure that is more appropriate for normal random variables. That’s why it is used with returns and not with prices.

Suppose you believe the prices of two things are related, but there may be leads or lags in the effect. For example, the price of crude oil is related to the price of gasoline at the pump, but it can take weeks for changes in crude prices to be reflected at the pump. In this case you might find that there was a small correlation of returns, but a high correlation of prices.In finance, we are generally concerned with effects that do not lead and lag. If the price of BP stock moved the same way as Shell, but a week later, it would be easy to make money in the stock market. People would spot the correlation and exploit it until the price movements were simultaneous. Therefore, price correlations are not regarded as useful. Either they simply show the effect of return correlations, or they show the effect of a common factor (like inflation) that cannot be exploited to make money, or they are spurious.There are situations in finance where the above argument does not apply. However, people rarely go all the way to price correlations, instead they use cointegration to get something in between.

doubleV,does correlation really imply dependency? Or wasn't it the other way around.And no, correlation has nothing to do with normal distribution. Its only when you get around to summing up the parts that you have to use the appropriate method for the chosen distribution.However, I must say, these are my humble opionions from a faint memory of my beloved (not) Tech U ;-)Regards,Rutger

On a time-series level, people compute return rather than price correlations because returns are much more likely to be stataionary and simple correlation loses meaning when applied to non-stationary data. As Aaron says, if you really want to model the interdependence between non-stationary data, like price levels, then cointegration can be used. With regard to correlation, normality and dependence, correlation completely summarises dependence between normal (more generally elliptical) random variables. Once you move outside this class correlation doesn't tell you everything about dependence, indeed one can construct examples with a couple of variables that are essentially uncorrelated but which have exceptionally strong dependence.On a less technical level, I guess that people care about returns rather than prices as returns allow one to track how one's investments are changing one's wealth.richg.

Many thank Aaron, Rutger and richg - I think my understanding of this is improving.Aaron, I guess there are many ideas out there about combining correlation and cointegration whilst keeping the appropriate matrix positive semi-definate. Can you suggest any reading that might be useful?richg, could something like a correlation function be used to allow for a more descriptive correlation of non-normal random variables? Say a correlation measure that is a function of the scale of price returns? Say as an example, a correlation of 0.6 for returns within +/-4% and then 0.9 for returns outside this band?john

If you search Wilmott for cointegration you will get a lot of useful material and references.