Hi all,I have a basic doubt on how to estimate correlation: on price or on returns?My problem is to simulate for example with a GBM the price evolution of two stocks.Initially I thought to make the correlation estimation on prices but I saw that in literature is made mainly on returns.I don't understand why I should choose prices or returns and why the correlation can differ a lot if I use prices or returns.Thank you very much for your time!!!!Bye

It is not really intuitive, but I would strongly recommend that you carry out a controlled experiment. Go ahead and simulate the return for a reasonable number of days (say 250) of two uncorrelated stocks with prices following GBM with the same volatility. Run a regression on the returns as well as on the price series. Repeat a bunch of times (say 10,000). You should find that the distribution of betas from regressing returns look nicely normal around (the true value of) zero. You should also find that the betas from regressing prices look something like uniform between -1 and 1, and that this will not really change by increasing either the sample length or the number of MC runs. But don't take my word for it. Do it!

A related way to think about it is that the correlation is a property of the driving Brownian noise terms and the issuebecomes: what is the best way to estimate that, given the two time series? A good estimator will recover theparameter 'exactly' as the length of the series grows to infinity, and this will be true for the estimator using returns but notprices. The latter will not benefit from a very long series because the numerator and denominator will bedominated by the exponentially largest terms near the end of the series, assuming a positive growth rate.

QuoteBearish: But don't take my word for it. Do it!Definitely agree, a most enlightening Monte Carlo experiment that you can do in a few minutes of work.