# Log Returns when calculating correlation

Yo A colleague just asked me why we use log returns when calculating correlations… What is the reason? I’ve never considered it- though I probably read it somewhere along the way? Is it to dampen some of the extremes which might give a false correlation? Three weeks of flat-out drinking may have had an effect on me after all! APP

Practically, I doubt that you will see any significant difference between the log return correlations and simple return correlations. The main reason that people use log returns is that it’s easier to incorporate into mathematically consistent stochastic models.

Well returns can be negative whereas the log of a number must be positive. I think that property helps improve results in certain situations. I have vague memories of this being discussed when I was looking at Black-Scholes etc at college. There should be someone along soon who knows more about mathematics than I do to give a proper answer.

no, log returns can be negative. log(1) = 0, log(anything less than 1) < 0. Test it, type = ln(0.9) into Excel and see what you get. ohai is right… if we are computing the price return over time period 0 to time period 1, the larger the price difference over the time interval, the larger the variance between simple return and log return. Try typing = 120/100 - 1 into excel, and =ln(120/100) and see the difference. since correlations are only appropriate when the underlying distributions satisfy certain properties - such as being normally distributed, or distributed according to a t distribution - but have to be elliptical - you want to use log returns as these may be more normally distributed than simple returns.

upside infinity downside zero

I don’t think it’s really a question about correlations but rather a question about using log returns vs simple returns. There could be cases made for either log or simple returns. Practically, log returns are easier to work with. For example, return over two days is just the sum of individual returns whereas that can not be done with simple returns. That could be one of the reasons why log returns are now used in math models (even though simple returns were used by Bachelier at the end of the 19th century).

maratikus Wrote: ------------------------------------------------------- > (even though simple returns were used by > Bachelier at the end of the 19th century). At least I wasn’t the only guy here to look at his work!

mwvt9 Wrote: ------------------------------------------------------- > maratikus Wrote: > -------------------------------------------------- > ----- > > (even though simple returns were used by > > Bachelier at the end of the 19th century). > > At least I wasn’t the only guy here to look at his > work! I’m glad to be in good company!

actually in addition to what carson and alimesoda said---- actual returns upside is infinity while downside is -100 log returns are symmetric and thus are preferred

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1586656 You should use arithmetic returns in optimization, but there are plenty of cases where log returns should be used.

Thanks very much - that’s just the sort of document I was looking for.