I am computing tick data returns, 5 minute intervals for day's and about 9 months of data.Is there any argument as to why one method of computing is better than the other ?What assumptions am I making for one vs the other.Regards

the first one should be used if you try to compute volatility since you assume a lognormal process. the second one should be used if you try to analyze daily return like in the CAPM.what is your goal?

Goal: Ideally a strategy that will look at the returns and take a position in the security.Compute 5 min interval returns, then look at the cumulative returns.Thanks

then go for the option 2.

It is for the long run ... for small changes you use order 1 of taylor (ln): look at 10% up and 10% down in each notion.

The short answer for how to decide between the two is to understand when each gives correct (& incorrect) results:(p2-p1)/p1 is known as the 'simple return':Advantage: if you are generating a portfolio, w1*r1 + w2+r2 will yield the proper return (r's are returns, w's are weights)Disadvantage: if want to compute a two-period return from one-period returns, you must multiply the one-period returns. While this doesn't sound too onerous, with long time-series, it is very costly & inaccurate, it is also the reason that variance estimates will be incorrect.ln(p2/p1) is known as the 'continously compounded return':Advantage: if you are working with long time-series, the two period return is the sum of the two one-period returns. This is why it yields proper variance results.Disadvantage: w1*r1 + w2*r2 does not give the proper return if the r's are continuously compounded returns.(See Campbell, Lo, MacKinlay for a longer discussion)Matt.

Quote(See Campbell, Lo, MacKinlay for a longer discussion)Would you happen to have the title ?

I guess it's the bible "The Econometrics of Financial Markets"

QuoteOriginally posted by: StudentI guess it's the bible "The Econometrics of Financial Markets"Its very good for reference.. I wouldn't read it first page to last though rgds,Dimitris

The additivity of the second method (as written by matthewcroberts) should not be underestimated. In fact, if you're using the first method and compute some "average" returns without care, you might get some misleading results. For example, if you consider a stock having the following values: year 1 - 100, year 2 - 120, year 3- 100, 1. using the "log" returns, you'll get: R1-2= +18.23%, R2-3= -18.23%, average = 0%2. using the "relative" returns, you'll get: R1-2 = +20%, R2-3=-16.66%, average = +1.66%...

QuoteOriginally posted by: StudentI guess it's the bible "The Econometrics of Financial Markets"I would read Tsay first and then migrate

Drona,>> I am computing tick data returns, 5 minute intervals for day's and about 9 months of data....>> Compute 5 min interval returns, then look at the cumulative returnsMatt already said it, may be it is twice ... If you want cumulative the simple thing would be to 'add' and to have something like return(t1) + return(t2) = return(t1+t2).Remember log(a*b) = log(a) + log(b), log(a/b) = log(a) - log(b).Now take as return the expression x(ti, tj):= log(pi/pj) between 2 time stamps ti and tj you get your additivity:x(t3,t1) = log(p3/p1) = log(p3/p2 * p2/p1) = log(p3/p2) + log(p2/p1) = x(t3,t2) + x(t2,t1).So if your p's reads as prices that says in words: the cumulative returns over any of your time intervalls writes as return of the first and the last price.You will find advantages of the notion if you look at currencies (USD/EUR or EUR/USD) and bonds (returns, yields and futures).The connection between the notions is handwaving like this:If p and q are prices which are close then x = p/q is close to 1. Now look at log(x) as series expansion around 1 which is -1+x + higher terms. Up to second order - which means close to 1 - you ignore higher terms and wrightlog(p/q) = log(x) ~ -1 + x = -1 + p/q = (p-q)/q. Plus some error.So if prices dont change much the notions are close. If you do it often (9month/5min ...) the errors 'add up'. If p and q are quite different it is hmmm. And if you want a 'law' like the above on cumulative behaviour i suggest log, since i would not fight against a solution of a functional equation.If that was to basic: sorry. Otherwise: hope it helps.

Quote2. using the "relative" returns, you'll get: R1-2 = +20%, R2-3=-16.66%, average = +1.66%... You can't do that with 'relative' returns!It will be (1+.2)*(1+ -.16667) - 1 = 0% so you get the same results as log returns.

well that's exactly the idea, what you can't do with 'relative' you can with lognormal ((+20%-16.66%)/2 = 1.67% is misleading while (18.23% -18.23%)/2 = 0% makes perfect sense).excellent points guys!

Just a note of caution here. If you do ln(p2) - Ln(p1), this is only an approximation of the returns. This approximation is very good for (p2-p1)/p1 < 15% after 20%, you get significant rounding erros.If you do 5-min returns that should not be a problem tough, but beware of this for longer time horizons.Peace,Hiboumalin.