0

I have two series of trading profit results. I use the geometric mean to calculate the average in percent (CAGR). I would like to divide it by the standard deviation by combining the two series, but I´m having trouble calculating the combined standard deviation.

I found this thread, but it looks like it only works with arithmetic mean, not geometric:

Is it possible to find the combined standard deviation?

Is there a way to calculate the combined standard deviation here?

Update:

I got the geometric mean and corresponding geometric standard deviation for two separate data series. I now want to calculate the geometric mean and geometric standard deviation of the combined data series, using only the two mean/stdev values (not the original data points). Example:

Geometric mean 1: 0.070

Geometric stdev 1: 0.051

Number of datapoints: 7

.

Geometric mean 2: 0.053

Geometric stdev 2: 0.049

Number of datapoints: 16

I know how to calculate the combined geometric mean, but how can I calculate the combined stdev from the above values?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Macce
  • 1
  • 1
  • 1
    I can see that you might want the geometric mean of two series, but why do you think you want the geometric SD of two series? You have just two numbers for each case; if you are concerned that they may not be close, then quote their ratio, or both numbers. Otherwise put, there is not much to summarize here. – Nick Cox Oct 21 '14 at 10:44
  • "Geometric series" suggests standard elementary algebra; in statistics a "geometric series" is not defined or characterised by your wanting to take a geometric mean. – Nick Cox Oct 21 '14 at 10:45
  • Maybe I was a bit unclear. I'm trying to calculate the risk adjusted CAGR by dividing CAGR with the standard deviation for a combined series of data. So, I got two CAGR values and two standard deviations, one for each series. I know how to calculate the combined CAGR, but I've not been able to figure out how to get the combined stdev. – Macce Oct 21 '14 at 12:18
  • CAGR is jargon unknown to me and more generally I am still unclear on what you seek here. (I don't think this is mainstream "mathematical statistics" so you may need different tags to attract attention: some people only follow certain tags.) Perhaps you should show a sample of real or at least realistic data and what you have done and what you want to do. – Nick Cox Oct 21 '14 at 12:27
  • I was interpreting "series" literally, as if wanted e.g. the mean of two series for a series of years; it appears that you use it to mean any set of data values. As I understand it, geometric mean and SD are just like mean and SD generally, just that you work on the logarithms and exponentiate at the last step. Combining SDs is the same, but note that you need covariance as well as variances. – Nick Cox Oct 21 '14 at 14:10
  • Thanks! However, that information is way above my current math level, and I'm kind of lost without a detailed formula to solve it for me. Do you know of any website that shows a detailed way to solve it? I've come up empty so far, but I'm not even sure what to search for. – Macce Oct 22 '14 at 08:22
  • I've never heard of this particular problem before, but it's a three step (a) take logarithms (b) apply usual formula for combined SD (c) exponentiate. Sometimes there isn't an answer on the internet and you have to apply first principles. – Nick Cox Oct 22 '14 at 08:51
  • Note that the answer you linked to uses the raw data. The covariance appears only in a different version of the problem. See also http://stats.stackexchange.com/questions/117741/adding-two-or-more-means-and-calculating-the-new-standard-deviation/117749#117749 – Nick Cox Oct 22 '14 at 09:01
  • Thanks.. I'll give it a try and se if I can solve it. At least I can combine the two series and calculate from start to get the right answer and compare with that. – Macce Oct 22 '14 at 12:01

0 Answers0