My question regards combining several time series into just one series. I have four commodity time series (monthly nominal returns of ags, precious, industrials and energy) and want to combine these (equally weighted) into just one commodity time series. What is the best way of doing this? Either you can just take an average (arithmetic mean) of all four series, or you can take the geometric or the logarithmic mean. What is to prefer? Advantages/disadvatages with the three ways of computing the mean?
Now the series are combined by arithmetic mean and the problem that arises is that when I'm doing portfolio optimization (by markowitz mean-variance optimization) I sometimes can get portfolios above the frontier (over optimal portfolios). This I think is due to that for the calculation of the efficient frontier geometric mean is used. I guess I need to have some consistensy regarding this. What is the "correct" way is of adding these kind of time series together and why is that alternative to prefer over the others?
Another question I have is very related to this. If I want to calculate an annualized return (combining 12 monthly returns), what mean should I then use? I guess geometric mean would be correct for doing this. As of now I calculate (in excel) a one year return as (GEOMEAN(A1:A1000)^12) - 1, where A1:A1000 would be the entire series.
Thank you in advance!
Now the series are combined by arithmetic mean and the problem that arises is that when I'm doing portfolio optimization (by markowitz mean-variance optimization) I sometimes can get portfolios above the frontier (over optimal portfolios). This I think is due to that for the calculation of the efficient frontier geometric mean is used. I guess I need to have some consistensy regarding this. What is the "correct" way is of adding these kind of time series together and why is that alternative to prefer over the others?
Another question I have is very related to this. If I want to calculate an annualized return (combining 12 monthly returns), what mean should I then use? I guess geometric mean would be correct for doing this. As of now I calculate (in excel) a one year return as (GEOMEAN(A1:A1000)^12) - 1, where A1:A1000 would be the entire series.
Thank you in advance!