Suppose I have a portfolio of ETFs and I want to calculate its performance over time in the past. Which metric/formulae suits it best? Which of the parameters will vary over time in this formulae? Do we have to use any benchmarks? Do these benchmarks have to be global or in the same category? Let's suppose that there are no additional cash-in flows and no rebalances.
Annualized Rate Of Return is the most common metric for measuring portfolio performance. To calculate that for your portfolio (with no cash in/out-flows), divide the current balance by the initial balance, then take that to the
1/n power, where
n is the age of the portfolio in years (e.g. 1.5 for 18 months). Note that this only works because there hasn't been any cash flows - if there are, the method is a bit more complex.
So that gives you a number - is that good? You have to have something to compare it against. You can find annualized return for virtually any index like the S&P 500.
Do these benchmarks have to be global or in the same category?
If you want to compare how well you chose ETFs then it would be best to be at least in the same country, and probably in the same category if possible. Most people, though, have blended portfolios with a mix of domestic stocks, bonds, and international stocks, with maybe some alternative investments like real estate mixed in. For those, a composite index may be appropriate, where you take the weighted average of multiple indexes representing your investment allocation.
In addition to Rate of Return, I would also recommended to compare volatility (risk). For example if you compare ETFs TQQQ and QQQ for the year 2019, you'll see that TQQQ performed considerably better. However if you look at 2020 you will see that there are risks inherent in TQQQ structure
(all investments come with risks, and this is not a recommendation to buy or sell any security)