Following up this question: Why doesn't the sum of daily percentage changes of a stock index over a given time period, equals the period percentage change?
I have a list of percent changes, but they're normalized like this:
ln(c1 / c0)
where c1 is the price after the change and c0 is the price before the change.
I've read somewhere (here) that this formula is used specifically so that the results can be added and subtracted (or so I understood).
What I'm trying to achieve is this: stock X makes price changes from c0 to c1 in one period and from c2 to c3 in another. Is it correct to say, if I invest a sum N into the stock in those two periods, this sum would then be this?
N * (ln(c1 / c0) + ln(c3 / c2)) * 100
If not, what's the correct formula?
You are almost there but not quite.
Because those "percentage changes" are not percentages at all, you can happily add them (the way you did) but you can't multiply them by 100 as you would with an ordinary percentage. Your final formula should be $$N*e^{\ln \frac{c1}{c0}+\ln \frac{c3}{c2}}\rm .$$ That is: you add the changes, just as you have been doing, but you need to take the anti-logarithm after you have finished adding.