How to calculate the return over a period from daily returns?

Question

If I have daily returns of my portfolio over a period (let's say January to December), how do I calculate the total return over the period or per month?

What I did now is the following:

1. Calculate the cumulative return series as follows: cumprod(1+rt): this basically boils down to:

   end of day 1: daily return 5%, cumulative return: 1 * (1 + 5%) = 1.05

   end of day 2: daily return 3%, cumulative return: 1.05 * (1 + 3%) = 1.0815 ... etc

2. To calculate the return over the whole period (Jan to Dec), I take the value of the cumulative return at the end of the period and calculate the procentual change, e.g.:

   end of December: cumulative return: 40

   then total return over period = (40-1)/1 * 100 = 39%

3. Also, I were to calculate the return in February, I take:

   end of February: cumulative return: 20

   begin of February: cumulative return: 10

   then total return in February = (20-10)/10 * 100 = 100%

Answer 1

If you have daily returns just multiply as you did in step 1:

end of day 2: daily return 3%, cumulative return: 1.05 * (1 + 3%) = 1.0815 ... etc

For example, if daily return is 0.0261158 % every day for a year

annual return = (1 + 0.000261158)^365 - 1 = 10 %