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

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%

## 1 Answer

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 %

• Chris & @JohnAndrews I don't understand how the arrived at rate has any value for analysis or for making decisions. That is, how can one extrapolate an annual return (for example) from daily returns? Start with \$10,000 on Jan 1 and in one case have a daily return Jan 1 - Jun 30 of 2% and then July 1 to Dec 31 of 4% and in the 2nd case flip the return, that is 4% for Jan 1 to June 30. Those calculations, though they have the same number of days with the same daily returns result in different IRR results. – Karl Jul 5 '17 at 19:07
• @Karl On a non-leap year Jan 1 to Jun 30 is 180 days and July 1 to Dec 31 is 183 days. – Chris Degnen Jul 6 '17 at 7:46