# What is a cumulative return series?

I guess this is pretty easy but I cannot find a definition anywhere. I am trying to reproduce a paper and they say they use a cumulative return series at some point. Does anyone know exactly what this is?

I have two ideas, first: may it just be the cumulative (total) returns so that the series is:

total return     cumulative return series
10%                   10%
20%                   32% (10%+10%*20%+20%)
5%                   37.016% (32%+5%+5%*32%)


and so on.

Or is it like the price series but calculated with total return data? like this:

price           total return     cumulative return series
5                 10%                    5.5
5.4(ignored)      20%                    6.6 (5.5*(1+0.2))


and so on.

If someone has the definition of what a cumulative return series is and especially what is its starting value, it would be great if you could kindly tell me! Thank you very much.

• Hi: The cumulative return is defined as the return on 1 dollar if it had been invested in whatever asset the returns came from. So, suppose the three total return numbers were monthly and that one was compounding monthly. Then, the cumulative return would be, 10 percent ( i.e: (1+0.10) -1 ) at the end of the first month. At the end of the second month, it would be (1+ 0.1) *(1+0.2) - 1 = (1.10 * 1.2) - 1. For the third month, you'd take the previous number and multiply it by 1.05 and subtract 1. This last return multiplied by 1 dollar would be dollars gained or lost by the investor. Jul 27 at 11:03
• Hi, thank you so much for helping me out here too! I guess I now know what to do Jul 27 at 19:40
• I'm glad it helped. Notice that I made it simple in that I assumed the both the returns were monthly AND the compounding was monthly. Things start getting a little trickier when this is not the case but the concept remains the same. Jul 27 at 20:10
• Luckily, both your assumptions are true in my case Jul 28 at 9:05
• @markleeds, consider posting your comment as an answer. Jul 30 at 13:40