Question

Finance Question: Confused about different ways to calculate Returns. I'm supposed to take all of the values ( i assume of which are returns for these index and make three new series for 12-month rolling annual returns. What does 12 month rolling annual returns mean mathematically? like return from Dec '17 divided by Dec '16 then next value would be Jan '17/Jan'16 and so on?  

Date Jan-16 MSCI US MOM -3.69 -1.31 5.28 -0.65 2.47 3.00 2.69 -1.45 0.50 Feb-16 Mar-16 Apr-16 May-16 Jun-16 Jul-16 Aug-16 Sep-16 Oct-16 Nov-16 Dec-16 Jan-17 Feb-17 Mar-17 Apr-17 May-17 Jun-17 Jul-17 Aug-17 Sep-17 Oct-17 Nov-17 Dec-17 -1.96 -0.58 1.09 3.31 3.72 2.15 2.54 4.82 0.40 3.43 1.50 2.85 5.00 2.81 0.10 MSCI US VALUE MSCI US MIN VOL -4.35 -1.39 -0.19 1.09 6.68 6.01 1.14 -0.45 1.59 1.61 1.10 4.58 2.92 1.48 0.50 -1.95 -0.19 -0.65 -1.49 -2.81 4.78 0.64 2.76 2.39 0.44 1.32 3.59 4.55 -0.76 0.12 -0.16 1.45 0.06 2.08 1.83 -0.39 1.39 2.02 -0.97 0.83 2.91 0.54 1.18 1.93 2.93 3.13 0.21 1.22 Annualized Return Cumulative Return Annualized Std. Dev.

Answer 1

Rolling returns are basically annualized average returns for a period, ending with the listed year. Rolling returns are useful for examining the behavior of returns for holding periods. For example, the five-year rolling return for 2020 covers Jan. 1, 2016, through Dec 31, 2020. The five- year rolling return for 2020 is the average annual return for 2016 through 2020. So for your question, • • • • Calculate average returns for Jan 16 to Dec 16. This is your 14 12 month rolling return. Again calculate average returns for Feb 16 to Jan 17. This is your 2nd 12 month rolling return. Again calculate average returns for Mar 16 to Feb 17. This is your 3rd 12 month rolling return. So on till calculate average returns for Jan 16 to Dec 17. This is your 13th 12 month rolling return