Caculate a total return index from Libor indices

Hi everyone,

I am looking to recreate a total return index for Libor rates (1 month and 3 month) similar to the ones in Bloomberg as they were discontinued after June 2018. I tried something very simple such as Daily Return on Libor 1 month * (30/360) to get an approximation but my result is very far off. I also tried something that I am very unsure about. I calculated the present value of the 1 month Libor rate on a daily basis (equivalent to a redemption of an instrument with a value of one that pays Libor 1 month everyday): 1+(30/360)*1 month Libor rate. Then I computed the total return from this present value with: Last Total Return Value (starting at 100) * ((Current Present value + Libor 1 month rate * (1/360))/Last present value. But I still cant get back to the total return index indicated by Bloom.

Can anyone help me on this subject ?

Many thanks. Best, Ervin