I have a table of asset (mutual fund) returns and the percentage that each asset is in a particular stock sector:
Asset Return Tech % Tech Returns Energy % Energy Returns Other % Other Returns
A 1.1 100 1.1 0 0 0 0
B 1.05 50 0.525 50 0.525 0 0
C 1.025 0 0 100 1.025 0 0
D 0.935 33 0.30855 33 0.30855 34 0.3179
I know how to calculate the overall portfolio return:
Overall Return = ((1+0.011)*(1+0.0105)*(1+0.01025)*(1+0.00935)-1.0)*100
= 4.1737 %
Now, I'd like to calculate the returns coming from each sector but I can't seem to figure out how to get the sector returns to accumulate up to the overall return above. I can see that for a given asset, the returns aggregate across the sectors by summing them up.
So, I thought I could aggregate each sector vertically and then sum them up accordingly:
Tech Return = ((1+0.011)*(1+0.00525)*(1+0.0)*(1+0.003085)-1.0)*100
= 1.9443 %
Energy Return = ((1+0.0)*(1+0.00525)*(1+0.01025)*(1+0.003085)-1.0)*100
= 1.8687 %
Other Return = ((1+0.0)*(1+0.0)*(1+0.0)*(1+0.003179)-1.0)*100
= 0.3179 %
Expect Overall Return = Tech Return + Energy Return + Other Return
= 4.1309 %
I would appreciate any help on identifying where I may be going wrong