Say there is a mutual fund and its annual return in the past 3 years i.e. 2017, 2018, 2019 were -10%, +20%, and -10% respectively.
A and B invest $100 in this fund at different time points. A invests in 2017 and B begins investing in 2018. The return at the end of each year was:
2017
A invested $100 so return is $90 (=100*0.9)
B invested $0 so return is $0
2018
Return for A is 90*1.2 = $108
Return for B is 100*1.2 = $120
2019
Return for A is 108*0.9 = $97.20
Return for B is 120*0.9 = $108
Thus at the end of 2019 A has a return of $97.20 and B has a return of $108. Though A was invested for 3 years, he lost money while B made money.
Now my doubt is, it was A's investment during the down time in 2017 that enabled the fund to provide a 20% return in 2018. How can A be at a loss and B gets all the gains? Did I miss something in my calculations?