Is there a proper way to average and annualize stochastic returns across scenarios? Let’s say that returns are quarterly and presented as 1+qtrlyRet. I’ve come up with at least three ways that one might arrive at the average annual return across the scenarios:
1) accumulate $1, invested at time 0, to the end of the projection; take arithmetic average; annualize (^1/projYrs-1)
2) accumulate $1, invested at time 0, to the end of the projection; annualize (^1/projYrs-1); take arithmetic average
3) take arithmetic average quarterly return across all projQs and scenarios; annualize(^4-1)
See attached image for a quick numerical example… average annual ret across scenarios using method one is in H11; method 2 in H14; method 3 in H17