Biff wrote...
. . . I am trying to calculate the
annualized rate of return for a portfolio over 3 years. If after
year 1 the return is +25%, year 2 -25% and year three +25%, the
arthemetic mean gives me 8.33% which is not reality, while the
geometric mean is 5.4%. The multiplication of the the returns
plus one should be positive before taking the nth root. Does
this make sense?

You have to add 1 to the percentage returns (converting them into
ratios of ending values to beginning values), then take the geometric
mean of these POSITIVE values, then subtract 1 from that result. You'd
either need to use either of the following array formulas.

=GEOMEAN(Range_of_Percentages+1)-1

or

=EXP(AVERAGE(LN(Range_of_Percentages+1)))-1