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> B either rises 30% or falls 10% each year — with 50/50 probability. So, in any one year, B “averages” (30 - 10)/2 = 10%, the same as A. You cannot use arithm
by ajuc 5y ago
> B either rises 30% or falls 10% each year — with 50/50 probability. So, in any one year, B “averages” (30 - 10)/2 = 10%, the same as A.
You cannot use arithmetic (additive) mean for percents. Percents aren't additive.
X * 0.9 * 1.1 != X
You should use geometric (multiplicative) mean for percents and the results would be the same on average.
- yorwba 5y agoYou absolutely can use the arithmetic mean for percents and the result that B rises 10% in an average year is correct. The counterintuitive part is that the typical 10-year period is not the same as a sequence of 10 average years. Instead, some years will have higher growth than average and others lower. In the example, the split is exactly 50-50, so the typical annualized growth rate is given by the geometric mean. The reason typical growth is relevant is because the question asks about the probability that B is higher, not how much higher it would be on average.