Also if I use as an example a $100 investment that gains 10% in the first six months and loses 10% in the final six months, with the arithmeic return calculation I get: 
 Vi=100,  Vf=99,  ROR=(99-100)/100=-1% (how true: I lost 1% of my investment after one year!) 
 and not zero as the text seems to imply. 
 With the geometric average calculation I get: 
 square root of (1.1*0.9)=0.995, equivalent to -0.5% which is actually higher than the result of the arithmetic average (i.e. it makes the rate of return look better than it really was!)   
 I suspect that what mutual fund companies call cumulative total return are calculated using the aritmetic average formula, and what they call average annual total returns are calculated using the geometric average formula, but it would be nice if some expert could verify that and explain it clearly.