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annualized return

I remember when we get annualized return
only need to compound each period's return
for example quater 1-4 return is 1% 1% 2% 2% we only need to 1.01 x1.01x1.02x1.02
but in book 5 p120 EOC12 they calculate annualized return as (1.01 x1.01x1.02x1.02)>(1/4) x 4 is there any inconsistency here?
I remember in evaluation ,we also only need to compound each period's return

Hi, this is the formula for giving a geometric average annual return for multiple years.

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time weighted return use LIRR , should be 1.01 x1.01x1.02x1.02 ,this is precise

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