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Consider the rate of return for an investment in year 2000 increased by 105% and in 2001 it increased to 42%. what is the average rate of return in 2000-01. I'm confused as to which formula to use (1) Simple GM: (1.05*.42)^0.5= 0.66= 66%

or

(2) Geometric average return = ((1+1.05)*(1+0.42))^0.5-1 = 0.706

which formula should be used?

Harry
  • 1,387
  • I suspect the question might not accurately describe what you really mean. It will help if you can give a specific example, to clarify what you mean by rate of return and its relative increases. Ideally, this example would include an investment value at the start of 2000, 2001 and 2002, along with the rates of return you are attributing to those. – TMBailey Oct 09 '21 at 07:32
  • Your first method would have problems with a $105%$ increase followed by a $10%$ decrease, having to square-root a negative number. Instead look at an increase of $42%$ as the same as multiplying by $1.42$, so the geometric mean is $\sqrt{2.05 \times 1.42} \approx 1.706$ or a $70.6%$ increase. This means your $105%$ increase followed by a $42%$ increase has about the same effect as two $70.6%$ increases – Henry Oct 09 '21 at 11:09

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