The question asks us that when using the stock return data, why a geometric mean return calculation is most likely preferred over a geometric mean calculation:
A) returns can be negative
B) return data can be less than one
C) the geometric return is closer in value tp arithmetic mean?
I am completely clueless about this question. Anyone know how to answer this?
I believe it’s A. If you use the geometric mean formula and just use returns as 8%, 9% etc but you have a year of negative returns i.e. -5%, when you plug in the values into the the formula, you can’t take an nth root of a negative number. (You can but you end up with i along with your answer which doesn’t figure into finance)
That’s why you add 1 to each return to end up with 1.08, 1.09 and .95 and take the nth root of the product of these numbers and subtract 1
I thought it was the other way round. I thought when they said geometric mean return they were using returns as inputs and when they said geometric mean calculation they meant to use returns after adding 1.
Is there somewhere I can clarify this difference between ‘geometric mean return’ and ‘geometric mean’?
The geometric mean is the nth root of the product of the input values. If you have an even number of values, and the product is a negative number (e.g., exactly one value is negative), you cannot compute the geometric mean. (Let’s not get into a discussion of imaginary numbers.)
For the geometric mean return, you add 1 to the input values (returns) to get growth factors, compute the geometric mean (as above) of the growth factors, then subtract 1 from the mean growth factor to get the mean return. Unless you have a return less than -100% – not likely – this calculation is never a problem.
I suspect that they wanted you to choose A, but it’s a stupid question. The reason you don’t use the geometric mean (without adding 1) is that even if you can get an answer, it’s meaningless.