Final answer:
The geometric average return of a stock is calculated by multiplying the adjusted returns (1 +/- percentage return), taking the nth root (where n is the number of periods), and converting back to a percentage.
Step-by-step explanation:
The question asks about calculating the geometric average return for a stock with monthly returns of −12.52%, −6.36%, 28.15%, and −0.02%. To find the geometric average return, one must multiply the returns as factors in a multiplication operation, adjusting for the percentage by adding 1 (or subtracting 1 in the case of negative percentages), and then take the appropriate root (in this case, the fourth root since there are four monthly returns) of the result before subtracting 1, to convert back to a percentage format.
To calculate the geometric average return, follow this formula:
(1 - 0.1252) * (1 - 0.0636) * (1 + 0.2815) * (1 - 0.0002) = Product
Now, take the fourth root (since we have four months of returns):
Fourth root of Product = Geometric Mean
Then, to convert back to percentage, subtract 1 and multiply by 100:
(Geometric Mean - 1) * 100 = Geometric Average Return in %