Final answer:
The arithmetic mean return is 17.495% per annum, while the geometric mean return is approximately 16.51% per annum for the security based on the given data.
Step-by-step explanation:
To calculate the annual arithmetic mean return and geometric mean return on a security, we need to look at the total returns over the investment period and then apply the respective formulas. For the arithmetic mean return, we simply sum up the yearly returns and divide by the number of years. The geometric mean return is calculated by finding the product of the yearly returns (1 + return), taking the nth root (where n is the number of years) and subtracting one.
First Year Return = ((Price after one year + First-year dividend) - Purchase price) / Purchase price = (($34 + $6) - $29) / $29 = $11 / $29 = 0.3793 or 37.93%
Second Year Return = ((Selling price after two years + Second-year dividend) - Price after one year) / Price after one year = (($27 + $6) - $34) / $34 = -$1 / $34 = -0.0294 or -2.94%
Arithmetic mean return = (37.93% - 2.94%) / 2 = 17.495% per annum
To calculate the geometric mean return, we multiply the returns for each period: (1 + 0.3793) * (1 - 0.0294), take the square root (since we have two periods), and then subtract one.
Geometric Mean Return = [(1 + 0.3793) * (1 - 0.0294)]^(1/2) - 1 ≈ 0.1651 or 16.51%