Final answer:
The approximate geometric mean, when given an arithmetic mean of 13% and a variance of 0.08, is calculated using the relationship G ≈ A - (1/2)σ². The calculation results in an approximate geometric mean of 9%.
Step-by-step explanation:
To find the approximate geometric mean when the arithmetic average return is 13% and the variance of returns is 0.08, we can use the relationship between the arithmetic mean, variance, and geometric mean. The formula to approximate the geometric mean (G) from the arithmetic mean (A) and variance (σ²) is:
G ≈ A - (1/2)σ², where A is the arithmetic mean and σ² is the variance.
Given that the arithmetic mean A is 13% (or 0.13 as a decimal) and the variance σ² is 0.08, we calculate the geometric mean as follows:
G ≈ 0.13 - (1/2) × 0.08 = 0.13 - 0.04 = 0.09 or 9%
Hence, the approximate geometric mean is 9%.