Answer:
To estimate the return of the asset over the next 5 years, 10 years, and 20 years, we need to understand the difference between arithmetic and geometric average returns.
Arithmetic average return is calculated by summing all the returns and dividing by the number of observations. In this case, the arithmetic average return is 13.20%.
Geometric average return, on the other hand, is a more accurate measure of the compound growth rate over a period of time. It is calculated by taking the product of all returns, raising it to the power of 1/n (n being the number of observations), and subtracting 1. In this case, the geometric average return is 10.36%.
Given that the geometric average return is lower than the arithmetic average return, this suggests that there is a lot of volatility in the returns over the 30 years, with some very high returns balanced out by some very low returns.
Given that the asset has a geometric average return of 10.36% over 30 years, we can estimate that the asset will return around that rate for the next 5, 10, or 20 years.
For 5 years: 10.36%
For 10 years: 10.36%
For 20 years: 10.36%
It's important to keep in mind that these are rough estimates and that actual returns can vary widely from these projections, especially in the short term. Additionally, this estimation is based on the past performance which doesn't guarantee the future results.