Asked by Giovanni Figueroa on Jun 03, 2024
Verified
What are the arithmetic and geometric average returns for a stock with annual returns of 26%, 4%, -30%, 43%, and 7%?
A) 10.0%; 7.0%
B) 10.0%; 8.8%
C) 10.0%; 21.8%
D) 12.5%; 7.0%
E) 12.5%; 8.8%
Arithmetic Average
A statistical measure of central tendency calculated by summing a set of values and dividing by the number of values in the set.
Geometric Average
A method of calculating the average rate of return that accounts for compounding, commonly used for investment portfolios.
- Understand the difference between arithmetic and geometric average returns.
Verified Answer
AS
Ahmad SobohJun 05, 2024
Final Answer :
A
Explanation :
The arithmetic average return is calculated by summing the annual returns and then dividing by the number of years. (26% + 4% - 30% + 43% + 7%) / 5 = 10%. The geometric average return is calculated by multiplying the returns (expressed as growth factors, where 1 + return rate is the growth factor for each year), taking the nth root (where n is the number of returns), and then subtracting 1. For these returns, the calculation is [(1.26) * (1.04) * (0.70) * (1.43) * (1.07)]^(1/5) - 1 ≈ 7.0%.
Learning Objectives
- Understand the difference between arithmetic and geometric average returns.
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