Average Return
The average return is the simple mathematical average of a series of returns generated over a specified period of time. An average return is calculated the same way that a simple average is calculated for any set of numbers. The numbers are added together into a single sum, then the sum is divided by the count of the numbers in the set.
Definition: The average rate of return is the simple mathematical average of a series of returns generated over a specified period. The calculation method is the same as calculating the simple average of any set of numbers: sum these numbers to get a total, then divide the total by the number of numbers in the set.
Origin: The concept of the average rate of return originates from the calculation method of the average in statistics. It was first applied in the financial field to simplify the evaluation of investment returns. With the development of financial markets, the average rate of return has become a basic tool for investors to evaluate investment performance.
Categories and Characteristics: The average rate of return can be divided into arithmetic average rate of return and geometric average rate of return.
- Arithmetic Average Rate of Return: This is the simplest calculation method, suitable for short-term investments or situations with small fluctuations in returns. The calculation formula is:
Arithmetic Average Rate of Return = (R1 + R2 + ... + Rn) / n, where R represents the return for each period, and n is the number of periods. - Geometric Average Rate of Return: Suitable for long-term investments or situations with large fluctuations in returns, it can more accurately reflect the actual growth rate of the investment. The calculation formula is:
Geometric Average Rate of Return = [(1 + R1) * (1 + R2) * ... * (1 + Rn)]^(1/n) - 1.
Specific Cases:
- Case 1: Suppose an investor has returns of 10%, 20%, and -5% over three years. The arithmetic average rate of return is: (10% + 20% - 5%) / 3 = 8.33%. The geometric average rate of return is: [(1 + 0.10) * (1 + 0.20) * (1 - 0.05)]^(1/3) - 1 ≈ 7.81%.
- Case 2: A fund has annual returns of 5%, 15%, 10%, -10%, and 20% over five years. The arithmetic average rate of return is: (5% + 15% + 10% - 10% + 20%) / 5 = 8%. The geometric average rate of return is: [(1 + 0.05) * (1 + 0.15) * (1 + 0.10) * (1 - 0.10) * (1 + 0.20)]^(1/5) - 1 ≈ 7.86%.
Common Questions:
- Question 1: Why is the geometric average rate of return usually lower than the arithmetic average rate of return?
Answer: The geometric average rate of return takes into account the compounding effect and volatility of returns, thus more accurately reflecting the actual growth of the investment. - Question 2: In what situations is it more appropriate to use the arithmetic average rate of return?
Answer: The arithmetic average rate of return is suitable for short-term investments or situations with small fluctuations in returns because it is simple to calculate and can quickly provide the average level of returns.
