The most appropriate "mean" to use when calculating the mean annual return from an investment portfolio over a 10-year period is: The most appropriate "mean" to use when calculating the mean annual return from an investment portfolio over a 10-year period is: Geometric mean Arithmetic mean Weighted mean Harmonic mean

1. Break Down the Problem

   • Determine which type of mean is most suitable for calculating the mean annual return from an investment portfolio over a 10-year period.

2. Relevant Concepts

   • Arithmetic Mean: This is the simple average of a set of numbers, calculated by summing them up and dividing by the count of numbers. It is suitable for data sets that are additive in nature.
   • Geometric Mean: This is the nth root of the product of n numbers and is more appropriate for data sets that are multiplicative, such as investment returns over time.
   • Weighted Mean: This takes into account the relative importance of each number in the data set, which is useful when different data points contribute unequally to the final average.
   • Harmonic Mean: This is the reciprocal of the arithmetic mean of the reciprocals of a data set, often used for rates and ratios.

3. Analysis and Detail

   • Investment returns are typically compounded over time, meaning each year's return builds on the previous year's returns. This compounding effect is best captured by the geometric mean, which accounts for the multiplicative nature of investment growth.
   • The arithmetic mean would not accurately reflect the true average return over time because it does not consider the compounding effect.
   • The weighted mean is not applicable unless specific weights are assigned to different years, which is not typically the case in calculating average annual returns.
   • The harmonic mean is not suitable for this context as it is generally used for averaging rates, like speed or density, rather than returns.

4. Verify and Summarize

   • Verify that the geometric mean is indeed the most appropriate by considering the nature of investment returns, which are compounded.
   • Summarize that the geometric mean provides a more accurate representation of the average annual return over a multi-year period.

Final Answer

The most appropriate "mean" to use when calculating the mean annual return from an investment portfolio over a 10-year period is the Geometric Mean. This is because it accurately accounts for the compounding nature of investment returns over time.