Compounded Average Growth Rate

PRDTM2-786 AI Trading C3 L1 4 Compounded Average Growth Rate V4

Understanding Compounded Returns

Comparing arithmetic and compounded returns shows distinct differences in measuring investment performance over time:

Arithmetic Returns
- Simple calculations, providing average returns for individual periods.
- Not time-additive, potentially misleading over multiple periods.
Compounded Returns
- Accounts for growth on both initial investment and any subsequent earnings.
- Provides a more precise measurement over extended times.

Example Calculation

Situation: Managing a portfolio starting at $10 million.
- Year 1: Increases to $11 million (Arithmetic return of 10%).
- Year 2: Decreases to $9.9 million (Cumulative -1% return).

Summary

Compounded returns provide a more accurate reflection of performance by considering the accumulation effect over time. Accurately measure investment efficiency by understanding and applying the appropriate formulas.

Which of the following statements accurately describe compounded returns and how they are calculated?

Compounded returns are calculated by multiplying the returns for each period and raising the product to the power of the number of periods.

Compounded returns account for the fact that returns are earned not only on the initial investment but also on subsequent returns.

Arithmetic returns can be multiplied across periods to calculate compounded returns.

The compounded annual growth rate (CAGR) can be calculated by dividing the ending value by the beginning value and raising it to the power of the inverse of the number of years, then subtracting 1.

Compounded returns are only useful for calculating short-term performance and should not be used for multi-year analysis.

SOLUTION:

Compounded returns account for the fact that returns are earned not only on the initial investment but also on subsequent returns.
The compounded annual growth rate (CAGR) can be calculated by dividing the ending value by the beginning value and raising it to the power of the inverse of the number of years, then subtracting 1.

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