How to Calculate Annualized Rate of Return
The Annualized Rate of Return (ARR) is a crucial metric for investors to understand the performance of an investment over a period longer than one year. It smooths out the effects of compounding and provides a standardized way to compare investments with different holding periods.
Calculating ARR involves knowing the initial investment value, the final investment value, and the number of years the investment was held. The formula used is:
ARR = [(Ending Value / Beginning Value) ^ (1 / Number of Years)] – 1
This formula essentially finds the geometric average return per year. It's important to note that this calculation assumes that returns are reinvested and that the investment period is measured in full years. For periods that are not exact years, adjustments can be made, but the core ARR formula provides a valuable baseline.
Why is ARR Important?
- Comparison: ARR allows for direct comparison of investments held for different durations.
- Performance Measurement: It provides a clear picture of how effectively an investment has grown over time.
- Forecasting: While not a guarantee of future performance, ARR can be used as a basis for projecting potential future returns.
Example Calculation
Let's say you invested $10,000 in a stock. After 5 years, your investment has grown to $18,000.
- Beginning Value: $10,000
- Ending Value: $18,000
- Number of Years: 5
Using the formula:
ARR = [($18,000 / $10,000) ^ (1 / 5)] – 1
ARR = [(1.8) ^ (0.2)] – 1
ARR = 1.1247 – 1
ARR = 0.1247 or 12.47%
This means your investment averaged a return of approximately 12.47% per year over the 5-year period.