Two ways to describe the same growth
Return on investment (ROI) answers: how much did this investment grow in total, from start to finish? It is calculated as the gain divided by the original investment, expressed as a percentage, and it does not reference time at all.
Compound annual growth rate (CAGR) answers a different question: what constant annual growth rate, compounded every year, would have produced this same total result? Unlike ROI, CAGR always accounts for the length of the holding period, making it the more useful figure for comparing investments held over different timeframes.
The formulas
ROI is calculated as (ending value minus beginning value) divided by beginning value, multiplied by 100. It requires only the starting and ending values.
CAGR is calculated as (ending value divided by beginning value) raised to the power of 1 divided by the number of years, minus 1, multiplied by 100. This formula finds the single constant growth rate that compounds to the same ending value over the given number of years.
Worked example: $10,000 growing to $16,000 over 3 years
ROI: ($16,000 minus $10,000) divided by $10,000 equals 0.60, or 60%. This is the total return over the full 3-year period, with no adjustment for how long it took to get there.
CAGR: ($16,000 divided by $10,000) raised to the power of (1 divided by 3), minus 1. That's 1.6 raised to the power of 0.3333, which is approximately 1.1697, minus 1, giving approximately 0.1697, or about 16.97% per year.
Both numbers describe the exact same investment outcome. The 60% ROI tells you the total growth over the whole period; the 16.97% CAGR tells you the annual rate that, compounded three times, produces that same 60% total growth.
| Metric | Formula | Result | Answers |
|---|---|---|---|
| ROI | (16,000 − 10,000) / 10,000 | 60% | Total growth over 3 years |
| CAGR | (16,000 / 10,000)^(1/3) − 1 | ≈16.97% | Equivalent constant annual rate |
When to use which
ROI is useful for a quick, simple summary of total performance, especially when comparing investments held over the exact same time period — in that case, the higher total-return investment is straightforward to identify.
CAGR becomes essential when comparing investments held over different lengths of time, since a 60% ROI over 3 years and a 60% ROI over 10 years represent very different annual growth rates. CAGR also better represents 'smoothed' growth even when actual year-to-year returns were volatile, because it describes the equivalent steady rate rather than the real (often uneven) path the investment took.
الأسئلة الشائعة
What is the difference between ROI and CAGR?
ROI is total growth over the entire holding period expressed as one percentage, with no time component. CAGR is that same growth converted into an equivalent constant annual rate, making it the better metric for comparing investments held over different lengths of time.
Why is CAGR lower than ROI for the same investment?
CAGR spreads the total ROI across each year of the holding period rather than presenting it as one lump total. For any holding period longer than one year, the annualized CAGR will be numerically smaller than the cumulative ROI, since it represents a per-year rate rather than the whole-period total.
Can I compare ROI figures for investments held different lengths of time?
Not meaningfully. A 60% ROI over 3 years is a much stronger annual performance than a 60% ROI over 10 years. CAGR removes this distortion by converting both to an annual basis, making cross-timeframe comparisons fair.
Does CAGR account for volatility or ups and downs during the period?
No — CAGR only uses the beginning and ending values, describing a smoothed, constant equivalent rate. It does not reflect the actual year-to-year path, which may have included gains and losses that netted out to the same final result.
المراجع
- CFA Institute — investment performance measurement standards (ROI and annualized return concepts).
- U.S. Securities and Exchange Commission (SEC) — investor education on comparing investment returns.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Chapter 2: How to Calculate Present Values.