Annualized Return (CAGR): The Real Number for Evaluating Your Investments

What Is CAGR (Compound Annual Growth Rate)?

CAGR is the single, smoothed annual rate that turns a starting value into an ending value over a given number of years, assuming gains are reinvested each year. It answers the question: at what steady annual pace would my investment have needed to grow to reach this result?

The formula is:

CAGR = (Ending Value ÷ Beginning Value)^1/n − 1

where n is the number of years.

Worked Example: $10,000 Doubling Over 10 Years

Suppose you invest $10,000 and after 10 years you have $20,000. Your CAGR is:

(20,000 ÷ 10,000)^1/10 − 1 = 2^0.10 − 1 ≈ 7.18% per year

No matter how bumpy the road — some years +20%, others −10% — CAGR tells you the outcome is equivalent to a steady 7.18% annual growth. This is exactly the Rule of 72 at work: 72 ÷ 7.18 ≈ 10 years to double.

Why CAGR Beats the Arithmetic Average

The arithmetic (simple) average adds up annual returns and divides by the number of years. It seems logical, but it ignores a critical phenomenon: losses do more damage than gains can repair.

Here is the classic example:

• Year 1: +50% → $10,000 becomes $15,000
• Year 2: −50% → $15,000 becomes $7,500

Arithmetic average: (50% + (−50%)) ÷ 2 = 0%

CAGR: (7,500 ÷ 10,000)^1/2 − 1 = −13.4% per year

You lost 25% of your money, yet the average claimed 0%. This is called volatility drag: volatility always erodes compounded returns. The larger the annual swings, the bigger the gap between your displayed average and your real CAGR.

Comparison Table: Average vs. CAGR on a Volatile Return Sequence

In all three cases the arithmetic average is similar, yet CAGR reveals that volatility cost real percentage points. That is why total compounded return is the true barometer of performance.

Limitations of CAGR: What It Does Not Tell You

CAGR is useful, but it has two important blind spots:

1. It hides the journey. Two investments can share the same 10-year CAGR even though one dropped 40% midway and the other grew steadily. CAGR does not measure lived risk — a volatile portfolio might have forced you to sell at the worst moment.
2. It assumes a single lump-sum investment. CAGR applies to a fixed starting capital with no contributions or withdrawals. If you make regular contributions such as monthly RRSP deposits or take withdrawals, CAGR does not capture your actual experience. In that case, use the money-weighted return (MWR), which accounts for the timing of your cash flows.

According to GetSmarterAboutMoney.ca — the investor-education site of the Ontario Securities Commission — investors should always verify which return-calculation method a fund or broker uses when displaying historical performance, since results can differ materially.

When to Use CAGR — and When Not To

Use CAGR to:

• Compare two funds or ETFs over the same period with no additional contributions
• Project the future growth of a lump-sum capital, for example retirement planning
• Evaluate the historical performance of an index such as the S&P/TSX Composite — available on the TMX Group website

Avoid CAGR or supplement it if:

• You have made multiple deposits or withdrawals → use money-weighted return
• You want to measure risk → add standard deviation or the Sharpe ratio
• The period is short, under three years → CAGR becomes less meaningful

Frequently asked questions