Annual Return

What is an annual return?

An annual return (or annualized return) measures the average percentage growth of an investment per year over a specified period. It reflects total returns—capital appreciation plus distributions such as dividends—and is typically expressed as a compounded (geometric) rate rather than a simple arithmetic average.

Key takeaways

• Annualized return shows the compounded yearly rate of growth for an investment over a holding period.
• It is more useful than a simple average when comparing investments or evaluating performance across different time horizons because it accounts for compounding.
• Annualized returns can be calculated for stocks, bonds, mutual funds, ETFs, commodities, retirement accounts, and certain derivatives.

How annual return is calculated

Basic simple return:
* Simple return = (Ending value − Beginning value) / Beginning value

Compound annual growth rate (CAGR), the common annualized measure:
* CAGR = (Ending value / Beginning value)^(1 / Years) − 1

CAGR expresses what constant annual growth rate would produce the observed change over the holding period.

Example: stock investment

An investor buys a stock for $20 and, over five years, receives $2 in total dividends and sells the stock for $35.
* Beginning value = $20
Ending value (including dividends) = $35 + $2 = $37
Holding period = 5 years

CAGR = (37 / 20)^(1/5) − 1 ≈ 0.131 → 13.1% per year

This 13.1% annualized return shows the compounded yearly growth that yields an 85% total gain over five years.

Annual return for retirement accounts (e.g., 401(k))

When contributions or withdrawals occur during the measurement period, simple beginning/ending comparisons can be misleading. A basic adjusted-period total return is:
* Adjusted return = (Ending balance − Contributions during period − Starting balance) / Starting balance

Because timing and size of cash flows affect results, money-weighted or time-weighted methods (or formulas like Modified Dietz) are commonly used to more accurately account for inflows and outflows.

Other return measures

• Time-weighted rate of return: Removes the impact of external cash flows to show the portfolio’s performance due to investment decisions. Preferred for comparing manager performance.
• Money-weighted rate of return (internal rate of return): Reflects the investor’s actual experience by incorporating the timing and size of cash flows.
• Modified Dietz: An approximation that weights cash flows by the portion of the period they were invested; useful when exact IRR computation is impractical.
• Monthly-to-annual: You can compute periodic returns (e.g., monthly) and convert to an annual rate by compounding the periodic rate (1 + r_month)^12 − 1.

Calculating overall return or ROI

• Return on investment (ROI) = (Final value − Initial cost − Fees) / Initial cost × 100%
  Include commissions, fees, and other costs for an accurate percentage.

Practical notes

• Annualized returns smooth results and make comparisons easier, but they hide year-to-year volatility.
• Negative returns can be annualized using the same formulas, but be cautious interpreting averages when returns fluctuate widely.
• For accounts with frequent cash flows, prefer money-weighted measures or methods that properly account for timing.

Bottom line

Annualized return quantifies how an investment performed on average each year, accounting for compounding. Use CAGR for straightforward buy-and-hold comparisons, but choose time-weighted or money-weighted measures (or Modified Dietz) when cash flows or manager performance comparisons matter. When in doubt, consult a financial professional to ensure the method matches your needs.