Yearly Rate of Return Method

An annual (annualized) return measures the average yearly growth of an investment over a specified period. Unlike a simple return, the annualized return represents the geometric mean and reflects the effect of compounding. It’s commonly used to compare the performance of liquid investments such as stocks, bonds, mutual funds, and ETFs.

Key takeaways

• Annualized return shows the compound annual growth rate (CAGR) needed to turn the beginning value into the ending value over the holding period.
• Use the simple return to measure total gain or loss, and use CAGR to express that result as an average annual rate.
• For accounts with cash flows (contributions/withdrawals), use money-weighted or time-weighted methods (or Modified Dietz) to account for timing of flows.

Basic formulas

• Simple (total) return:
  Simple return = (Ending value − Beginning value) / Beginning value
• Compound annual growth rate (CAGR):
  CAGR = (Ending value / Beginning value)^(1 / Years) − 1

Example calculation

An investor buys a stock for $20 on Jan 1, 2024, receives $2 in dividends over five years, and sells the stock for $35 on Jan 1, 2029.
Ending value (including dividends) = $35 + $2 = $37.
Total return = (37 − 20) / 20 = 0.85 = 85%.

Annualized return (CAGR):
CAGR = (37 / 20)^(1 / 5) − 1 ≈ 13.1%

CAGR gives the single annual rate that, compounded each year, produces the same overall gain.

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

When measuring a single-period return for an account with contributions or withdrawals:
1. Compute net contributions during the period (contributions − withdrawals).
2. Adjust the final value by subtracting net contributions: Adjusted final = Ending value − Net contributions.
3. Total return for the period: (Adjusted final − Beginning balance) / Beginning balance.
4. Convert to an annualized rate if the period is not one year using CAGR-style compounding or use time-weighted/money-weighted methods for multi-period accuracy.

Note: If there are multiple cash flows at different times, money-weighted (internal rate of return) or time-weighted returns are preferred because they account for the timing and impact of flows differently.

Other return measures

• Money-weighted rate of return (MWR): Equivalent to the internal rate of return (IRR). It reflects the investor’s actual return including the timing and size of cash flows.
• Time-weighted rate of return (TWR): Removes the effect of external cash flows and measures the manager’s investment performance; used to compare managers or funds.
• Modified Dietz: An approximation that weights cash flows by the time they are in the period; simpler to compute than IRR and commonly used for interim performance calculations.

Converting periodic returns

To annualize a periodic return properly, compound it rather than simply multiplying:
* From monthly return r_m: Annualized = (1 + r_m)^12 − 1
* From daily returns, use the appropriate compounding exponent (e.g., 252 trading days): Annualized = (1 + r_d)^252 − 1

Quick ROI formula

Return on investment (ROI) for the overall period:
ROI = (Final value − Initial cost) / Initial cost
Include fees, commissions, and markups in costs for accurate ROI.

Practical notes

• Annualized returns smooth volatile results to enable comparison, but they do not show year-to-year variability.
• Large drawdowns require larger subsequent gains to recover; annualized figures help illustrate compounding effects.
• Choose the return measure that matches your goal: MWR for investor experience, TWR for manager performance.

Calculations can be done with financial calculators or spreadsheet functions (e.g., XIRR, IRR) when cash flows are irregular. If unsure which method to use, consult a financial professional.