What is an annual return
– Definition: The annual return is the year-by-year average growth rate of an investment over a specified period, expressed as a percentage. In practice it is usually calculated as a geometric (compound) average rather than a simple arithmetic mean, so it reflects the effect of compounding.
Key terms (brief)
– Simple return: (Ending value − Beginning value) / Beginning value. Measures total gain or loss over a period before annualizing.
– Compound annual growth rate (CAGR): The annualized compound rate that turns the beginning value into the ending value over N years: CAGR = (Ending / Beginning)^(1/N) − 1.
– Time-weighted rate of return (TWRR): Removes the effect of external cash flows (contributions/withdrawals) so performance reflects the investment manager’s returns.
– Money-weighted rate of return (MWRR) / Internal Rate of Return (IRR): Accounts for the timing and size of cash flows; useful for investor-level returns.
– Modified Dietz: An approximation method for money-weighted return that weights cash flows by how long they were in the account during the period; often used for monthly/quarterly reporting.
How annual return works (concept)
1. Measure beginning and ending values for the period.
2. Include all return components: price change, dividends/interest, and any returns of capital.
3. If there were no intermediate cash flows, compute CAGR to report an annualized rate that incorporates compounding.
4. If there were contributions or withdrawals, use a money-weighted method (IRR) or an approximation such as Modified Dietz; for manager performance comparisons use TWRR.
Step-by-step checklist to compute a basic annual return (no external cash flows)
1. Record Beginning value (BV).
2. Record Ending value (EV), and add any cash distributions (dividends, interest) received during the period to EV (or include them in total ending value).
3. Compute total return: TotalReturn = (EV + Distributions − BV) / BV.
4. If you want an annualized rate over N years, compute CAGR = ( (EV + Distributions) / BV )^(1/N) − 1.
5. Express as a percentage.
Checklist for accounts with cash flows (401(k), contributions during the year)
1. Record starting balance for the period.
2. Record ending balance for the period.
3. Subtract contributions made during the period from the ending balance (or otherwise adjust the ending value to remove investor cash flows).
4. Alternatively, compute IRR (money-weighted return) or use Modified Dietz to weight contributions by time-in-period.
5. Convert the period return to an annual rate if needed.
Worked numeric example (stock held 5 years)
– Scenario: Buy price = $20. Sell price = $35 after 5 years. Total dividends received over the hold = $2.
– Step 1: Compute total ending value including dividends = 35 + 2 = 37.
– Step 2: Total return over 5 years = (37 − 20) / 20 = 17 / 20 = 0.85 = 85%.
– Step 3: Annualize with CAGR: CAGR = (37 / 20)^(1/5) − 1.
– Compute ratio: 37 / 20 = 1.85
– Fifth root: 1.85^(0.2) ≈ 1.131
– Subtract 1: 0.131 → 13.1% per year (approximately).
– Interpretation: An investor who grew $20 to an equivalent of $37 over five years achieved an average compounded annual gain of about 13.1%.
Quick numeric example for a 1-year 401(k) with contributions
– Start balance = $10,000. Ending balance = $11,500. Contributions during year = $1,000.
– Adjusted ending value = Ending − Contributions = 11,500 − 1,000 = 10,500.
– Total return for the year ≈ (10,500 − 10,000) / 10,000 = 500 / 10,000 = 5.0%.
– Note: This simple adjustment assumes contributions are made evenly or you accept approximate result; for precise investor return use Modified Dietz or IRR that weights timing of flows.
When to use which method
– No or negligible intermediate cash flows: CAGR (annualized return) is appropriate.
– Manager performance comparisons: Use time-weighted returns (TWRR).
– Investor-level returns with significant contributions/withdrawals: Use money-weighted returns