Rate of return measures an investment's gain or loss relative to invested capital over a stated period and calculation basis.
The rate of return measures an investment’s gain or loss relative to invested capital over a stated period. A complete return should identify the beginning and ending dates, treatment of income and cash flows, fees, taxes, currency, and whether the result is cumulative or annualized.
The phrase “rate of return” names a family of measures rather than one universal formula. A holding-period return works when there are no intervening external cash flows. Portfolios with contributions or withdrawals may require time-weighted, money-weighted, or cash-flow-weighted methods.
When no external cash flow occurs between purchase and sale or valuation:
where:
If income is reinvested, a total-return series should incorporate the reinvestment convention rather than adding the same distribution twice.
Assume an asset is purchased for $1,000, pays $40 of income, and is sold or valued at $1,120:
The return has two components:
| Component | Amount | Return contribution |
|---|---|---|
| Price change | $120 | 12% |
| Income | $40 | 4% |
| Total | $160 | 16% |
This example ignores transaction costs, management fees, taxes, and reinvestment timing. Including those items would change the investor’s net result.
The additive identity applies to the same single period and denominator. Over multiple periods, returns should be compounded rather than simply added.
A price-only stock index can understate the return earned by an investor who receives and reinvests dividends. A total-return index depends on assumptions about reinvestment, taxes, and timing.
For cumulative holding-period return (R_{cum}) over (T) years, the annualized return is:
If an investment earns 15% over 18 months, then (T=1.5):
The annualized value is a constant equivalent growth rate. It does not mean the investment earned 9.77% in each calendar year or will do so in the future.
For periods shorter than one year, annualizing a volatile short result can create an unrealistic-looking number. The calculation should be labeled and interpreted cautiously.
Multi-period cumulative return is found geometrically:
For returns of 10%, -5%, and 8%:
Adding the returns produces 13%, which is not the compounded result.
For periodic returns (R_t):
The arithmetic average describes the average one-period observation and is often used in expected-return modeling. The geometric average describes the constant compounded rate over the full path. Volatility generally makes the geometric average lower than the arithmetic average when returns vary.
The exact real-return relationship is:
where (\pi) is inflation over the same period. If nominal return is 8% and inflation is 3%:
Simply subtracting inflation gives 5%, a useful approximation at modest rates but not the exact compounded result. The chosen inflation measure should match the objective as closely as practical.
Beginning-to-ending account growth is not an investment return when money was added or withdrawn.
Example: an account begins at $100,000, receives a $50,000 contribution, and ends at $153,000. The account grew 53% in dollars, but only $3,000 of the change is investment gain. Even dividing $3,000 by beginning value can be misleading because the contribution was invested for only part of the period.
Choose the method based on the question:
| Method | Main question |
|---|---|
| Holding-period return | What did one investment earn without intervening external cash flows? |
| Time-weighted return | How did the investment strategy perform after neutralizing external cash-flow timing? |
| Money-weighted return | What return did the investor’s dated cash flows earn? |
| Modified Dietz | What cash-flow-weighted period return is estimated without valuing at every cash flow? |
Investor.gov defines an annual return as profit or loss over a one-year period and notes that calculation methods can differ. Its guidance on shareholder reports emphasizes average annual total returns, sales charges, broad-market benchmarks, and the fact that past positive performance may not continue.
This article provides general financial education. It is not personalized investment, performance-reporting, tax, accounting, legal, or fiduciary advice.