Simple rate of return measures gain or loss relative to beginning value without annualizing. Learn the formula, examples, comparisons, and limitations.
The simple rate of return is an investment’s gain or loss over one stated holding period divided by its beginning value. It can include price change and income, but it does not by itself annualize the result, compound multiple periods, or correct for the timing of deposits and withdrawals.
For a holding period with no external deposits or withdrawals:
where:
If costs are excluded, the result is a gross or before-cost simple return. If selected costs are deducted, it is a net simple return under that definition.
Assume an investment begins at $5,000, ends at $5,350, and pays $100 of cash income. The calculation excludes fees and taxes:
The components are:
| Component | Dollar amount | Return on beginning value |
|---|---|---|
| Price change | $350 | 7% |
| Income | $100 | 2% |
| Total | $450 | 9% |
The 9% is the return for the complete stated period. It is not automatically a yearly return unless the holding period is exactly one year.
Consecutive returns apply to changing wealth bases. If an investment gains 20% and then loses 20%:
Adding 20% - 20% gives zero and misses the loss. An initial $100 rises to $120, then falls to $96.
For consecutive periodic returns:
This compound relationship converts a sequence of simple periodic returns into cumulative total return.
For assets held throughout the same period, with beginning-value weights (w_i):
If 60% of a portfolio earns 10% and 40% earns -5%, the one-period portfolio return is:
This weighted addition works across assets for the same period because the weights share a beginning-value denominator. It does not justify adding the portfolio’s returns across time.
Suppose an investment earns a simple cumulative return of 15% over 18 months. Dividing by 1.5 gives an arithmetic rate of 10% per year, but the equivalent compound annualized return is:
| Measure | What it reports |
|---|---|
| Simple cumulative return | Gain or loss over the entire holding period |
| Simple arithmetic annualization | Cumulative return divided by years; ignores compounding |
| Compound annualized return | Constant yearly compound rate linking beginning and ending value |
Annualizing a short-period return can produce an extreme number because it assumes repeated compounding. It does not forecast that repetition.
A continuously compounded or logarithmic return is:
Log returns add across time, while simple returns compound across time. Simple returns are usually easier to interpret as percentage gains or losses and aggregate naturally across assets using beginning-value weights. Log returns are useful in some statistical models but do not aggregate across assets in the same direct way.
For small returns, simple and log returns are close. The difference grows as the magnitude of return increases.
The basic formula becomes ambiguous when money enters or leaves during the period. A deposit increases ending value but is not investment performance; a withdrawal reduces ending value but is not necessarily a loss.
A rough adjustment that subtracts net deposits from ending value can still misstate return when the cash flow occurred early rather than late. Timing-sensitive methods are preferable when cash flows are material.
“Simple rate of return” can refer to several calculations in different contexts:
| Similar label | Distinct meaning |
|---|---|
| Simple holding-period return | Gain or loss divided by beginning investment value |
| Simple interest rate | Interest calculated on principal without interest-on-interest compounding |
| Accounting Rate of Return | Accounting profit divided by a stated investment base |
| Internal Rate of Return | Discount rate that sets net present value of dated cash flows to zero |
These measures can produce different answers from the same project. Always inspect the numerator, denominator, dates, and compounding convention.
“Simple” describes the return calculation, not its economic basis. A simple return can also be:
These labels answer independent questions. A return can be simple, net of management fees, nominal, pre-tax, and measured in U.S. dollars at the same time.
Before comparing simple returns, verify:
This article provides general financial education. Return calculations do not guarantee future results or provide personalized investment, tax, legal, accounting, or portfolio advice.