Hong Life CalculatorsUnderstanding the rate of return calculator — concept and principle
This calculator measures the return on an investment account when you have added or withdrawn money during the period. It uses the Modified Dietz method, which separates investment gains from deposits and weights each cash flow by how long it was invested.
How it is calculated
- Investment gain = end value − start value − net money added.
- Average capital = start value + W × money added, where W is the share of the period the money was invested (1 if added at the start, 0.5 halfway, 0 at the end).
- Modified Dietz return R = (EV − BV − CF) ÷ (BV + W × CF).
- For periods over a year, annualized return = (1 + R)^(1/years) − 1; shorter periods are not annualized.
The principle
Deposits raise the account value but are not profit, so they must be removed from the gain. They also change how much money was at work: a deposit made halfway through the year was invested for only half the period. Dividing the gain by the time-weighted average capital gives a fair rate of return. The method is widely used in performance reporting because it approximates a money-weighted return without iteration.
Worked example
Default inputs: start 50,000 USD, end 58,500 USD, 4,000 USD added halfway, 1-year period.
- Investment gain = 58,500 − 50,000 − 4,000 = 4,500.00 USD.
- Average capital = 50,000 + 0.5 × 4,000 = 52,000.00 USD.
- R = 4,500 ÷ 52,000 ≈ 8.65%; for exactly one year the annualized return is also 8.65%.
- Simple change in value ignoring the deposit = 8,500 ÷ 50,000 = 17%, which overstates the return.
- If the money had moved at the start: 4,500 ÷ 54,000 ≈ 8.33%; at the end: 4,500 ÷ 50,000 = 9%.
| Value at the start of the period | Rate of return (Modified Dietz) |
|---|---|
| 12,500 | 289.66% |
| 25,000 | 109.26% |
| 37,500 | 43.04% |
| 50,000 | 8.65% |
| 62,500 | -12.4% |
| 75,000 | -26.62% |
| 100,000 | -44.61% |
How to read the result
Compare the return with a benchmark for the same period, such as an index fund. The simple change in value is misleading whenever money was added or taken out. With several deposits, weight each by its own W and add them.
Common mistakes
- Treating deposits as part of the gain.
- Annualizing a return over a few months, which can exaggerate it.
- Entering withdrawals as positive amounts instead of negative.
- Comparing a money-weighted return with a fund's time-weighted return without noting the difference.
Frequently asked questions
How do you calculate return with deposits?
Subtract deposits from the gain and divide by the average capital invested, as in the Modified Dietz method.
Why not just compare start and end values?
Because deposits raise the end value without being investment gains.
What is the difference between money-weighted and time-weighted returns?
Money-weighted returns depend on when you added money; time-weighted returns remove that effect and are used to judge managers.
Sources: CFA Institute, Global Investment Performance Standards (GIPS), Modified Dietz method · Dietz, P. O. (1966). Pension Funds: Measuring Investment Performance. Free Press.