Computing the annualised rate of return on an investment is not a complicated calculation provided you have the necessary investment performance data. An annualised rate of return is a time-weighted return calculation. Under the time-weighted conversion, quarterly and monthly cumulative returns of an investment can be annualised for the purpose of evaluating the investment's current performance against other investments for which annual performance figures exist. Any investor who wants to compare the current performance of any investment against the historical performance of other prospective investments will benefit from being able to calculate the annualised rate of return.

- Skill level:
- Moderate

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## Instructions

- 1
Establish the total number of periods in a year for which you intend to observe your investment's performance. For example, you might want to calculate the rate of return from the start of the year to the end of each month, for a total of 12 observations in a year, or on a quarterly basis, for a total of four observations in a year.

- 2
Establish the current observation number for your investment. For example, if you are evaluating your investment from the start of the year and on a monthly basis, the observation number you make at the end of the month of June would be six, because June is the sixth month of the year.

- 3
Calculate the cumulative return for your observation. For example, if your investment started the year at £65,000 and your investment has a current value of £72,800 at the end of June, the sixth month, your cumulative return for June would be 12 per cent. To arrive at this figure, subtract £65,000 from £72,800 and divide this difference by £65,000 and then take the resultant quotient and multiply by 100: ($112,000 - 100,000) ÷ 100,000 X 100 = 12 per cent.

- 4
Calculate the time-weighted return. For example, if your cumulative return to date is 12 per cent, your total time period covers 12 monthly observations, and you are in the sixth month observation, you would add the number 1 to 12 per cent divided by 100, all to the power of the quotient of the total number of observations, 12, divided by the number 6, which corresponds with the sixth month observation. Subtract the aforementioned calculation by 1 to arrive at your time-weighted return. In this example, the time-weighted return would yield 0.0024: [(1 + 0.12/100)^(12 ÷ 6)] - 1 = 0.0024 .

- 5
Multiply the time-weighted return by 100 to arrive at your annualised rate of return. For example, if your time-weighted return yielded 0.0024, multiply by 100 to arrive at your annualised rate of return, 0.24 or 24 per cent: 0.0024 X 100 = 0.24 or 24 per cent.

#### Tips and warnings

- Annualised rates of return are not substitutes for the actual year ending or total rate of return for an investment.