The annual return is the return on an investment generated over a year and calculated as a percentage of the initial amount of investment. If the return is positive (negative), it is considered a gain (loss) on the initial investment. The rate of return will vary depending on the level of risk involved.

Summary

The annual return is a measure of how much the investment has grown or shrunk in one year.

The annualized return is the geometric average of annual returns of each year over the investment period.

The annualized return is useful when you want to see the performance of an investment over time or to compare two investments with different time periods.

Annual Return Formula

The return earned over any 12-month period for an investment is given by the following formula:

All the interest and dividends received during the 12-month period should be included in the final value of the investment.

Annual Return Example

Assume that you purchased 200 shares at a price of $10 each. You receive $1 in cash dividends after one year, and the share now trades at $9.50. How can you evaluate the performance of the investment that you made a year ago?

It is reasonable to say that the investment can be deemed profitable if the return is positive. Let’s calculate the annual return. In our example:

1. Initial value of the investment

Initial value of the investment = $10 x 200 = $2,000

2. Final value of the investment

At the end of one year, you will hold cash from dividends and 200 shares trading at $9.50. Hence,

Cash received as dividends = $1 x 200 = $200

Current value of shares = $9.50 x 200 = $1,900

Final value of the investment = $200 + $1,900 = $2,100

3. Annualized rate of return

Annualized Return

In the above example, we calculated the return on the investment over a single period of 12 months. However, in practicality, you invest your money in different assets with different time periods. To compare the returns on such investments with a one-year return, you need to annualize them. The rate of return per year, measured over a period either longer or shorter than a year, is known as the annualized return.

There are two options for calculating the annualized return depending on the available information.

Option 1: When you are given the annual returns for each year of the investment period, then:

Where:

R_{1} – The annual return for year 1, R_{2} is the annual return for year 2, and so on

n – The number of years you wish to annualize

For example, assume that you purchased 200 shares at a price of $10 each, and you decided to hold onto the shares for three years. The stock rises 10% in the current year, increases by 14% next year, and falls by 15% in the year after. What is the rate of return during the three years that you’ve owned the shares?

Here, R_{1} = 15%, R_{2} = 14%, and R_{3} = -10%

Therefore, you realized an annual return of 5.67% on your investment.

Option 2: When are given a dollar value of returns instead of an annual rate of returns, then:

Where:

n – The number of years you wish to annualize

For example, assume that you purchased 200 shares at a price of $10 each, and you decided to hold onto the shares for three years. You receive $1 per share in cash dividends per year. After three years, you decide to sell all the shares at $12. What is the rate of return during the three years that you’ve owned the shares?

Note that the dollar value of the investments is given here.

1. Initial value of the investment

Initial value of the investment = $10 x 200 = $2,000

2. Final value of the investment

Cash received as dividends over the three-year period = $1 x 200 x 3 years = $600

Value from selling the shares = $12 x 200 = $2,400

Final value of the investment = $600 + $2,400 = $3,000

3. Annualized rate of return

Therefore, you realized an annualized return of 14.47% on your investment.

Additional Resources

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