# How to Annualize Monthly Returns

by Bryan Keythman

An investment’s return is its change in value over a period of time, which is typically expressed as a percentage. A return can be positive or negative. A higher return results in greater profit. An investor may compare different investments using their annual returns as an equal measure. If you know an investment’s return for a period that is shorter than one year, such as one month, you can annualize the return. This converts the monthly return into an annual return, assuming the investment would compound, or grow, at the same monthly rate.

Substitute the decimal form of an investment’s return for any one-month period into the following formula: [((1 + R)^12) - 1] x 100. Use a negative number for a negative monthly return. In the formula, R represents the decimal form of the investment’s one-month return and 12 represents the number of months in a year. This formula compounds the monthly return 12 times to annualize it. For example, assume you want to annualize a 2-percent monthly return. Substitute 0.02 into the formula to get [((1 + 0.02)^12) - 1] x 100.

Add the numbers inside the parentheses. In this example, add 1 to 0.02 to get 1.02. This leaves [(1.02^12) - 1] x 100.

Raise the number in parentheses to the power of its exponent. In this example, raise 1.02 to the 12th power to get 1.268. This leaves (1.268 - 1) x 100.

Subtract the numbers in parentheses. In this example, subtract 1 from 1.268 to get 0.268. This leaves 0.268 x 100.

Multiply the remaining numbers to calculate the annualized monthly return as a percentage. Continuing with the example, multiply 0.268 by 100 to get a 26.8 percent annualized return. This means that if the investment grew at a 2-percent monthly rate for a period of one year, it would generate a 26.8 percent annual return.

#### References

• Financial Management Theory and Practice, 13th Edition; Eugene F. Brigham and Michael C. Ehrhardt
• Investments: Principles of Portfolio and Equity Analysis; Michael G. McMillian et al.