How to Calculate a Continuously Compounded Return

There are two schools of thought in investment analysis: fundamental and technical. Fundamental analysis helps analysts to determine what to buy and technical analysis helps to determine when to buy it. One calculation used by both schools of thought is the rate of return, specifically, continuously compounded return. This measure is used not only to measure investment return, but it assumes investment returns are also reinvested instantaneously. The natural logarithm is used to help calculate the return metric.


Step 1

Calculate investment return for the asset. If you have a bond, the return is considered to be the coupon payment. However, in general you can calculate the return for any asset by dividing the profit made from the investment by the cost of the investment. If the profit made from an investment is $200 and the cost of the investment is $1,000, the return is $200 divided by $1,000 or 20 percent.


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Step 2

Find a spreadsheet or calculator to help calculate the natural log. This cannot be calculated by hand. You will need a spreadsheet or calculator in order to do this calculation. The symbol for the natural log on most spreadsheets or calculators is "ln." See the Resources for an online natural log calculator.


Step 3

Add 1 to the regular return associated with the asset. In this case the return is 20 percent. One plus 20 percent is 1.20.

Step 4

Take the natural log of 1 plus the rate of return. The calculation is "ln 1.20." The answer is .18232.

Step 5

Multiply the natural log by 100 for the continuously compounded return percentage. The answer is 18.23 percent.


Continuously compounded return will always be less than the normal return.


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