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# Log return definition and calculation in Excel

The least known of the three return calculation methods is used for continuously compounded returns over very short timeframes like minutes or hours.
1. Define - Define log return.
2. Calculation - See how it is calculated and interpreted.
3. Context - Use it in a sentence.
4. Quiz - Test your knowledge.
###### by Paul Alan Davis, CFA, August 24, 2016
Updated: December 16, 2018
##### Once measurement periods extend past a day, the continuously compounded log return isn't as practical and common as the geometric and arithmetic versions.

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## Log Return

Intermediate

Log return is one of three methods for calculating return and it assumes returns are compounded continuously rather than across sub-periods. It is calculated by taking the natural log of the ending value divided by the beginning value. (Using the LN on most calculators, or the `=LN()` function in Excel)

Synonyms: logarithmic return, continuously compounded return

### How it is Calculated

As an example, let's say the ending value of an invesment was \$11 and the beginning value was \$10. The Excel function would read `=LN(11/10)` for a result of 9.53%.

In math and statistics, a distinction is often made between discrete and continuous data. Log return is the more theoretical continuous version. In the practical world, however, most people think of returns broken into discrete periods instead.

• Arithmetic return - One period, not-compounded, discrete.
• Geometric return - Multi-period, compounded, discrete.
• Logarithmic return - Infinite-periods, compounded, continuous.

So log return is the non-discrete version, so continuous, meaning if the whole period was broken into an infinite number of periods, what would that return be? See, it's theoretical.

Other than for very short periods of time (less than 1 day), and for theoretical applications involving calculus and precisely measuring curves, log returns are not commonly used.

### In a Sentence

Tom:  If log return  compounds most frequently, why is the rate the lowest?
Doc:  Chew on this. Let's say \$1 grew to \$1.10 in a year; the non-compounding return is 10%.

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### Quiz

Click box for answer.

The log return is best suited for long periods of time. | True or False

False. It is best suited for daily or hourly periods.

#### Questions or Comments?

Still unclear on log returns? Check out the tutorial page and video on Stock return calculation methods from the Quant 101 Series on YouTube. There we go over when to use arithmetic, geometric and log returns.

### Related Terms

Our trained humans found other terms in the category return math you may find helpful.

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