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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
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.
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.
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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Click box for answer.
False. It is best suited for daily or hourly periods.
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.
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