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What do log returns show?
So log return is the non-discrete version, so continuous, meaning it answers what the ending value would be if the whole period was broken into an infinite number of sub-periods.
How do you calculate logarithmic return?
For example, if a stock is priced at 3.570 USD per share at the close on one day, and at 3.575 USD per share at the close the next day, then the logarithmic return is: ln(3.575/3.570) = 0.0014, or 0.14%.
Why study an asset return and not its price?
A return is a percentage defined as the change of price expressed as a fraction of the initial price. It turns out that asset returns exhibit more attractive statistical properties than asset prices themselves. Therefore it also makes more statistical sense to analyze return data rather than price series.
Can we add log returns?
Log returns can be added across time periods. For example, let’s say you have a stock worth $100 that rose to $120 in the first time period and then goes back to $100 in the second time period. Log returns, however, being the continuously compounded return, can be added across time.
How is log return used to calculate return?
Log return is one of three methods for calculating return and it assumes returns are compounded continuously rather than across sub-periods.
Why are log returns assumed to be infinity?
Mathematically there’s a problem: when you assume a student-t distribution (a standard choice) of log returns, then you are automatically assuming that the expected value of any such stock in one day is infinity!
When do you add log returns do you compound?
When you add log returns, you compound. Across different stocks within the same time period, there are no compounding element here. So for computing portfolio return across contribution from securities within the same time period, use simple returns instead. Here is the end of Part I or the more theoretical stuffs.
When to use percentage change or log return?
So instead we take percentage change, which is the standard “return” most people think about (i.e. when they invest $100 and get a 5% change, that means they end up with $105). But instead we use “log returns”, log(today’s price/yesterday’s price).