Why should we use log returns?

Log return is used for statistical evaluation such MSPE and out-of-sample R-square. Simple return is used for calculating economic value such as CER gain and Sharpe ratio. This is because Log return and simple return have the additivity property for, respectively, time-series and cross-section perspectives.

Why do we prefer to use logarithmic returns instead of simple returns or the price series itself?

Why use the logarithm of returns, rather than price or raw returns? Benefit of using returns, versus prices, is normalization: measuring all variables in a comparable metric, thus enabling evaluation of analytic relationships amongst two or more variables despite originating from price series of unequal values.

What do log returns tell us?

Log-return is just another measure of return, so it tells you all of the information that’s usually contained in any measure of return. The mathematics are different, however, and more conclusions can be drawn from that.

How do you use 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. Going by simple returns, you will get a 20\% increase in the first time period and -16.7\% decrease in the second time period.

Why do we choose simple rate of return over log return for portfolio analysis?

Log returns cannot be added across securities of a portfolio in the same time period. 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.

Why do we use natural log in finance?

We prefer natural logs (that is, logarithms base e) because, as described above, coefficients on the natural-log scale are directly interpretable as approximate proportional differences: with a coefficient of 0.06, a difference of 1 in x corresponds to an approximate 6\% difference in y, and so forth.

What is stock log return?

Logarithmic or continuously compounded 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\%.

What would it mean if your rate of return were positive?

Interpreting Rate of Return Formula If the old or starting value is lower, then you have a positive rate of return – a percent increase in value. If the starting value was higher, then you have a negative rate of return, or a percent decrease in value.