Annualisation of logarithmic retururn

Description

In finance, return is a profit on an investment. It comprises any change in value, and interest or dividends or other such cash flows which the investor receives from the investment. Rate of return is a profit on an investment over a period of time. Annualisation is the process of converting a return R to an annual rate of return r, where the length of the period t is measured in years and the rate of return r is per year.
Under an assumption of reinvestment, there is a relationship between a logarithmic return R and a logarithmic rate of return r over a period of time of length.

Related formulas

Variables

rAnnualised logarithmic rate of return (per period of year) (dimensionless)
R Logarithmic return (dimensionless)
tTime length ( in years) (dimensionless)