# 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.

## Variables

r | Annualised logarithmic rate of return (per period of year) (dimensionless) |

R | Logarithmic return (dimensionless) |

t | Time length ( in years) (dimensionless) |