to convert the return to a compound rate of return : For example, a 33.1% return over 3 months is equivalent to a rate of: per month with reinvestment. Annualization is the process described above of converting a return to an annual rate of return , where the length of the period is measured in years and the rate of return is per year. According to the CFA Institute's Global Investment Performance Standards (GIPS), "Returns for periods of less than one year must not be annualized." This is because an annualized rate of return over a period of less than one year is statistically unlikely to be indicative of the annualized rate of return over the long run, where there is risk involved. Annualizing a return over a period of less than one year might be interpreted as suggesting that the rest of the year is most likely to have the same rate of return, effectively projecting that rate of return over the whole year. Note that this does not apply to interest rates or yields where there is no significant risk involved. It is common practice to quote an annualized rate of return for borrowing or lending money for periods shorter than a year, such as overnight interbank rates. Logarithmic or continuously compounded return The logarithmic return or continuously compounded return, also known as force of interest, is: and the logarithmic rate of return is: or equivalently it is the solution to the equation: where: = logarithmic rate of return = length of time period 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%. Annualization of logarithmic return Under an assumption of reinvestment, the relationship between a logarithmic return and a logarithmic rate of return over a period of time of length is: so is the annualized logarithmic rate of return for a return , if is measured in years. For example, if the logarithmic return of a security per trading day is 0.14%, assuming 250 trading days in a year, then the annualized logarithmic rate of return is 0.14%/(1/250) = 0.14% x 250 = 35% Returns over multiple periods When the return is calculated over a series of sub-periods of time, the return in each sub-period is