Also known as: Logarithmic rate of return

Financial mathematicians use the steady return to calculate the risk of an investment opportunity. Since a linear return cannot be assumed, a logarithmic formula is used.

## Definition / explanation

When it comes to investments, the aim is to achieve the highest possible return. The return includes the overall success of such an investment. In order to be able to assess the respective risk precisely, the steady return (also called logarithmic return) from financial mathematics is used.

By calculating the logarithmic rate of return, percentage changes can be determined over a specified period of time. The determination of the normal return only includes positive numbers as a result.

Using the logarithmic formula, negative values can also be found, which leads to a more realistic result in terms of risk.

## Calculation / formula for continuous return

r (ti, T) = ln [S (ti + T)] - ln [S (ti)]

T = time for which the return is determined
S = time-dependent price
r = rate of return

In simple words, the difference between the natural logarithm of the price of the last day and that of the first day gives the return, which is dependent on time and time period.

## Summary

• the steady return is used to determine the risk associated with financial investments
• the observation takes place over a certain period of time
• the logarithmic formula is used for the calculation
• the calculation is used to determine real numbers
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