# How to calculate log return

Written by bradley james bryant
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Logarithmic (log) is an exponential function. It is used in the world of finance to model the compounding of interest in interest calculations. The exponential function and the base of the function depend on the annual (nominal) interest rate and the compounding frequency of the interest being paid. You can also use the natural log to determine the return on stock.

Skill level:
Easy

### Things you need

• Calculator or spreadsheet

## Instructions

1. 1

Determine the annual market rate of interest for the security. This is the stated rate and is usually a part of the title of the bond issue, i.e., 12% General Electric 2040, translates into a bond issued by General Electric which pays a market rate of 12 per cent and has a maturity date of 2040.

2. 2

Open an Excel page. Click on a cell and enter the following formula: =LOG(1 + stated rate of interest). For instance, a bond with a stated rate of interest of 12 per cent is: "=LOG(1.12)". The answer is .1133 or 11.33 per cent.

3. 3

Determine the log return for stocks. Stock is a little different because it does not bear interest. In this case you have to take the natural log of the ending value divided by the starting value. For instance, if you purchase a stock at £71 that has now grown to £65, the ratio is £71/\$100 or 1.1 and the equation is: "=LOG(1.1)". The answer is 9.53 per cent.

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