# GEO­MET­RIC AV­ER­AGE EXPLAINED

Finweek English Edition - - MARKETPLACE -

In the world of in­vest­ments, an arith­metic av­er­age (the sum of a se­ries of numbers di­vided by the count of that se­ries of numbers) is not al­ways ap­pro­pri­ate.

Let’s imag­ine you have in­vested in the stock mar­ket for five years, and your re­turns each year were 90%, 10%, 20%, 30% and -90%. Your arith­metic av­er­age re­turn over this pe­riod would be 12% [(90+10+20+30-90)/5].

How­ever, when it comes to an­nual in­vest­ment re­turns, these numbers are not in­de­pen­dent of each other. If you lose money in one year, you have less cap­i­tal to gen­er­ate re­turns the fol­low­ing year, and vice versa. There­fore the geo­met­ric av­er­age of your in­vest­ment re­turns will pro­vide a more ac­cu­rate pic­ture.

To do this, we sim­ply add one to each num­ber (to avoid any prob­lems with neg­a­tive per­cent­ages). Then, mul­ti­ply all the numbers to­gether, and raise their prod­uct to the power of one di­vided by the count of the numbers in the se­ries. Take the an­swer and sub­tract 1.

In this ex­am­ple, it would be cal­cu­lated as fol­lows: [(1.9 x 1.1 x 1.2 x 1.3 x 0.1) ^ 1/5] - 1. This equals a geo­met­ric av­er­age an­nual re­turn of -20.08% − sub­stan­tially be­low the 12% arith­metic av­er­age.