# Arithmetic Vs Geometric Mean

Can someone list advantes/disadvantages of both and also answer this q: If you are given both and asked to caluculate coefficient of variance and sharpe ratio which one would you use and why?

Arithmetic mean is an equally weighted mean that doesn’t take into account the compounding of returns. Simpler but not as precise as the geometric mean which takes compounding into account. However, geometric mean is sometimes biased downwards. I have a doubt about your question because i think it is a bit too general, but it seems to me that geometrically linked returns are more relevant. However, since the best unbiased estimator of a population mean is the arithmetic average, this is the one i would use for calculations of CV and Sharpe ratio.

Arithmetic mean is influenced by extreme value Geometric mean cannot directly use negative value

strangedays Wrote: ------------------------------------------------------- > > Geometric mean cannot directly use negative value I don’t think this is a disadvantage of using geometric mean. It can include negative return.

arithmetic is upward biased

geometric is downward biased for value weighted index.

CF of 100, 125, 100 will give you wrong return measure if used with arithmetic mean.

mambovipi Wrote: ------------------------------------------------------- > If you are given both and asked to caluculate > coefficient of variance and sharpe ratio which one > would you use? Thanks for all that info, but what would be the answer to the above Q?

Well, usually the sharpe ratio is viewed as somewhat similar to a Z-statistic, and since the mean estimator is the arithmetic mean i’d say this is the one to choose. However, be well aware that the geometric mean is more precise, especially when there is higher volatility.