Back to Basics: Calculating the growth rate of your portfolio

Back to Basics: Arithmetic Mean and Geometric Mean for your portfolio:

When you look at a Mutual Fund or a Money manager's returns, did you ever wonder on how to come up with the actual return on that portfolio for a given time series? Ok, here is the answer for you. To Calculate the growth rate of your portfolio you just calculate the geometric mean of all the annual returns. For e.g.

If a Fund A has the following returns from 1996-2002

1996 25%
1997 42%
1998 -65%
1999 2%
2000 12%
2001 -30%
2002 10%

1/6√(1+.25)(1+.42)(1-.65)(1+.02)(1+.12)(1-.3)(1+.1) - 1 = -.08 = -8%

So, in this caase the fund lost 8% every year for the seven year period or it grew at the rate of negative 8 percent. I'm sure you would not be happy to invest in this fund!
Coming to Arithmetic Mean, usually you say the average return for a fixed period such as an year, a half year, a quarter etc. Typically we consider the returns for an year averaged for that whole period and we come up with an annual return.

Finally to conclude: You have to use Geometric Mean to calculate the growth rate. You refer to an average return as an Arithmetic Mean only for a specific interval to get a better approximation of returns for that interval.

That's all for now. We will talk about other statistical measurements next time.