## Friday, November 23, 2012

### Arithmetic Mean: The Return of the Comback

PERSONAL FINANCE 101

Some of you may remember how, in a previous post, I have relegated the arithmetic mean--more popularly known as "average"--to irrelevance. In the example that I used, we saw how the geometric mean is the more appropriate measure of investment performance since it accounts for compounding every period.

I have recently realized, however, that the arithmetic mean is not as inutile as I first thought. How exactly? Please refer to this series of returns earned by a mutual fund in the past 5 years.

Year 1 = 10%
Year 2 = 4%
Year 3 = -7%
Year 4 = 15%
Year 5 = 11%

The arithmetic mean of these returns is 6.60%, while the geometric mean is 6.31% (do you still remember how to compute for these?). Nothing has changed: the geometric mean is still the appropriate measure of investment performance, meaning that if you invested in the fund at the beginning of Year 1 (and reinvested all income/earnings), your investment will have grown by 6.31% per year and not by 6.6%.

So what is the arithmetic mean for? If we want to predict or forecast how much the mutual fund in our example will earn the following year (Year 6) and assuming that the returns in the past five years are equally likely (meaning the probability that the fund will earn 10% or 4% or -7% or 15% or 11% is the same), then we should use the arithmetic mean. In this case, the simple average gives us the expected return for the following year. In the example, we can therefore say that on any given year, using past performance as basis, the fund will earn 6.6% on average.

So remember, if your want to measure the performance of a multi-period investment on an annual, compounded basis, use geometric mean. But if you want to forecast the return for one period using historical data, the arithmetic mean is more appropriate.

***

PS. I apologize to those of you who have sent me emails/questions for not being able to respond immediately. I've had a really busy quarter, but December will definitely be better, so I promise to answer all your questions soon, FIFO. :)