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There are many ways to measure annual returns. For example you could
merely average the returns over two periods. Then you are faced with
the
decision as to whether you should use an arithmetic average (merely
add
them up and divide by the number of observations) or a geometric average
(multiply 1 plus the return for each year and then take the nth
root--where n is the number of observations).
Why does this matter you ask? Consider the following: The Nasdaq was
up
about 86% last year. This year it is down about 36%. If you take the
arithmetic average of the two you are up 25+% per year. However if
you
take the geometric average you are only up
[(1.87)(.64)]^.5, or up a bit over 19% for the two years or 9.1% per
year.
This is a big difference. So which is right? The geometric average.
Why? Consider a wealth index.
Here you consider an investment of $1000 at the beginning of the period.
How much would you have now? $1000*1.86=$1,860 after 1 year. Then
$1,860*.64 = 1190. Which over two years is about 9.1% per year.
While these numbers seem amazingly, if you were to look at the Internet
only portion of the Nasdaq, the returns are even more volatile with
the
Internet Index down over 70% this year! This has almost erased a 400%
jump that had occurred in 1998 and 1999.
http://cnnfn.cnn.com/2000/12/26/markets/markets_newyork/
http://biz.yahoo.com/fo/001228/1228simons.html
Copyright FinanceProfessor.com 2001.
Permission granted for in class use.