Date: Wed, 21 Sep 2005 10:14:23 CST
From: Rich Carreiro 
Newsgroups: misc.invest.financial-plan
Subject: Re: Relative risk of funds and indexes
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"raylopez99"  writes:

> That said, this topic is very rich in theory--I believe a Dr. Sharpe
> won the Nobel for work in this area ("Sharpe's Ratio").

Actually, I think it was for the since-somewhat-discredited CAPM.

> Intuitively, the curve for rate of return for the stock gets narrower
> (variance decreases) over time, but the "tails" of the curve for return
> get longer (both ends of the curve, so it's also true somebody will get
> filthy rich over time), and therein lies the paradox.  Most people
> (area under the curve) will see their rate of return converge to the
> mean (thus Money magazine and AAII will encourage you to hold onto a
> mutual fund, correctly predicting that it will 'come back), but a FEW
> unfortunates will actually LOSE MORE  MONEY THE LONGER THEY HOLD THEIR
> STOCK

Not quite -- *all* the people who hold any particular stock during a
particular time will experience the same return (how else could it
be?).  So it's not like someone who makes a killing on a stock during
some interval will be balanced by someone who loses everything on the
same stock in the same interval.  Rather, in the universe of all
securities with the same random walk parameters, most securities will
do average, few will do very well, and few will do very badly.

In other words, I think what the statement you are referring to is
really saying is that if you have an ensemble of independent
securities that each have the same random walk parameters (i.e. same
mean, variance around the mean, etc.), let that ensemble evolve over N
periods, for each of the securities in the ensemble calculate its
average return per period, and finally histogram those returns, *then*
you'll get what you said -- a distribution that is sharply peaked
around the mean return but having low, long tails.

Or, since we're assuming a random walk (which means the security is
"self-independent", to make up a term), you could compute the avg
return of Security X over N periods, write that down, compute the avg
return of X over the next N periods, write that down, rinse, lather,
repeat, and histogram that and also get the histogram you described.

-- 
Rich Carreiro                            rlcarr@animato.arlington.ma.us