According to Bernstein, the Mean Annual Stock Return over the period 1802 to 1997 (that's  
<B>196</B> years) is 8.4% and, over this same 
period, the Root Mean Square (RMS) deviation of Annual Returns (that's the Standard Deviation)  
from this Mean is 17.5%.<P>
He concludes that, over <B>10</B>-year periods, the RMS deviation of Annual Returns from this 
8.4% Mean is 17.5%/SQRT(<B>10</B>) = 5.54%.<P>
Over <B>196</B> years, the RMS deviation from the 8.4% Mean is 17.5%.<BR>
Over <B>10</B> years, the RMS deviation from the 8.4% Mean is 5.54%.<BR>
Does this seem curious?<BR>
Is this SQUARE-ROOT-of-TIME ritual valid?<BR>
The statement: <I>"...the probability of a return worse than two standard deviations (2SD) 
below the mean is 2.3%"</I> assumes a Normal distribution of Annual Returns: 
NORMDIST(-2,0,1,TRUE) = 0.023 or 2.3%<BR>
Is that valid?<P>


Hi Bill:<P>

As always, I've enjoyed reading your<BR>
http://www.efficientfrontier.com/ef/402/siegel.htm<P>

However, (as always!) I'm a bit confused and hope you can clear things up.<P>

If I understand correctly: 
the Mean Annual Stock Return over the period 1802 to 1997 (196 years) 
is 8.4% and, over this same  period, the Root Mean Square (RMS) deviation 
of Annual Returns (the SD)  from this 8.4% Mean is 17.5%.<P>

However, you conclude that, over "10-year" periods, the RMS deviation of Annual Returns from 
this 8.4% Mean is <BR>17.5%/SQRT(10) = 5.54% (statistically speaking).<BR>
	Over 196 years, the RMS deviation from the 8.4% Mean is 17.5% (from historical data).<BR>
	Over 10 years, the RMS deviation from the 8.4% Mean is 5.54% (from random walk arguments).<BR>
Is that what you are saying?<P>

Many thanks for any clarification you can give.<BR>
Peter Ponzo