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<DIV><FONT size=2>This is a message I sent to a trader. I wonder if it might
stimulate a <STRONG>line of thought on probabiltiy and statistics</STRONG>. I am
looking for a <STRONG>good visualization for a </STRONG><STRONG>Gaussian
process.</FONT></STRONG></DIV>
<DIV><FONT size=2>George</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2><BR> </DIV></FONT>
<DIV><FONT color=#000000 size=2>Norman,</FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT><FONT size=2>There is a great tape of a
lecture by Richard Feynman on intro to Quantum Mechanics. His deep baratone
voice booms out "..nobody can tell you anymore than this... science has
given up[on exact forecasts]" When you start from a premise of Gaussian
distribution of price changes ( for Black-Scholes it was difference in logs of
price) you get different forecasts or realizations each time you run the
simulation. If the process is tightly constrained as in 2% volatility then all
the realizations will be in a tight up trending pattern (downtrend if you put in
</FONT></DIV>
<DIV><FONT size=2>(-) expected rate of return). </FONT></DIV>
<DIV><FONT size=2>The key is the phrase voltility. I associate Blk-Scholes with
a standard deviation calculation about a moving mean. They equated risk with
standard deviation. If volatility is zero, the stock moves in a straight line
from 100 to 164 (in my example of 64% rate of return). All charts are 1 year.
</FONT></DIV>
<DIV><FONT size=2>(I had to cut off to fit but you can run the same simulations
at the Mathworks site. Having a cable modem let me run 10 simulations in 10
minutes.)</FONT></DIV>
<DIV><FONT size=2>As you add volatility 2% 4% 8% 16% 32% the noise eventually
swamps and overwhelms the trend. At 48% volatility(ie noise), you simply cannot
tell if there is trend. And for some reason they all become bearish as
volatility expands. Maybe this is a self fullfilling prophecy. Volatility causes
the smart money to head for a safe harbor. Remember the PBS special
"Trillion $ Bet"? To me the message was BIG BIG money is bet on these
kind of math models.</FONT></DIV>
<DIV><FONT size=2>This Gaussian distribution of price changes can be visualized
by any random process. Be carefull: many random gambling games such as roulette
produce random <STRONG><U>Uniform</U></STRONG> distributions not
<STRONG><U>Gaussian</STRONG> </U>. I visualize a dart board. If the dart lands
dead center the change in the dow is +or -500 pts . Not very likely. If the dart
lands in the outer most shell with the largest area the dow moves +-40 pts. Fire
21 darts. Where the dart lands gives you the <STRONG>change</STRONG> in dow pts
or % change if you want to use logs. Plot the dow for the month of March 2000.
Fire 21 more darts. Plot the dow again for the month of March 2000. Repeat 40
Marches. Now average all your March dart board predictions for the dow. That is
your forecast. I am of course giving you my simplified description of a
Monte Carlo simulation. The academics sophisticate it to the nth power. I don't
think they can beat an average day trader because their models don't respond to
conditions as they unfold.</FONT></DIV>
<DIV><FONT size=2>Probability books can give a better example than my dart board
but you get the idea. The thing about the market is that sometimes we get
<STRONG>runs</STRONG> of very large price changes. Volatility begets volatility.
Those distributions of price changes are not Gaussian. This is not taken into
account by the Gaussian academics.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>George </FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2></FONT><FONT face=Arial size=2><B>-----Original
Message-----</B><BR><B>From: </B>nwinski <<A
href="mailto:nwinski@xxxxxxxxxxxxxxx";>nwinski@xxxxxxxxxxxxxxx</A>><BR><B>To:
</B>gposnak <<A
href="mailto:gposnak1@xxxxxxxx";>gposnak1@xxxxxxxx</A>><BR><B>Date:
</B>Tuesday, February 29, 2000 5:05 PM<BR><B>Subject: </B>Re:
simulations<BR><BR></DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: 5px"></FONT>George,
<P> Sorry, I don't get it. One of the earlier
forecasts had IBM going up for the same period the attached forecast has it
going down. As Jerry Seinfeld would say, "what's the deal?"
<P>Befuddledly,
<P>Norman
<P>gposnak wrote:
<BLOCKQUOTE TYPE = CITE> <FONT color=#000000><FONT
size=-1>Norman,</FONT></FONT><FONT color=#000000><FONT size=-1>Note the
trend becomes universally bearish as volatility rises to 200% even
though expeceted return remains at +64%. Of course this is just under
<B>this</B> Blk-Scholes model.</FONT></FONT><FONT
color=#000000><FONT
size=-1>George</FONT></FONT></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>
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From: "gposnak" <gposnak1@xxxxxxxx>
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Subject: [RT] Fw: simulations
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<DIV><FONT size=2>This is a message I sent to a trader. I wonder if it might
stimulate a <STRONG>line of thought on probabiltiy and statistics</STRONG>. I am
looking for a <STRONG>good visualization for a </STRONG><STRONG>Gaussian
process.</FONT></STRONG></DIV>
<DIV><FONT size=2>George</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2><BR> </DIV></FONT>
<DIV><FONT color=#000000 size=2>Norman,</FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT><FONT size=2>There is a great tape of a
lecture by Richard Feynman on intro to Quantum Mechanics. His deep baratone
voice booms out "..nobody can tell you anymore than this... science has
given up[on exact forecasts]" When you start from a premise of Gaussian
distribution of price changes ( for Black-Scholes it was difference in logs of
price) you get different forecasts or realizations each time you run the
simulation. If the process is tightly constrained as in 2% volatility then all
the realizations will be in a tight up trending pattern (downtrend if you put in
</FONT></DIV>
<DIV><FONT size=2>(-) expected rate of return). </FONT></DIV>
<DIV><FONT size=2>The key is the phrase voltility. I associate Blk-Scholes with
a standard deviation calculation about a moving mean. They equated risk with
standard deviation. If volatility is zero, the stock moves in a straight line
from 100 to 164 (in my example of 64% rate of return). All charts are 1 year.
</FONT></DIV>
<DIV><FONT size=2>(I had to cut off to fit but you can run the same simulations
at the Mathworks site. Having a cable modem let me run 10 simulations in 10
minutes.)</FONT></DIV>
<DIV><FONT size=2>As you add volatility 2% 4% 8% 16% 32% the noise eventually
swamps and overwhelms the trend. At 48% volatility(ie noise), you simply cannot
tell if there is trend. And for some reason they all become bearish as
volatility expands. Maybe this is a self fullfilling prophecy. Volatility causes
the smart money to head for a safe harbor. Remember the PBS special
"Trillion $ Bet"? To me the message was BIG BIG money is bet on these
kind of math models.</FONT></DIV>
<DIV><FONT size=2>This Gaussian distribution of price changes can be visualized
by any random process. Be carefull: many random gambling games such as roulette
produce random <STRONG><U>Uniform</U></STRONG> distributions not
<STRONG><U>Gaussian</STRONG> </U>. I visualize a dart board. If the dart lands
dead center the change in the dow is +or -500 pts . Not very likely. If the dart
lands in the outer most shell with the largest area the dow moves +-40 pts. Fire
21 darts. Where the dart lands gives you the <STRONG>change</STRONG> in dow pts
or % change if you want to use logs. Plot the dow for the month of March 2000.
Fire 21 more darts. Plot the dow again for the month of March 2000. Repeat 40
Marches. Now average all your March dart board predictions for the dow. That is
your forecast. I am of course giving you my simplified description of a
Monte Carlo simulation. The academics sophisticate it to the nth power. I don't
think they can beat an average day trader because their models don't respond to
conditions as they unfold.</FONT></DIV>
<DIV><FONT size=2>Probability books can give a better example than my dart board
but you get the idea. The thing about the market is that sometimes we get
<STRONG>runs</STRONG> of very large price changes. Volatility begets volatility.
Those distributions of price changes are not Gaussian. This is not taken into
account by the Gaussian academics.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>George </FONT></DIV>
<DIV> </DIV>
<DIV><FONT size=2></FONT><FONT face=Arial size=2><B>-----Original
Message-----</B><BR><B>From: </B>nwinski <<A
href="mailto:nwinski@xxxxxxxxxxxxxxx";>nwinski@xxxxxxxxxxxxxxx</A>><BR><B>To:
</B>gposnak <<A
href="mailto:gposnak1@xxxxxxxx";>gposnak1@xxxxxxxx</A>><BR><B>Date:
</B>Tuesday, February 29, 2000 5:05 PM<BR><B>Subject: </B>Re:
simulations<BR><BR></DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: 5px"></FONT>George,
<P> Sorry, I don't get it. One of the earlier
forecasts had IBM going up for the same period the attached forecast has it
going down. As Jerry Seinfeld would say, "what's the deal?"
<P>Befuddledly,
<P>Norman
<P>gposnak wrote:
<BLOCKQUOTE TYPE = CITE> <FONT color=#000000><FONT
size=-1>Norman,</FONT></FONT><FONT color=#000000><FONT size=-1>Note the
trend becomes universally bearish as volatility rises to 200% even
though expeceted return remains at +64%. Of course this is just under
<B>this</B> Blk-Scholes model.</FONT></FONT><FONT
color=#000000><FONT
size=-1>George</FONT></FONT></BLOCKQUOTE></BLOCKQUOTE></BODY></HTML>
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