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Aaron,
No references needed. Its a simple demonstration which I've
borrowed from one of Chuck LeBeau's Traders Club Bulletins:
"Here are the numbers: Risk is always 5% of current capital.
(I'm going to round the numbers to two decimals.)
Capital $ Risk W/L Account balance
100.0 5.00 L 95.00
95.00 4.75 L 90.25
90.25 4.51 L 85.74
85.74 4.29 L 81.45
81.45 4.07 L 77.38
OK we are already tired of losing. Let's have five winners
in a row and see if we can get our money back.
Capital $ Risk W/L Account balance
77.38 3.87 W 81.25
81.25 4.06 W 85.31
85.31 4.27 W 89.58
89.58 4.48 W 94.06
94.06 4.70 W 98.76
As you can see we had an equal number of winners and losers
yet somehow we lost money. Perhaps it is because we had bad
luck and got started in the wrong direction. Lets reverse
the sequence of trades so that we start out on a winning
streak instead of losing. Maybe that will help.
Capital $ Risk W/L Account balance
100.00 5.00 W 105.00
105.00 5.25 W 110.25
110.25 5.51 W 115.76
115.76 5.79 W 121.55
121.55 6.08 W 127.63
Looks good so far. Starting off with winners looks much
better than starting with losses. But now we have five
losers coming up.
Capital $ Risk W/L Account balance
127.63 6.38 L 121.25
121.25 6.06 L 115.19
115.19 5.76 L 109.43
109.43 5.47 L 103.96
103.96 5.20 L 98.76
Hmmm. It doesn't seem to matter if we start out with a
string of winners or a string of losses. Somehow we wound up
losing the same amount of money either way."
The full bulletin is at:
http://traderclub.com/discus/messages/107/681.html?SundayApr
il3020001039pm
I recommend Chuck's group for some interesting discussions
although some of the members are a bit puerile. His
bulletins are excellent material.
So the problem is that if your system has marginal
expectancy then fixed fractional will reduce it further.
The other side of it makes up for this. On the positive
side, because you reduce bet size in a losing streak you can
start with a larger percentage bet for a given maximum
drawdown. As you can see from my previous posting this not
only gives you a higher return for a given maxDD but you
also get a smaller maxDD at 2 Standard Deviations indicating
a reduced risk of ruin.
Regards, John
----- Original Message -----
From: "Schindler Trading" <schindlertrading@xxxxxxxxxxx>
To: "John Lynch" <kiwi_trader@xxxxxxxxxxxx>;
<omega-list@xxxxxxxxxx>
Sent: Sunday, August 25, 2002 11:55 AM
Subject: Re: Geometric Capital Growth / Optimal-f
Mr. Lynch:
Fixed fractional has a negative expectancy? What do you
mean? Do you have
any references? I don't believe this is true, but I've got
an open mind.
At Schindler Trading we use fixed fractional position sizing
and believe it
is the wisest choice -- as I believe you also concluded
after your Monte
Carlo testing.
Regards,
Aaron Schindler, CFA
Schindler Trading
1243 Yorkshire Lane
Barrington, IL 60010
telephone: 847-719-2846
fax: 847-719-2846
email: aaron@xxxxxxxxxxxxxxxxxxxx
www.schindlertrading.com
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