|
PureBytes Links
Trading Reference Links
|
The number of wins or losses or the order and wins and losses is also
completely irrelevant to this discussion.
I repeat..if you have a positive expectancy on your trades (even if its
1 in 10 wins) then you should increase your bets after a win and
decrease
after a loser....
END OF STORY..this is 100% fact.
The ongoing line of discussion here clearly tells me there is a fatal
misunderstanding of mathematics, system expectancy. Otherwise when to
use a betting model would answer itself immediately.
Adrian
> -----Original Message-----
> From: Schindler Trading [mailto:schindlertrading@xxxxxxxxxxx]
> Sent: Monday, 26 August 2002 11:26 AM
> To: John Lynch; omega-list@xxxxxxxxxx
> Subject: Re: Geometric Capital Growth / Optimal-f
>
>
> Fixed fractional sizing does not have a negative expectation.
>
> Chuck LeBeau has done a disservice to his readers. A system
> model that gets exactly 5 wins and 5 losses and for every 10
> trades and always gets exactly 5 wins and 5 losses is a poor
> model of a system. If you have ever traded a strategy you'll
> recognize that a strategy can sometimes have a good run and
> do 6 or 7 wins in a 10 trade set. And sometimes it'll have a
> bad set and see only 3 or 4 wins in a 10 trade set.
>
> A better model of a strategy is the binomial distribution.
> This is the distribution of the number of times heads shows
> up when you flip a coin. We assume each trade and each toss
> of the coin are independent. Chuck LeBeau would have us
> believe that if we have tossed the coin 9 times (made 9
> trades) and have gotten 5 heads (winners) and 4 tails
> (losers) then we will automatically have a tail (loser) on
> the next flip (trade) -- might as well skip the trade! That
> is not true. The next flip (trade) still has a 50/50 chance
> of turning up heads or tails (winner or loser for a strategy
> with a 50% chance of having a winner).
>
> We won't necessarily have exactly 5 wins and 5 losses for
> every 10 trades. If we flip a coin 10 times the most likely
> result is 5 heads and 5 tails, but there is a chance of
> having anywhere from 0 heads and 10 tails all the way up to
> 10 heads and 0 tails.
>
> Now if we take Dennis' email where we bet 25% of the
> available capital each trade, and start with $100, he showed
> that with 5 wins and 5 losses you would end up with $72.42.
> But the full range of possibilities, with the ending capital,
> and the chance of that possibility happening are:
>
> 0 wins, $5.63, 0.1%
> 1 win, $9.39, 1.0%
> 2 wins, $15.64, 4.4%
> 3 wins, $26.07, 11.7%
> 4 wins, $43.45, 20.5%
> 5 wins, $72.42, 24.6% (Dennis' example)
> 6 wins, $120.70, 20.5%
> 7 wins, $201.17, 11.7%
> 8 wins, $335.28, 4.4%
> 9 wins, $558.79, 1.0%
> 10 wins, $931.79, 0.1%
>
>
> To get the expectation for this model of a strategy, we need
> to multply the ending capital for each possibility by the
> chance of that possibility occurring and then add across all
> possibilities. If you do this you'll find that the strategy
> has a $100 expectation -- exactly what we started with! Fixed
> fractional trading does not have a negative expectation. Nor
> does it turn good systems into losing systems.
>
> You might think intuitively -- "well my strategy has ups and
> downs and I'll always be playing the largest size on the
> losers and then after the losers I'll be playing smaller size
> when I have winners, so it makes sense that I would lose
> money on a 50/50 system." I reply that the human brain is
> not very good at intuiting probabilities. Each trade is
> independent. Whether we previously had a winner or a loser
> and whether we just upped or reduced the size, doesn't affect
> whether the next trade will be a winner or a loser.
>
> Maybe it would be easier to think of it this way if you want
> to be intuitive... Having 0 wins is just as likely as having
> 10 wins. With 0 wins we lose about $94. But with 10 wins we
> make a whopping $832! Average these out and you are way
> ahead. Keep doing this with opposing pairs... 1 win loses
> less money than 9 wins gains. Etc. The positive expectation
> of the five opposing pairs offsets the expected loss from
> exactly 5 wins.
>
> I think backtesting and the proper use of the statistics
> gained in backtesting are the most important thing in being a
> profitable trader and it pains me to see Chuck LeBeau
> misleading people.
>
>
> 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
>
>
>
>
> ----- Original Message -----
> From: "John Lynch" <kiwi_trader@xxxxxxxxxxxx>
> To: "Schindler Trading" <schindlertrading@xxxxxxxxxxx>;
> <omega-list@xxxxxxxxxx>
> Sent: Sunday, August 25, 2002 7:25 PM
> Subject: Re: Geometric Capital Growth / Optimal-f
>
>
> > 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
> >
>
|