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> yes I understood the Kelly principle. The rules of the game
>determine the outcome, when you win you gain 200% when you loose you
>loose 100%, your optimal fraction in the wager should be 25% of your
>account.
It is interesting that I mainly live off my intuition but I couldn't
arrive at the 25% intuitively.
RV had to give me the math or I would never have figured it out.
(No wo/man is an island!)
In fact if anything it defies 'common sense' and I had to get out a
piece of paper and a calculator (spreadsheet) before I could believe
it.
Same with MM and Portfolio Management.
It would take me a year full time to sit down and write the readers
digest version of Vince et al, with diagrams and trade examples, but
I guarantee anyone who has been around trading for years could easily
understand it and would say wow (unless of course they are amongst
the 5% who already know what he was on about).
>Doesn't Vince's optimal f use a prior history of trades to
>determine the optimal fraction?
Yes.
It uses iterative trial and error (computer required).
It is biased to the worst loss experienced during that period.... as
you know, worse losses might be just around the corner.
It also trades off drawdown against higher returns.
Most people tend to trade left of the optimum because of the above.
>Seems to me that if you have something that works you just need to
>make sure there is no possibility of being wiped out
A lot of traders recommend around 2% fixed fraction to apply your
principle.
I understand that.
I am not advocating that people go out and trade optF, rather, just
for them to get an understanding of it and to have some good reasons
for why they stake the way they do.
It isn't good enough for me to run at 2% FF just because 49/50
authors say that is what they do.
BTW
You can use MonteCarlo instead of Vince .... they can both take you
to the same conclusion.
I am trying to boil it all down to a couple of formulas so it is
either easier to understand OR doesn't require the massive attack of
MCS.
My desire to see the trade series as Matrices is part of it.... you
can see from my example that it would be very easy to calculate the
arithmetic mean and standard dev for any trade series, or part
thereof, if AFL had some basic MatrixFunctions (RV uses GeometricMean
as his ObjectiveFunction and the GM is very easy to approximate from
the AMean and StDev .... no complex math required).
Based in what I have in front of me so far I'm optimistic I can I do
it.
brian_z
--- In amibroker@xxxxxxxxxxxxxxx, "Edward Pottasch" <empottasch@xxx>
wrote:
>
> hi Brian,
>
> yes I understood the Kelly principle. The rules of the game
determine the outcome, when you win you gain 200% when you loose you
loose 100%, your optimal fraction in the wager should be 25% of your
account. It is a nice game to play with people who never heard of
it, makes you look real clever. Doesn't Vince's optimal f use a
prior history of trades to determine the optimal fraction? Seems to
me that if you have something that works you just need to make sure
there is no possibility of being wiped out and hope the stockmarket
is still there the next year (which I am starting to doubt).
>
> regards, Ed
>
>
>
> ----- Original Message -----
> From: brian_z111
> To: amibroker@xxxxxxxxxxxxxxx
> Sent: Saturday, January 31, 2009 9:44 AM
> Subject: [amibroker] Re: Sell and Buy on different days
>
>
> Well, I wasn't at the front of the queue when the maths
processors
> were being installed.
>
> I mainly work on understanding the principles, with a lot of help
> from Excel, and then apply the simplified principles in my own
way.
>
> I do a lot of ad-libbing because no one can provide us with a
> complete or persoanlised answer.
>
> Looks like you are pretty happy with what you already have at
your
> fingertips.
>
> For academic interest only:
>
> Use a biased coin, that pays more on heads than tails.
>
> If you bet on the toss, it seems obvious that you will win, over
> time, if you bet on the outcome.
>
> However, ff you flip the coin and bet all of your stake on heads
and
> it comes up tails you have lost all o n the firs bet, so clearly
the
> amount we bet each toss affects the end result.
>
> Kelly is the maths used to calc the optimum stake for coin
tossing,
> where the amount one or lost is always the same.
>
> It is no use for trading.
>
> OptimalF calcs return the amount to stake when the wins and
losses
> are not all the same.
>
> It is actually the staking system that gets you back above the
water
> line in the shortest possible time.
>
> On one hand it definitely shows us where our stake high enough
> because there is no further gain to be had from increasing it.
>
> On the other hand, trading at optF usually means you will suffer
> large drawdowns and this has put a lot of people off it.
>
> For a more comfortable drawdown a lof of traders operate at less
that
> optimum.
>
> Note that the maths isn't hard ... it's accepting the truth of it
and
> then actually doing it that is the hard part.
>
> >Played with clever ways to adapt the position size but never
seen it
> >work for me. Complex portfolio type systems I do not like to
trade
> >anymore
>
> It is easier than academia makes it look (Fund Managers have an
> entirely different background and brief to myself).
>
> I hope I have the time in the future to post some easy methods.
>
> You are probably like me ... better of practising than theorising.
>
> >the idea Andy posted is very interesting and works remarkebly
well
> >for a long only system. Seems this can be made into a stable
> >25%/year return system without using compounding. Long only
systems
> >are far less complex to execute in the practice.
>
> That's very generous of you and Andy to discuss it publicly.
>
> I'll have another look at it.
>
> Cheers,
>
> brian.
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Edward Pottasch" <empottasch@>
> wrote:
> >
> > hi Brain,
> >
> > Have to admit I am not smart enough for stuff Ralph Vince is
> talking about. Optimal f etc. never really understood how to use
it
> (as if I understood it at all). The Kelly principle is as far as
I
> got but how to use it in trading? Money management which I used
when
> I was trading a portfolio type EOD system was simply put 3% of
the
> account in each trade and no margin. Played with clever ways to
adapt
> the position size but never seen it work for me. Complex
portfolio
> type systems I do not like to trade anymore, although the idea
Andy
> posted is very interesting and works remarkebly well for a long
only
> system. Seems this can be made into a stable 25%/year return
system
> without using compounding. Long only systems are far less complex
to
> execute in the practice.
> >
> > Would like to have a look in the kitchen how the real quants
> operate, like Simons of the Renaissance Hedge fund. The guy is a
> mathematician but I believe these days these guys make money by
> simple making the market. If you make the market you know where
it is
> heading :)
> >
> > regards, Ed
> >
> >
> >
> >
> >
> > ----- Original Message -----
> > From: brian_z111
> > To: amibroker@xxxxxxxxxxxxxxx
> > Sent: Saturday, January 31, 2009 5:05 AM
> > Subject: [amibroker] Re: Sell and Buy on different days
> >
> >
> > Mike and Ed,
> >
> > Thanks for your feedback.
> >
> > You guys sure got me thinking.
> >
> > Thanks for your perserverance also .... I realise that my
tenses
> are
> > wobbling and the logic fades in and out a little ... my work
> contains
> > more errors than it would if I wrote the book formally.
> >
> > A little more ..
> >
> > ....referencing my previous matrix example.
> >
> > My comments so far have assumed that the trade samples are
> > independent.
> >
> > If we had 100 Eq at the end of day 3 then the outcome, after
day
> > four, would equal the mean of the GF's for each simultaneous
> trade
> > e.g.
> >
> > ... going back to the future ... on day 4 we take option 1 ...
> record
> > the result and then go back and take option 2 etc, being
careful
> to
> > do everything exactly the same except for the X,Y,Z
selection ...
> > then compare:
> >
> > day 4
> > eq 100
> >
> > GrowthFactor, Eq
> >
> > X 1.05, 100 -> 105
> > Y 0.98, 100 -> 98
> > X 1.02, 100 -> 102
> >
> > ave GF == 1.016repeat, ave eq == 101.6 repeat
> >
> > OR nominally, in the time warp, we had 300 and now have 305
> >
> > and 305/300 == GF 1.016repeat for the period
> >
> > If they are independent trades then we throw them in the bucket
> with
> > the a -> i samples.
> >
> > a -> i and X,Y,Z are just time markers, like buttons on a game
> board,
> > and we have to turn them over to find their trade value.
> >
> > If we do that a massive number of times, tending to oo, the
> outcome,
> > for each box in the matrix, will tend to the mean value of all
> > trades ... even on day four, which will just approach the mean
> more
> > quickly than the other time slots.
> >
> > (if we want to imagine this we can picture the 10 box matrix
> > repeating itself end to end infinitely and the trades falling
> into
> > the empty boxes sequentially ... since time is constant there
is
> no
> > reason not to do this ... it is the values in the boxes that
have
> > variance and are non-stationary and not the sample space).
> >
> > The proof is that after massive sampling, if we transpose the
> indexed
> > array back and stack the 10 box submatrices on top of each
other,
> and
> > then average the columns + calc the StDev, they would all be
the
> mean
> > trade +- variance
> >
> > Note that since the trade samples do not necessarily have a
> normal
> > dist we need to do some random sampling first, and then apply a
> > distribution to the newly selected sample space, which produces
a
> > kind of psuedo mean distribution for the trade sample set (MCS
> just
> > does this for us automatically so we tend not to notice that
step
> > whereas in BS I do that first).
> >
> > Considering correlation of simultaneous trades:
> >
> > - using EOD as the simplest example (in any case trades must be
> on
> > the same bar or they would not be simultaneous)
> > - trading long only (a bull system)
> > - it might happen that on a market bull day you get more
signals
> and
> > more wins
> >
> > day. 1, 2, 3, 4
> > market. bear, bear, bear, bull
> > P or L. loss, loss, loss, 10 trades all win
> >
> > So we are up 10/3 wins/losses but the market itself is 1/3
> >
> > Looking at the staking if you bet fixed fraction:
> >
> > - losing some eq initially,
> >
> > bet. 110,105,100 then 100/10 is bet on each trade and the
outcome
> is
> > the ave result of the 10 trades.... as an aside this needs to
be
> ave
> > == 10% to get us back to the start eq of 110.
> >
> > Effectively we have achieved the result of the ave trade i.e.
it
> is
> > as if we only made one trade in real terms.
> >
> > So, if correlation , between simultaneous trades, exists then
we
> > could count it as one trade and only throw one win in the freq
> dist
> > bin and give it a value of the ave trade for the bar.
> >
> > On the other hand, the reverse could hold i.e. on market bear
> days we
> > could get 10 signals that are all losses to our bull system,
and
> thus
> > happily balance the books.
> >
> > We also have to ask ourselves, "Why not just trade the market
and
> not
> > worry about correlation"?
> >
> > It is also possible that horizontal correlation (dependency)
can
> > occur in the trade matrix ... RalphVince gives the calcs to
> handle
> > that situation in his books... certainly on google as well.
> >
> > BTW I agree with you that we need to think about the
implications
> of
> > the BT alphabetically selecting symbols to trade and being
bound
> by
> > eq limits.
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@>
> wrote:
> > >
> > > O.K Mike ... you live and learn :-)
> > >
> > > Possibly correlation, or NOT, of simultaneous trades to the
> market,
> > > or sector, is a related subject ... didn't discuss that
detail
> in
> > > relation to my X,Y & Z example .. that is where trade sample
> space
> > > anlaysis can provide the answer.
> > >
> > >
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx, "Mike" <sfclimbers@> wrote:
> > > >
> > > > --- In amibroker@xxxxxxxxxxxxxxx, "brian_z111"
<brian_z111@>
> > wrote:
> > > > >
> > > > > > In any case it could be traded if you organise your
funds
> in
> > > such
> > > > a
> > > > > >way that all symbols in your list can be held
> simultaneously.
> > > > >
> > > > > That isn't really practical and we can calculate very
> accurate
> > > > > predictions, subject to variance and non-stationarity,
> before
> > we
> > > > risk
> > > > > our money.
> > > >
> > > > Why impractical? I have been doing exactly that,
profitably,
> for
> > > just
> > > > under 2 years. There is much room for experimentation in
> exactly
> > > how
> > > > the funds get distributed among the signals. But, even a
> simple
> > > equal
> > > > division of equity between all signals (up to a fixed
maximum
> > > > percentage of equity per trade in the event that there are
> few
> > > > signals) can prove profitable when applied to a strategy.
> > > >
> > > > Mike
> > > >
> > > >
> > > > > >there are a lot of additional problems that arise like
an
> > > > uncomplete
> > > > > >database during testing
> > > > >
> > > > > You can't get a good result out of a bad database....
just
> > avoid
> > > > > trades were you can't get the data you need.
> > > > >
> > > > >
> > > > > >Not sure if a random selection on an extended list for
> testing
> > > > > >purposes is reliable. Who knows in the practice you will
> find
> > > that
> > > > > >the signals that come early during the trading session
> usually
> > > are
> > > > > >loosers. This could be tested however using intraday
data,
> > > > >
> > > > >
> > > > > Yes it is reliable, in fact it is the only way that it
can
> be
> > > done.
> > > > >
> > > > > Returning to the example in my previous post:
> > > > >
> > > > > a b c X d e f g h i
> > > > > a b c Y d e f g h i
> > > > > a b c Z d e f g h i
> > > > >
> > > > > The XY & Z samples were produced by the same system (same
> > rules)
> > > as
> > > > > the a -> i samples, so they are part of the same series
and
> > share
> > > > the
> > > > > same profile (frequency distribution and probabilities).
> > > > >
> > > > > If you have a list of trades for an EOD system and then
> want to
> > > find
> > > > > out if the intraday time affects the result then you are
> > ranking
> > > > your
> > > > > daily signals using an intraday factor and you have to
add
> at
> > > least
> > > > > one more trading rule to do that.
> > > > >
> > > > > This is effectively a new system and it will produce its
> own
> > > trade
> > > > > series , with it's own characteristics.
> > > > >
> > > > > As always, if we do analyse the trade sample space, we
have
> to
> > > make
> > > > > sure we are left with enought samples to provide a valid
> sample.
> > > > >
> > > > > NEW RULE == NEW SYSTEM == NEW AND UNIQUE TRADE SERIES
> > > > >
> > > > >
> > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Edward Pottasch"
> > <empottasch@>
> > > > > wrote:
> > > > > >
> > > > > > In any case it could be traded if you organise your
funds
> in
> > > such
> > > > a
> > > > > way that all symbols in your list can be held
> simultaneously.
> > > EOD
> > > > > systems are tricky though since there are a lot of
> additional
> > > > > problems that arise like an uncomplete database during
> testing
> > > > (ENRN,
> > > > > WCOM etc missing), no shorts available during trading.
Not
> sure
> > > if a
> > > > > random selection on an extended list for testing purposes
> is
> > > > > reliable. Who knows in the practice you will find that
the
> > > signals
> > > > > that come early during the trading session usually are
> loosers.
> > > This
> > > > > could be tested however using intraday data,
> > > > > >
> > > > > > regards, Ed
> > > > > >
> > > > > >
> > > > > > ----- Original Message -----
> > > > > > From: Mike
> > > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > > Sent: Thursday, January 29, 2009 10:32 PM
> > > > > > Subject: [amibroker] Re: Sell and Buy on different days
> > > > > >
> > > > > >
> > > > > > Ha ha.
> > > > > >
> > > > > > Just goes to show how people can get tunnel vision
> > sometimes.
> > > > > Since I
> > > > > > do a lot of custom backtester code, I immediately
> suggested
> > > > > filtering
> > > > > > at that level.
> > > > > >
> > > > > > But, your suggestion of a random value for
PositionScore
> > > > directly
> > > > > > would be far easier and less prone to coding error.
> > > > > >
> > > > > > Mike
> > > > > >
> > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Edward Pottasch"
> > > > <empottasch@>
> > > > > > wrote:
> > > > > > >
> > > > > > > you are right on this Mike. Testing a system like
this
> > > using a
> > > > > > random positionscore is a good indication if it can be
> made
> > > into
> > > > > a
> > > > > > system that can be used in the practice. Andy has an
idea
> > > that
> > > > is
> > > > > > tough to execute but not impossible in my opinion,
> > > > > > >
> > > > > > > regards, Ed
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > ----- Original Message -----
> > > > > > > From: Mike
> > > > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > > > Sent: Thursday, January 29, 2009 8:37 PM
> > > > > > > Subject: [amibroker] Re: Sell and Buy on different
days
> > > > > > >
> > > > > > >
> > > > > > > Andy,
> > > > > > >
> > > > > > > Use caution when backtesting EOD strategies where
there
> > are
> > > > > more
> > > > > > > signals than there are funds or positions to be
filled;
> > > > > > >
> > > > > > > If your strategy is to buy OCA, what logic are you
> > putting
> > > in
> > > > > > place to
> > > > > > > determine which symbol to buy when multiple symbols
hit
> > > your
> > > > > limit
> > > > > > > order on the same bar?
> > > > > > >
> > > > > > > Since you are using EOD data, you have no idea which
> > symbol
> > > > > would
> > > > > > have
> > > > > > > hit the limit order first. You only know that x of y
> > > symbols
> > > > > hit
> > > > > > the
> > > > > > > limit order on that day.
> > > > > > >
> > > > > > > AmiBroker will just select the first in the list
> > > > > (alphabetically?
> > > > > > ). As
> > > > > > > such, your backtest results will be heavily biased in
> > favor
> > > of
> > > > > > that
> > > > > > > ordering and will not reflect live trading results.
> > > > > > >
> > > > > > > Generally, PositionScore can be used to influence
> > ordering.
> > > > > But,
> > > > > > an
> > > > > > > OCA approach by definition does not follow
> PositionScore.
> > > > > > >
> > > > > > > So, you might want to modify your custom backtester
> code
> > to
> > > > > > randomly
> > > > > > > select from the available signals and set the
remaining
> > > ones
> > > > to
> > > > > > > PosSize 0 in order to override the default
> > prioritization.
> > > > Then
> > > > > > run
> > > > > > > your backtest many times and take the average of the
> > > results
> > > > as
> > > > > a
> > > > > > best
> > > > > > > guess estimate (i.e. Monte Carlo Permutations)
> > > > > > >
> > > > > > > Mike
> > > > > > >
> > > > > > > --- In amibroker@xxxxxxxxxxxxxxx, Andrew Senft
<senft@>
> > > wrote:
> > > > > > > >
> > > > > > > > Hey Ed,
> > > > > > > >
> > > > > > > > Thank you so much for the code on the Amibroker
Yahoo
> > > group
> > > > > > board!
> > > > > > > It
> > > > > > > > seems to be working from what I've seen so far. I'm
> > doing
> > > an
> > > > > > > > optimization on that particular code (your first
> code)
> > > right
> > > > > > now.
> > > > > > > >
> > > > > > > > The second code (the one from your email) didn't
> work.
> > > That
> > > > > is,
> > > > > > > there
> > > > > > > > were sales of one stock and buy of another stock on
> the
> > > same
> > > > > > day.
> > > > > > > Not
> > > > > > > > sure what your code was doing but it gave a lot
> bigger
> > > > > profits
> > > > > > using
> > > > > > > the
> > > > > > > > backtester. Could you comment on this please?
> > > > > > > >
> > > > > > > > Mind you that this is my first attempt to writing
> code
> > > for
> > > > > any
> > > > > > stock
> > > > > > > > type software. I'm still using the 30 day free
trial
> of
> > > the
> > > > > > > Amibroker
> > > > > > > > software but I think that I'm getting closer as I'm
> > > chugging
> > > > > > along.
> > > > > > > >
> > > > > > > > My agenda is to use this on a basket of ETF's.
> Perhaps
> > 10
> > > to
> > > > > 20
> > > > > > > or
> > > > > > > > so. Not sure how many I need since the 30 day trail
> > > > backtests
> > > > > up
> > > > > > > to a
> > > > > > > > basket of 5 stocks. My idea is to place the
possible
> > > stock
> > > > > > trades
> > > > > > > > using the whole basket of ETF stocks at night for
the
> > > next
> > > > > > trading
> > > > > > > > session. I have an IB account so I figure I could
use
> > an
> > > OCA
> > > > > > limit
> > > > > > > > order. Basically whenever a trade gets hit first
> (meets
> > > the
> > > > > > limit
> > > > > > > price
> > > > > > > > level), it trades. The other possible trades all
get
> > > > canceled
> > > > > > right
> > > > > > > > away. So one trade actually goes through for the
day.
> > > > > > > >
> > > > > > > > BTW, I like ETF's because the drawdowns are not as
> > > scary....
> > > > > > okay,
> > > > > > > > usually not as scary. Ha! I've been backtesting
with:
> > > > > > > >
> > > > > > > > QQQQ, DIA, SPY, MDY, IWM
> > > > > > > >
> > > > > > > > Thank you again!
> > > > > > > >
> > > > > > > > Andy
> > > > > > > >
> > > > > > > > Edward Pottasch wrote:
> > > > > > > > >
> > > > > > > > > Andy,
> > > > > > > > >
> > > > > > > > > I have sent an alternative solution to your
private
> > > Email.
> > > > > Let
> > > > > > me
> > > > > > > know
> > > > > > > > > if you received it.
> > > > > > > > >
> > > > > > > > > Ed
> > > > > > > > >
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > ----- Original Message -----
> > > > > > > > > *From:* Andy <mailto:senft@>
> > > > > > > > > *To:* amibroker@xxxxxxxxxxxxxxx
> > > > > > > <mailto:amibroker@xxxxxxxxxxxxxxx>
> > > > > > > > > *Sent:* Thursday, January 29, 2009 12:40 PM
> > > > > > > > > *Subject:* [amibroker] Re: Sell and Buy on
> different
> > > days
> > > > > > > > >
> > > > > > > > > This is got to be a very simple task but
> > unfortunately
> > > > > > > AmiBroker told
> > > > > > > > > me that I would have to write Backtester
Interface
> > code
> > > > for
> > > > > > > this. I'm
> > > > > > > > > sure this has been done a million times. Anyone
> have
> > > > sample
> > > > > > > code?
> > > > > > > > > I'm using EOD data to trade one stock at a time
> from
> > a
> > > > > basket
> > > > > > > of
> > > > > > > > > stocks. The problem is that a selling of a stock
> can
> > > occur
> > > > > on
> > > > > > > the
> > > > > > > > > same day as a buy of *another* stock. Of course
the
> > > > problem
> > > > > is
> > > > > > > that
> > > > > > > > > the sell trade can occur after the buy trade.
> > > > > > > > >
> > > > > > > > > --- In amibroker@xxxxxxxxxxxxxxx
> > > > > > > > > <mailto:amibroker%40yahoogroups.com>, "Andy"
> <senft@>
> > > > wrote:
> > > > > > > > > >
> > > > > > > > > > How do I fix the below code so it doesn't buy a
> > > > different
> > > > > > > stock on a
> > > > > > > > > > sell day?
> > > > > > > > > >
> > > > > > > > > > ------------------------------------------------
--
> --
> > --
> > > --
> > > > > > > > > > // Backtester Options
> > > > > > > > > > SetOption("MaxOpenPositions", 1 );
> > > > > > > > > > SetOption("AllowSameBarExit", False);
> > > > > > > > > >
> > > > > > > > > > // Optimization numbers
> > > > > > > > > > BuyPeriod = Optimize("BuyPeriod",16,10,20,2);
> > > > > > > > > > BuyFactor = Optimize
("BuyFactor",1.2,0.5,1.5,.1);
> > > > > > > > > > SellPeriod = Optimize("SellPeriod",20,10,20,2);
> > > > > > > > > > SellFactor = Optimize
> ("SellFactor",0.8,0.5,1.5,.1);
> > > > > > > > > >
> > > > > > > > > > // ATR formulas
> > > > > > > > > > TodaysBuyTarget = High - BuyFactor * ATR
> (BuyPeriod);
> > > > > > > > > > YesterdaysBuyTarget = Ref(High,-1) - BuyFactor *
> > > > > > > > > Ref(ATR(BuyPeriod),-1);
> > > > > > > > > > YesterdaysSellTarget = Ref(Low,-1) + SellFactor
*
> > > > > > > > > Ref(ATR(SellPeriod),-1);
> > > > > > > > > >
> > > > > > > > > > // Buy/Sell signals and prices
> > > > > > > > > > Buy = YesterdaysBuyTarget > Low;
> > > > > > > > > > BuyPrice = IIf(YesterdaysBuyTarget > Open, Open,
> > > > > > > > > YesterdaysBuyTarget);
> > > > > > > > > > Sell = YesterdaysSellTarget < High;
> > > > > > > > > > SellPrice = IIf(YesterdaysSellTarget < Open,
Open,
> > > > > > > > > YesterdaysSellTarget);
> > > > > > > > > > Buy = ExRem(Buy,Sell);
> > > > > > > > > > Sell = ExRem(Sell,Buy);
> > > > > > > > > >
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > --------------------------------------------------
--
> --
> > --
> > > --
> > > > > > > ------
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > No virus found in this incoming message.
> > > > > > > > > Checked by AVG - http://www.avg.com
> > > > > > > > > Version: 8.0.176 / Virus Database:
270.10.15/1921 -
> > > > Release
> > > > > > Date:
> > > > > > > 1/28/2009 6:37 AM
> > > > > > > > >
> > > > > > > > >
> > > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
>
------------------------------------
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