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If the $50 stock always ranges between 49 and 51, it has an ATR of 2.
Likewise if the $10 stock always ranges between 9 and 11, it also has
an ATR of 2 (although it has a much higher beta).
So with volatility based position sizing where you use 1 ATR as your
stop, if you are willing to risk 2% of a $100,000 portfolio ($2000),
you could buy 1000 shares of either stock. The difference is one half
your capital ($50,000) is tied up in one case and only one tenth
($10,000) in the other.
If anybody has a different interpretation, jump in (please).
Dan
--- In amibroker@xxxxxxxxxxxxxxx, "Pal Anand" <palsanand@xxxx> wrote:
>
> ATR shows volatility in absolute terms (cannot predict direction or
> duration, only activity levels), so, lower price stocks will have
> lower ATR levels than higher price stocks. A $10 stock would have
a
> much lower ATR value than a $50 stock, hence, one would end up
buying
> more shares of the $10 stock than the $50 stock.
>
> rgds, Pal
> --- In amibroker@xxxxxxxxxxxxxxx, "danielwardadams"
> <danielwardadams@xxxx> wrote:
> >
> > I was gone most of the day so didn't have a chance to keep up
with
> > the posts.
> >
> > I agree that the results are the opposite of what one would
expect.
> I
> > think in the cases you cite, the formulas should be
> 100,000*Risk/ATR.
> > So if your risk tolerance is 2% and the ATR is 2, the position
size
> =
> > 100,000*.02/2 = 2000/2 = 1000 where the 1000 is shares of stock
and
> > is independent of the price of the stock, i.e., you can buy 1000
> > shares of ANY priced stock that has an ATR of 2 and your risk
would
> > be the same. In the case of the $50 stock, your position equity
> would
> > be $50*1000 = $50,000 when ATR=2. Similarly, you could buy
> > twice (not half) as much of the stock when ATR=1.
> >
> > Although the position sizing being independent of the price of
the
> > stock seems counterintuitive, I just reread the chapter in Van
> > Tharp's book on this ("Trade Your Way to Financial Freedom") and
I
> > think that's the way it's supposed to be.
> >
> > I'm not sure what this means for our 20% maximum position equity
> > allocation (to achieve diversification).
> >
> > Dan
> >
> >
> > --- In amibroker@xxxxxxxxxxxxxxx, Al Venosa <advenosa@xxxx> wrote:
> > > Ed:
> > >
> > > Your formula doesn't make much sense to me. The term
stoploss/ref
> > (C,-1)
> > > is simply the volatility of the stock, expressed as a fraction
of
> > the
> > > price, times a multiplier. Thus, for a $50 stock whose ATR is,
> say,
> > 2
> > > (highly volatile), and if you are using a multiplier of 2 with
an
> > equity
> > > of $100 K, then your positionsize statement specifies that the
> > position
> > > size of the trade will be only $8,000 (100,000 * 4/50). For a
> less
> > > volatile stock (one whose ATR is only 1), then your
positionsize
> > would
> > > be only $4,000. So, you are allocating less money for less
> volatile
> > > stocks and more money for more volatile stocks, and the amount
> > allocated
> > > in each case is tiny relative to your equity. This is the
> opposite
> > of
> > > what volatility-based trading is all about. Did you leave
> something
> > out?
> > >
> > > Al Venosa
> > >
> > > ed nl wrote:
> > >
> > > > well I just mentioned this because the range is rather
narrow.
> > When
> > > > testing this MM stuff on my system I noticed that it behaved
> very
> > poor
> > > > especially between 1998 and 2001. This is exactly the period
> the
> > > > markets were very volatile. SInce volatility reduces the
> position
> > > > size my system hardly invested any money.
> > > >
> > > > I tried giving risky trades more weight using (not sure if
this
> > is
> > > > correct but it does approximately what I intended):
> > > >
> > > > *PositionSize* = -100 * (stopLoss / Ref(*C*,-1));
> > > > this as I expected gives a better result than just using a
> > constant
> > > > percentage over the last 3 year and also better than the
> correct
> > MM
> > > > approach. Between 1998 and 2001 however it performs worse,
> > suffering
> > > > when the market goes crazy.
> > > >
> > > > rgds, Ed
> > > >
> > > >
> > > >
> > > > ----- Original Message -----
> > > > *From:* danielwardadams <mailto:danielwardadams@x...>
> > > > *To:* amibroker@xxxxxxxxxxxxxxx
> > <mailto:amibroker@xxxxxxxxxxxxxxx>
> > > > *Sent:* Sunday, December 12, 2004 4:06 PM
> > > > *Subject:* [amibroker] Re: PositionSize / Capital
> > > >
> > > >
> > > > I love it. This also helps avoid the tiny positions
> somebody
> > (Al?)
> > > > mentioned yesterday (and I've experienced also). But why
do
> > you say
> > > > it will usually probably use the 10 or 20% sized
positions?
> > Shouldn't
> > > > that mean you're setting your risk parameter
> unrealistically
> > low?
> > > >
> > > > --- In amibroker@xxxxxxxxxxxxxxx
> > > > <mailto:amibroker@xxxxxxxxxxxxxxx>, "ed nl" <ed2000nl@x
> > > > <mailto:ed2000nl@x>...> wrote:
> > > > > This way you can use a range: Maximum 20% minimum 10%
of
> > equity:
> > > > >
> > > > > rsk = -2; // 2%
> > > > > PositionSize = Min(-10,Max(-20,rsk * Ref(C,-1) /
> stopLoss));
> > > > >
> > > > > In practice it most of the time it probably either uses
> 10%
> > or 20%.
> > > > >
> > > > > Ed
> > > > >
> > > > >
> > > > >
> > > > > ----- Original Message -----
> > > > > From: danielwardadams
> > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > Sent: Sunday, December 12, 2004 3:40 PM
> > > > > Subject: [amibroker] Re: PositionSize / Capital
> > > > >
> > > > >
> > > > >
> > > > > Al & Ed,
> > > > > This is exactly where I ended up yesterday (hours
after
> > my post).
> > > > > When I tried it, though, I always ended up taking the
> 20%
> > > > positions
> > > > > rather than those defined by my risk. Thinking it
> wasn't
> > working,
> > > > I
> > > > > gave up and went to bed.
> > > > >
> > > > > But since someone else thinks this should work,
> obviously
> > I need
> > > > to
> > > > > play with it some more.
> > > > >
> > > > > Dan
> > > > >
> > > > > --- In amibroker@xxxxxxxxxxxxxxx, "ed nl"
> <ed2000nl@xxxx>
> > wrote:
> > > > > > Al,
> > > > > >
> > > > > > about the part: "Your suggestion to limit
> > positionsize not to
> > > > > exceed any more than 20% of equity may be the
solution
> > since it
> > > > goes
> > > > > hand in hand with the philosophy of money management.
> > That is, do
> > > > not
> > > > > allow any one position to exceed, say, 10 or 15
percent
> > of your
> > > > > equity. The Turtles did that, and I think lots of
> traders
> > do
> > > > that,
> > > > > too. So, I see nothing wrong with that. Have you
coded
> > this in
> > > > AFL"
> > > > > >
> > > > > > I think you can solve this using:
> > > > > >
> > > > > > rsk = -2; // 2%
> > > > > > PositionSize = Max(-20,rsk * Ref(C,-1) / stopLoss);
> > > > > >
> > > > > > now it will never use more than 20% of equity.
> > > > > >
> > > > > > About the minimum number of trades I don't know. In
> my
> > system
> > > > that
> > > > > would be impossible because sometimes good entries
just
> > dry up
> > > > and I
> > > > > can't find even find 5.
> > > > > >
> > > > > > rgds, Ed
> > > > > >
> > > > > > ----- Original Message -----
> > > > > > From: Al Venosa
> > > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > > Sent: Sunday, December 12, 2004 3:11 PM
> > > > > > Subject: Re: [amibroker] Re: PositionSize /
Capital
> > > > > >
> > > > > >
> > > > > > Dan:
> > > > > >
> > > > > > Thanks for the ideas. You're not rambling; you're
> > thinking,
> > > > and
> > > > > this discussion is healthy. Good ideas may stem from
the
> > > > discussion,
> > > > > so by all means, keep posting.
> > > > > >
> > > > > > I don't think you need a new built-in function
> called
> > MinPos.
> > > > > Maybe TJ came up with a solution the other day by
> > suggesting you
> > > > set
> > > > > the max open positions to some large value like 10 of
> 15,
> > even
> > > > though
> > > > > you plan to take on no more than 5 at any time. So,
if
> > you don't
> > > > use
> > > > > up all your equity using volatility-based
> positionsizing,
> > you
> > > > might
> > > > > add on new positions with this approach. I haven't
> tested
> > this
> > > > idea
> > > > > yet, but I will. The problem occurs when the opposite
> > happens,
> > > > > namely, all your equity is used up before you are
able
> to
> > add
> > > > your
> > > > > 4th and 5th positions. Your suggestion to limit
> > positionsize not
> > > > to
> > > > > exceed any more than 20% of equity may be the
solution
> > since it
> > > > goes
> > > > > hand in hand with the philosophy of money management.
> > That is, do
> > > > not
> > > > > allow any one position to exceed, say, 10 or 15
percent
> > of your
> > > > > equity. The Turtles did that, and I think lots of
> traders
> > do
> > > > that,
> > > > > too. So, I see nothing wrong with that. Have you
coded
> > this in
> > > > AFL?
> > > > > I'm like Yuki: good with concepts buy lousy with
> creative
> > > > > programming.
> > > > > >
> > > > > > Al Venosa
> > > > > >
> > > > > > danielwardadams wrote:
> > > > > >
> > > > > >
> > > > > > After thinking about this some more, I think
all
> > I've
> > > > described
> > > > > is
> > > > > > what could be accomplished with two more built-
in
> > > > variables.
> > > > > MinPos
> > > > > > could say you want no less than some minimum
> number
> > of
> > > > > positions (5
> > > > > > in my example) and MaxPositionSize could say
you
> > want to
> > > > > allocate no
> > > > > > more than X% of capital to any one position
(20%
> in
> > my
> > > > example).
> > > > > >
> > > > > > Within these constraints, your actual position
> > sizing
> > > > methond
> > > > > could
> > > > > > be anything you want.
> > > > > >
> > > > > > I'm probably rambling .........
> > > > > >
> > > > > > Dan
> > > > > >
> > > > > > --- In
> amibroker@xxxxxxxxxxxxxxx, "danielwardadams"
> > > > > > <danielwardadams@xxxx> wrote:
> > > > > > >
> > > > > > > Al & Anthony,
> > > > > > > I've also seen the lower returns for
volatility
> > based
> > > > versus
> > > > > equal
> > > > > > > equity position sizing in the past and didn't
> > know what
> > > > to do
> > > > > about
> > > > > > > it (assuming I wanted more positions for more
> > > > > diversification).
> > > > > > >
> > > > > > > I'm not sure how one would code it in .AFL,
but
> > would the
> > > > > following
> > > > > > > represent a reasonable compromise?
> > > > > > >
> > > > > > > (1) Start with an equal equity based model
> based
> > on,
> > > > say, 5
> > > > > > > positions (position size = -20). So each part
> of
> > the pie
> > > > > equals 20%
> > > > > > > of total equity.
> > > > > > > (2) Determine actual position size within
each
> > piece of
> > > > the
> > > > > pie
> > > > > > based
> > > > > > > on volatility based sizing. So, depending on
> your
> > risk
> > > > > parameter,
> > > > > > one
> > > > > > > might use only 17% of one piece of the pie,
13%
> of
> > > > another
> > > > > piece,
> > > > > > and
> > > > > > > 20%, 8%, and 11% of the other pieces.
> > > > > > > (3) Sum the used portions of the pie (in this
> case
> > > > > 17+13+20+8+11 =
> > > > > > > 69%) and see what you have left. 31% in case.
> > > > > > > (4) Allocate the remaining cash according to
> the
> > equal
> > > > equity
> > > > > > model.
> > > > > > > This means you get one more 20% piece of pie
> and
> > only
> > > > have
> > > > > 11% cash
> > > > > > > remaining.
> > > > > > > (5) Apply the above using your ATR based
> position
> > sizing
> > > > > > recursively
> > > > > > > until your cash is minimized. So if you only
> are
> > able to
> > > > use
> > > > > 9% of
> > > > > > > the piece of pie left in (4) you take the 11%
> > left from
> > > > that
> > > > > piece
> > > > > > > plus the 11% cash and you have 22% -- enough
> for
> > another
> > > > > position.
> > > > > > So
> > > > > > > in this case you end up with 7 positions and
> only
> > 2% left
> > > > in
> > > > > cash.
> > > > > > > So your cash is minimized and all your
> positions
> > adhere
> > > > to
> > > > > the ATR
> > > > > > > based position sizing.
> > > > > > >
> > > > > > > Like I say, I have no idea how to code it but
> > intuitively
> > > > it
> > > > > makes
> > > > > > > sense to me.
> > > > > > >
> > > > > > > Thoughts/comments?
> > > > > > >
> > > > > > > Dan
> > > > > > >
> > > > > > > (And, yes, I'm sure I'm not the first person
to
> > think of
> > > > it
> > > > > so my
> > > > > > > apologies to those who have gone before).
> > > > > > >
> > > > > > > --- In amibroker@xxxxxxxxxxxxxxx, "Anthony
> > Faragasso"
> > > > > > <ajf1111@xxxx>
> > > > > > > wrote:
> > > > > > > > Hello Al,
> > > > > > > >
> > > > > > > > You stated:
> > > > > > > >
> > > > > > > > "the lower the volatility, the lower the
risk
> > and
> > > > > therefore, the
> > > > > > > smaller the positionsize for that stock. "
> > > > > > > >
> > > > > > > > Is this a correct assumption ? ...Would you
> > want a
> > > > larger
> > > > > > > positionsize on a less risk position , and a
> > smaller
> > > > position
> > > > > on a
> > > > > > > more volatile one ?
> > > > > > > >
> > > > > > > > Anthony
> > > > > > > > ----- Original Message -----
> > > > > > > > From: Al Venosa
> > > > > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > > > > Sent: Saturday, December 11, 2004 7:53 AM
> > > > > > > > Subject: Re: [amibroker] PositionSize /
> > Capital
> > > > > > > >
> > > > > > > >
> > > > > > > > Ed,
> > > > > > > >
> > > > > > > > I, too, have confirmed many times with
> > backtesting
> > > > what
> > > > > you
> > > > > > > report, viz,, that positionsize = -x gives
> better
> > > > performance
> > > > > > results
> > > > > > > than using volatility-based MM
positionsizing.
> > The non-MM
> > > > > code I've
> > > > > > > used in the past is:
> > > > > > > >
> > > > > > > > posqty = Optimize("posqty",5,2,10,1); //
> no.
> > of
> > > > stocks
> > > > > active
> > > > > > at
> > > > > > > any given time
> > > > > > > > PositionSize = -100/posqty; //equal
equity
> > model
> > > > > > > >
> > > > > > > > I think I know what the problem is, but I
> > have not as
> > > > yet
> > > > > > figured
> > > > > > > out how to solve the problem with AFL. If you
> use
> > the MM-
> > > > > based
> > > > > > > positionsize statement as we have discussed
> (equal
> > > > volatility
> > > > > > model),
> > > > > > > i.e., PositionSize = -1 * C/StopAmt, and
> examine
> > the
> > > > > tradelist, you
> > > > > > > will likely discover that, often, not all 5
> > stocks are
> > > > active
> > > > > all
> > > > > > the
> > > > > > > time. In other words, either you have idle
> capital
> > > > earning
> > > > > nothing
> > > > > > or
> > > > > > > you have fewer active stocks than you want.
Why
> > is this?
> > > > > Because
> > > > > > some
> > > > > > > stocks, which might not be as volatilie as
> > others, use up
> > > > > more of
> > > > > > > your capital to initiate a position than a
more
> > volatile
> > > > > stock.
> > > > > > > Consequently, your capital is used up before
> you
> > have a
> > > > > chance to
> > > > > > > enter into your 4th or 5th stock. Instead of
> > having 5
> > > > open
> > > > > > positions,
> > > > > > > you might only have 3 because of this.
Checking
> > > > positionsize
> > > > > > > shrinking doesn't help because you'll
discover
> > you might
> > > > have
> > > > > tiny
> > > > > > > positions in your 5th stock. The fewer stocks
> you
> > have,
> > > > the
> > > > > less
> > > > > > > diversified you are, and therefore the more
> risky
> > your
> > > > > portfolio.
> > > > > > The
> > > > > > > more risk, the higher the DDs. This problem
> > cannot happen
> > > > > with the
> > > > > > > equal equity model since all positions are
> equal
> > in size,
> > > > by
> > > > > > > definition.
> > > > > > > >
> > > > > > > > One possible way around this might be to
> > increase
> > > > your
> > > > > margin
> > > > > > so
> > > > > > > that equity is expanded enough to allow full
> > funding of
> > > > all
> > > > > > > positions. But, again, this also increases
your
> > risk.
> > > > Another
> > > > > way
> > > > > > > might be dynamically setting your risk to fit
> the
> > > > volatility
> > > > > of
> > > > > > each
> > > > > > > stock individually (the lower the volatility,
> the
> > lower
> > > > the
> > > > > risk
> > > > > > and
> > > > > > > therefore, the smaller the positionsize for
> that
> > stock).
> > > > > However,
> > > > > > > this changes your model so that you no longer
> > have equal
> > > > > > > volatility/equal risk (getting closer to the
> > equal equity
> > > > > model).
> > > > > > So,
> > > > > > > the problem remains unsolved for the moment.
I
> > have not
> > > > had
> > > > > time to
> > > > > > > devote to cracking this problem yet, but some
> day
> > I hope
> > > > to
> > > > > do
> > > > > > this.
> > > > > > > If you have any ideas, I'm all ears.
> > > > > > > >
> > > > > > > > Al Venosa
> > > > > > > >
> > > > > > > >
> > > > > > > > ed nl wrote:
> > > > > > > > Thanks for your effort Al. It is very
> clear,
> > > > > > > >
> > > > > > > > In one of my earlier posts I posted
> > > > > > > >
> > > > > > > > // money management block
> > > > > > > > stopLoss = Ref(bbb*ATR(20),-1);
> > > > > > > > // trade risk
> > > > > > > > tr = IIf(Buy,(stopLoss /
> > BuyPrice),stopLoss /
> > > > > (ShortPrice +
> > > > > > > stopLoss));
> > > > > > > > // renormalisation coefficient
> > > > > > > > rc = 0.02 / tr;
> > > > > > > > // positionsize
> > > > > > > > PositionSize = rc * -100
> > > > > > > >
> > > > > > > >
> > > > > > > > it actually gives the same result as
your:
> > > > > > > > PositionSize = -2.0 * IIf
> > > > (Buy,BuyPrice,ShortPrice) /
> > > > > stopLoss
> > > > > > > > except for short positions. Exact the
> same
> > it would
> > > > be
> > > > > if I
> > > > > > > use: tr = IIf(Buy,(stopLoss /
> BuyPrice),stopLoss /
> > > > > (ShortPrice));
> > > > > > > >
> > > > > > > > Unfortunatelly I do not get better
> results
> > this
> > > > way.
> > > > > Using
> > > > > > just
> > > > > > > a simple PositionSize = -10 still gives
> somewhat
> > better
> > > > > results.
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > > rgds, Ed
> > > > > > > >
> > > > > > > >
> > > > > > > > ----- Original Message -----
> > > > > > > > From: Al Venosa
> > > > > > > > To: amibroker@xxxxxxxxxxxxxxx
> > > > > > > > Sent: Saturday, December 11, 2004
4:19
> AM
> > > > > > > > Subject: Re: [amibroker]
PositionSize /
> > Capital
> > > > > > > >
> > > > > > > >
> > > > > > > > ed nl wrote:
> > > > > > > >
> > > > > > > > Al,
> > > > > > > >
> > > > > > > > but how do you implement the risk
> > factor now?
> > > > > > > >
> > > > > > > > ed
> > > > > > > > Ed:
> > > > > > > >
> > > > > > > > Let us suppose you have established
> your
> > risk as
> > > > 1%
> > > > > (i.e.,
> > > > > > > the maximum you are willing to lose on a
> trade).
> > Let us
> > > > also
> > > > > > suppose
> > > > > > > your initial equity is $100,000. So, if the
> stock
> > you buy
> > > > (or
> > > > > > short)
> > > > > > > goes down by the amount based on your system,
> you
> > lose
> > > > only
> > > > > $1000,
> > > > > > > keeping you in the game. Now, let us say you
> > defined your
> > > > > > volatillty-
> > > > > > > based stop in terms of 2*ATR(20), which you
> > incorrectly
> > > > > assigned to
> > > > > > > the variable TrailStopAmount. I
> say 'incorrectly'
> > because
> > > > the
> > > > > > > TrailStop in AB was designed to mimic the
> > Chandelier
> > > > exit,
> > > > > which is
> > > > > > > basically a profit target type of stock (it
> hangs
> > down
> > > > like a
> > > > > > > chandelier from the highest high since the
> trade
> > was
> > > > > initiated, if
> > > > > > > long). I don't think you want the TrailStop
to
> be
> > your
> > > > money
> > > > > > > management stop. Rather, the MM stop is the
max
> > stoploss,
> > > > > defined
> > > > > > as:
> > > > > > > >
> > > > > > > > StopAmt = 2*ATR(20);
> > > > > > > > ApplyStop(0,2,StopAmt,1);
> > > > > > > >
> > > > > > > > So, if your stock declines by 2*ATR
(20)
> > from your
> > > > > entry,
> > > > > > you
> > > > > > > exit with a 1% loss. Let's take an example.
> Stock
> > A is
> > > > > selling for
> > > > > > > $40/share. It's ATR(20) is $1/shr or 2.5% of
> 40.
> > Your
> > > > stop
> > > > > amount
> > > > > > is
> > > > > > > 2*ATR(20), which is $2/shr. How much stock do
> you
> > buy?
> > > > You
> > > > > simply
> > > > > > > divide your risk, $1000, by 2*1, which is 500
> > shares.
> > > > This
> > > > > amounts
> > > > > > to
> > > > > > > an investment of $40/shr * 500 shrs or
$20,000.
> > All of
> > > > this
> > > > > can be
> > > > > > > coded in one simple line of AFL plus the 2
> lines
> > above
> > > > > defining the
> > > > > > > MM stoploss:
> > > > > > > >
> > > > > > > > PositionSize = -1 * BuyPrice/StopAmt;
> > > > > > > >
> > > > > > > > where -1 is 1% of current equity
(0.01
> *
> > 100,000
> > > > or
> > > > > $1000),
> > > > > > > BuyPrice = $40/shr, and StopAmt is 2. Keep in
> > mind that a
> > > > > negative
> > > > > > > sign means 1% of CURRENT equity, which means
> > compounded
> > > > > equity, not
> > > > > > > just a constant initial equity of $100,000.
If
> > you carry
> > > > > through
> > > > > > the
> > > > > > > above math with your renormalization
coefficient
> > > > notation,
> > > > > you wind
> > > > > > > up with the exact same answer.
> > > > > > > >
> > > > > > > > One more thing. When you place your
> order,
> > > > assuming
> > > > > you are
> > > > > > > trading with EOD data, you do not know what
the
> > buyprice
> > > > is
> > > > > until
> > > > > > you
> > > > > > > buy the stock, which is the next day. So,
what
> > most
> > > > traders
> > > > > do is
> > > > > > > base their positionsize on the closing price
of
> > the night
> > > > > before
> > > > > > the
> > > > > > > entry. Therefore, to place an order in the
> > evening to be
> > > > > filled in
> > > > > > > the morning at the open, your positionsize
> > statement
> > > > would
> > > > > actually
> > > > > > > be:
> > > > > > > >
> > > > > > > > PositionSize = -1 * C/StopAmt;
> > > > > > > >
> > > > > > > > where C is the closing price on the
> night
> > before
> > > > you
> > > > > buy.
> > > > > > So,
> > > > > > > if you use the code SetTradeDelays(1,1,1,1),
> then
> > the
> > > > above
> > > > > formula
> > > > > > > is OK. However, if you use SetTradeDelays
> > (0,0,0,0), then
> > > > you
> > > > > have
> > > > > > to
> > > > > > > ref the C back a day.
> > > > > > > >
> > > > > > > > This is probably more information
than
> > you were
> > > > > asking
> > > > > > about,
> > > > > > > but I hope it helps.
> > > > > > > >
> > > > > > > > Cheers,
> > > > > > > >
> > > > > > > > Al Venosa
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
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> > > > > > >
> > > >
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