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Hello,
Please ignore this post if it was stated somewhere that
Expectancy is only used with non-compounding systems. I think the
argument was that we are dealing with a ratio and that therefore
it doesn't matter. However, in the case of a compounding system I
have a problem with the PayOff ratio AveWin$/AveLoss$. If we
understand this ratio to mean
(average profit$ for the entire testing period) / (average
loss$ for the entire testing area)
then one would expect a log bias towards more recent trades in
the upper and lower terms before the ratio is calculated.
Especially so in high performance systems making several hundred
percent profit annually, in low performance systems it wouldn't
make that much difference.
In a compounding system the last trade profit could be in the
millions and the first only a few hundred dollars. In other words
early history would be insignificant in each term (upper or
lower). As a result in a compounding system the ratio would be
biased to more recent performance and the significance of
increasing the testing period would decrease as we lengthen the
test period. This would also explain the volatility of Expectance
we can see if we plot it as an indicator and the fact that if we
cut off the early five years the chart doesn't change much; this
is only possible if it is weighted by recent data:
(Expectance volatility, formula posted earlier)
One might assume that it would be better to break up the testing
period into smaller periods using an MA than average the separate
ratios. Or use percentage trade profits (AvgWin%/AveLoss%).
just a beginner's observation :-) If somebody can correct me
please do.
best regards,
Herman.
-----Original Message-----
From: William Wong [mailto:williamwongab@x...]
Sent: 21 October, 2002 3:58 AM
To: amibroker@xxxxxxxxxxxxxxx
Subject: Re: [amibroker] Expectancy Formulas
You guys are right, Dimitrov's formula gives expectation in $
terms.
If you divide it by avg loss, it becomes the formula I use.
The obvious benefit is that it allows you to compare across
different systems:
{Prob(Win) * Avg(Win) - Prob(Loss) * Avg(Loss)} / Avg(Loss)
= Prob(Win) * Payoff Ratio - (1 - Prob(Win))
= Prob(Win) * Payoff Ratio - 1 + Prob(Win)
= Prob(Win) * (1 + Payoff Ratio) - 1
For purpose of getting a positive expectation system, both
formulae are ok. Anyway the formula is documented in a few books
in different forms, but they all refer to the same: get a system
with positive expectation, as high as you can.
Al Venosa <avcinci@xxxx> wrote:
The definition of expectancy (E) I'm used to seeing is as
follows:
E = Probality of Win*Avg. Win - Probability of Loss * Avg.
Loss
Algebraically, this is equivalent to Dimitrov's formula
because if you divide the right side of the equation above by
Avg. Loss, you get Prob. Win * Avg. Win/Avg. Loss - Prob. of
Loss.
I've not seen Wong's formula before, but I'm open.
Al Venosa
avcinci@xxxx
>From: "Rick Parsons"
>Reply-To: amibroker@xxxxxxxxxxxxxxx
>To:
>Subject: [amibroker] Expectancy Formulas
>Date: Fri, 18 Oct 2002 10:02:34 -0400
>
>There seems to be two different formulas for Expectancy:
>
>Payoff Ratio (Ave $win / Ave $loss) = 10.66
>Percent winners = 98%.
>
>>From Wong: Expectation = (1 + pay off ratio) * %win - 1
> -0.23 = (1 + 10.66) * .98 - 1
>(somehow this doesn't seem right for these system
statistics)
>
>>From Dimitrov: (Avg.Win*PercentProfitable/Avg.Loss -
PercentLosing)
>
>(should this be: (Avg.Win*PercentProfitable/Avg.Loss *
PercentLosing) ?? )
>
>What is the correct formula?? And based on the numbers
above, what is the correct expectancy number?
>
>Thanks,
>Rick
>
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<BODY>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>Re: =3D=20
Prob(Win) * (1 + <FONT color=3D#ff0000>Payoff Ratio</FONT>) - 1=20
</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>Hello,=20
</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>Please=20
ignore this post if it was stated somewhere that Expectancy is only us=
ed=20
with non-compounding systems. </SPAN></FONT><FONT color=3D#0000ff face=
=3DArial=20
size=3D2><SPAN class=3D150194623-21102002>I think the argument was that we =
are=20
dealing with a ratio and that therefore it doesn't matter. However, in the =
case=20
of a compounding system I have a problem with the PayOff ratio=20
AveWin$/AveLoss$. If we understand this ratio to mean </SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002> (average profit$ for the=
entire=20
testing period) / (average loss$ for the entire testing area)=20
</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>then=20
one would expect a log bias towards more recent trades in the upper an=
d=20
lower terms <EM>before</EM> the ratio is calculated. Especially so in high=
=20
performance systems making several hundred percent profit annually, in low=
=20
performance systems it wouldn't make that much difference.</SPAN></FONT></D=
IV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>In a=20
compounding system the last trade profit could be in the millions and the f=
irst=20
only a few hundred dollars. In other words early history would be insignifi=
cant=20
in each term (upper or lower). As a result in a compounding=20
system the ratio would be biased to more recent performance and t=
he=20
significance of increasing the testing period would decrease as we lengthen=
the=20
test period. This would also explain the volatility of Expectance we c=
an=20
see if we plot it as an indicator and the fact that if we cut off the early=
five=20
years the chart doesn't change much; this is only possible if it is weighte=
d by=20
recent data:</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002><IMG=20
src=3D"cid:150194623@xxxx";></SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002>(Expectance volatility, formula posted=20
earlier)</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>One=20
might assume that it would be better to break up the testing period into sm=
aller=20
periods using an MA than average the separate ratios. Or use=20
percentage trade profits (AvgWin%/AveLoss%). </SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT><FONT color=3D#0000ff face=3DArial=
=20
size=3D2><SPAN class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>just a=20
beginner's observation :-) </SPAN></FONT><FONT color=3D#0000ff face=3DArial=
=20
size=3D2><SPAN class=3D150194623-21102002>If somebody can correct me please=
=20
do.</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002></SPAN></FONT> </DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN class=3D150194623-21=
102002>best=20
regards,</SPAN></FONT></DIV>
<DIV><FONT color=3D#0000ff face=3DArial size=3D2><SPAN=20
class=3D150194623-21102002>Herman.</SPAN></FONT></DIV>
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; PADDING-LEFT: 5p=
x">
<DIV align=3Dleft class=3DOutlookMessageHeader dir=3Dltr><FONT face=3DTah=
oma=20
size=3D2>-----Original Message-----<BR><B>From:</B> William Wong=20
[mailto:williamwongab@x...]<BR><B>Sent:</B> 21 October, 2002 3:58=20
AM<BR><B>To:</B> amibroker@xxxxxxxxxxxxxxx<BR><B>Subject:</B> Re: [amibro=
ker]=20
Expectancy Formulas<BR><BR></DIV></FONT>
<P>You guys are right, Dimitrov's formula gives expectation in $ terms.=20
<P>If you divide it by avg loss, it becomes the formula I use. The=
=20
obvious benefit is that it allows you to compare across different systems=
:=20
<P>{Prob(Win) * Avg(Win) - Prob(Loss) * Avg(Loss)} / Avg(Loss)=20
<P>=3D Prob(Win) * Payoff Ratio - (1 - Prob(Win))=20
<P>=3D Prob(Win) * Payoff Ratio - 1 + Prob(Win)=20
<P>=3D Prob(Win) * (1 + Payoff Ratio) - 1=20
<P>For purpose of getting a positive expectation system, both formulae ar=
e=20
ok. Anyway the formula is documented in a few books in different fo=
rms,=20
but they all refer to the same: get a system with positive expectation, a=
s=20
high as you can.=20
<P> <B><I>Al Venosa <avcinci@xxxx></I></B> wrote:=20
<BLOCKQUOTE=20
style=3D"BORDER-LEFT: #1010ff 2px solid; MARGIN-LEFT: 5px; PADDING-LEFT: =
5px">
<DIV>
<DIV>
<P>The definition of expectancy (E) I'm used to seeing is as follows:</=
P>
<P>E =3D Probality of Win*Avg. Win - Probability of Loss * Avg. Loss</P=
>
<P>Algebraically, this is equivalent to Dimitrov's formula because if y=
ou=20
divide the right side of the equation above by Avg. Loss, you get Prob.=
Win=20
* Avg. Win/Avg. Loss - Prob. of Loss.<BR><BR>I've not seen Wong's formu=
la=20
before, but I'm open.</P></DIV>
<DIV>Al Venosa<A=20
href=3D"mailto:Venosaavcinci@xxxx";><BR>avcinci@xxxx</A></=
DIV>
<DIV></DIV>
<DIV></DIV>
<DIV></DIV>
<DIV></DIV>>From: "Rick Parsons" <RICKPARSONS@xxxx>
<DIV></DIV>>Reply-To: amibroker@xxxxxxxxxxxxxxx=20
<DIV></DIV>>To: <AMIBROKER@xxxx>
<DIV></DIV>>Subject: [amibroker] Expectancy Formulas=20
<DIV></DIV>>Date: Fri, 18 Oct 2002 10:02:34 -0400=20
<DIV></DIV>>=20
<DIV></DIV>>There seems to be two different formulas for Expectancy:=
=20
<DIV></DIV>>=20
<DIV></DIV>>Payoff Ratio (Ave $win / Ave $loss) =3D 10.66=20
<DIV></DIV>>Percent winners =3D 98%.=20
<DIV></DIV>>=20
<DIV></DIV>>From Wong: Expectation =3D (1 + pay off ratio) * %win - =
1=20
<DIV></DIV>> -0.23 =3D (1 + 10.66) * .98 - 1=20
<DIV></DIV>>(somehow this doesn't seem right for these system statis=
tics)=20
<DIV></DIV>>=20
<DIV></DIV>>From Dimitrov: (Avg.Win*PercentProfitable/Avg.Loss -=20
PercentLosing)=20
<DIV></DIV>>=20
<DIV></DIV>>(should this be: (Avg.Win*PercentProfitable/Avg.Loss *=20
PercentLosing) ?? )=20
<DIV></DIV>>=20
<DIV></DIV>>What is the correct formula?? And based on the numbers a=
bove,=20
what is the correct expectancy number?=20
<DIV></DIV>>=20
<DIV></DIV>>Thanks,=20
<DIV></DIV>>Rick=20
<DIV></DIV>>=20
<DIV></DIV></DIV><BR clear=3Dall>
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