|
PureBytes Links
Trading Reference Links
|
The mathematical expression(s) OR antecedents of PowerFactor are:
where
Wins == 55
Losses == 45
ave%Won == 3
ave%Lost == 2
PowerFactor (notational format) is 3^55/2^45
InitialEquity == 1
then
finalequity == 1 * 1.03^55 * 0.98 *45 == 2.047485;//PowerFactor
equation
POF (geometric mean) == (2.04785/1)^(1/100) == 1.00719 etc;
There is a temporary post at the UKB with the POF equation
demonstrated in a spreadsheet.
Note: it is not recommended to use GM as an ObjectiveFunction without
a full understanding of the caveats (stated and implied) by
RalphVince's work on optimalF.
Also my take on it, including BinomialSimulation, won't be debugged,
at the very least, until after I post on the subject at the UKB (if
at all).
brian_z
http://www.amibroker.org/userkb/
--- In amibroker@xxxxxxxxxxxxxxx, "brian_z111" <brian_z111@xxx> wrote:
>
> PowerFactor is part of, what is for me, a rather ambitious project.
>
> I can't do it justice in an off the cuff post (that would be prone
to
> confusing both of us) - so you don't go away empty handed (everyone
> gets a prize).
>
> RalphVince's work is based on estimating the optimal fraction of
our
> captial to invest in any trade and the measure of success is the
> maximum geometric mean.
>
> GM = (final equity/initial equity)^ (1/number trades)
>
> It can be standardised to annual return by plugging in the ave time
> per trade + turn around time.
>
> He gives a method whereby we can estimate the GM from the trade
> returns (average $value or ave%) and the SD of the trade series.
>
> One of the criticisms of OptimalF is that it relies on the trade
> series largest loss, as the critical factor, but the largest loss
> might not be the largest that we can experience in the future, so
in
> this regard it is an agressive money management technique.
>
>
> That is where I am making an effort to clarify his work for my own
> use.
>
> I am using BinomialSimulation as a type of 'visual maths' to
> crosscheck my 'equations' against his and other accepted maths
tools.
>
> I am attempting to get a more accurate estimate of the 'worst case'
> scenario, in a way that has meaning to me.
>
>
> This is where ProfitFactor and PowerFactor come in (PowerFactor is
> really just the geoemtric mean in notation form - the notation
> reminds me of the important part the W/L ratio and the PayOff ratio
> play in the final trading outcomes (equity curve profiles derived
> from them).
>
> Outside of that it doesn't have any importance.
>
> As far as the valule of the geometric mean goes it would be far
> better to reference RV's work.
>
> From RV "The Mathematics of Money Management" - "The real growth
> function in trading (or any event where the PeriodReturn is not
> constant) is the multiplicative product of the PeriodReturns.
>
> So PowerFactor is just the notational form of that, say:
>
> Wins = 55
> Losses = 45
> ave%Won = 3
> ave%Lost = 2
> PowerFactor = 3^55/2^45
>
> As I said, it is just a notation to remind me of the importance of
> the PayOff ratio (3/2) and the fact that I can control that, at the
> design stage, via my stops - compared to W/L where the variance is
a
> function of sample error.
>
> Where I am heading in future posts is:
>
> a) to show the relationship between fixed amount (contracts or
number
> of shares) trading and reinvestment trading (compounded equity
> curves) and how that the difference is summarized by
> ProfitFactor/PowerFactor OR geometric mean
>
> b) to find a simpler way (equation) to calculate the worst case
risk
> (drawdown?), relative to time, using only the basic inputs from the
> trade series i.e. win, loss and amount won/lost as % (no MonteCarlo
> etc required).
>
> The pathway there is to include variance in the PF type equations.
>
> Hope I haven't made that too complicated - I am building to a more
> measured and understandable presentation at the UKB (look for
> upcoming posts on expectancy, blackswans, random generators etc).
>
> Where did I settle in Australia?
>
> I am in regional NorthQueensland 'amongst the plum trees with lots
of
> gum leaves' etc.
> NFA actually appeals to me more but my partner has other ideas.
>
> brian_z
>
>
>
>
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, Grant Noble <gruntus@> wrote:
> >
> > > Hope that gives you something stimulating to think about.
> >
> > Dude, I'm totally overstimulated! Do you have a formula for
> PowerFactor?
> > BTW where did you end up settling in Australia?
> > GRANT
> >
> > brian_z111 wrote:
> > > Grant,
> > >
> > > Apologies for late comments (I've been to the beach but
mentally
> > > flagged your question before I left).
> > >
> > > You might be interested in my generic opinion.
> > >
> > > My trumpeting on expectancy, ProfitFactor and PowerFactor are
> based
> > > on my efforts to identify and understand the root causes of
> equity
> > > curve growth and variance (underneath it all is there anything
> else
> > > that really concerns us).
> > >
> > > It is rather like the difference between the average driver and
a
> > > professional driver. Average drivers, on their annual holidays,
> are
> > > typically concerned about MPH, hours to arrival and fuel costs
> > > whereas a professional driver (F1 racer) is a 'power user;
> concerned
> > > about performance drivers e.g. engine power (HP or watts), oil
> > > pressure, fuel efficiency, road conditions etc, oil temperature.
> > >
> > > My personal approach is to focus my enquiry on the 'power'
> factors of
> > > trading performance.
> > >
> > > Hence the topic of my discussion with Gerry, who made some
> > > interesting observations on PowerFactor and the key metrics
that
> are
> > > associated with it.
> > >
> > > In Excel simulations of no win (breakeven) fair coin tosses,
that
> I
> > > have performed in the past, I was astounded at the range of
> possible
> > > equity outcomes (no two equity curves are the same and they
form
> a
> > > cone that fans out on either side of the breakeven line and
that
> > > continues to expand with time OR N tosses of the coin).
> > >
> > > This is what Ralph Vince was referring to when he said "that is
> just
> > > how perverse the equity curve of a fair coin is".
> > >
> > > He also gives the 1st and 2nd arcsine laws that predict the
> amount of
> > > time we can expect the equity curve to stay on one side of the
> b/e
> > > line and the max/min of the equity curve.
> > >
> > > Ralp Vince "The Mathematics of Money Management".
> > >
> > > The equity curve outcomes that I achieved in my 'push the excel
> buton
> > > and see' trials were very similar to the simulated equity
curves
> in
> > > Howards QTS book - page 309.
> > >
> > > My argument is:
> > >
> > > - we can only trade successfully with an edge
> > > - the edge is based on the 'predictable behaviour' of a market
> event
> > > e.g. chart pattern'
> > > - a predicatable pattern will exhibit the properties of a coin
> toss
> > > (albeit a biased coin)
> > > - the equity outcomes of a biased coin toss are varied
> > >
> > > therefore any evaluation method that doesn't reference variance
> is
> > > unlikely to be useful to me.
> > >
> > > That is why I have an interest in Binomial Simulation and
metrics
> > > like ProfitFactor and PowerFactor (they are close to the inputs
> of a
> > > Binomial Simulator - which is alternative approach to MCS and
it
> > > doesn't rely on a rescrambling of the sample set.
> > >
> > > So, based on my chosen approach I see no point in considering
the
> > > metrics of one equity curve - if you go OOS OR toss the coin
> again
> > > you will get an entirely different equity outcome.
> > >
> > > That is why I am more interested in what causes equity lines to
> grow
> > > (increases the geometric mean) and controls equity curve
drawdown
> (so
> > > I can put the setting where I want it).
> > >
> > > K-ration is a measure of equity curve smoothness whereas
> > > RiskRewardRatio is a 'root cause' metric.
> > >
> > > There are a lot of different opinions about what constitutes
> reward
> > > and risk but if you are talking about RR as defined in
> Markowitz's
> > > Modern Portfolio Theory then it is something I don't have a
great
> > > deal of understanding on but I definitely regard drawdown
as 'the
> > > risk', probability as teh drive and variance as a quantity not
to
> be
> > > ignored.
> > >
> > > BTW my efforts with BS are complementary to Ralph Vinces work
> > > (possibly it will make a little corner of his work more
> accessable to
> > > the maths layperson). IMO RV's work is brilliant. He is the
> analyst
> > > who 'blew me out of the water'.
> > >
> > > Hope that gives you something stimulating to think about.
> > >
> > > brian_z
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx, Grant Noble <gruntus@> wrote:
> > >>> The K-ratio isn't worth the space it takes up: RRR is simpler.
> > >> care to elaborate?
> > >>
> > >> gerryjoz wrote:
> > >>> In an earlier post, expectancy was associated with profit
> factor.
> > >>> It is more closely related to payoff ratio.
> > >>> In Van Tharp's book, 2nd edition, "Trade your way...", page
204
> et
> > >>> seq, he calculates
> > >>> Expectancy = average profit/ # trades
> > >>> divided by average loss.
> > >>> Payoff ratio is average profit/average loss,
> > >>> so
> > >>> Expectancy = payoff ratio/# trades.
> > >>> --which can give very low numbers, and makes the concept
rather
> > >>> dubious if you are using it as an absolute value for
comparing
> > > systems
> > >>> with different numbers of trades. It might be better to use
> > > trades per
> > >>> annum.
> > >>> To be fair Van Tharp only gives that way of calculating
> > > expectancy as
> > >>> a default if the risk of a trade isn't able to be calculated
> > > taking
> > >>> into account a pre-determined proportion of equity. For that,
> you
> > > need
> > >>> to read the whole chapter.
> > >>> Personally i find CAR/MDD, RRR more relevant, along with the
raw
> > >>> Payoff ratio.
> > >>>
> > >>> The K-ratio isn't worth the space it takes up: RRR is simpler.
> > >>>
> > >>> regards
> > >>> Gerry
> > >>>
> > >>>
> > >>>
> > >>>
> > >>>
> > >>> ------------------------------------
> > >>>
> > >>> Please note that this group is for discussion between users
> only.
> > >>>
> > >>> To get support from AmiBroker please send an e-mail directly
to
> > >>> SUPPORT {at} amibroker.com
> > >>>
> > >>> For NEW RELEASE ANNOUNCEMENTS and other news always check
> DEVLOG:
> > >>> http://www.amibroker.com/devlog/
> > >>>
> > >>> For other support material please check also:
> > >>> http://www.amibroker.com/support.html
> > >>> Yahoo! Groups Links
> > >>>
> > >>>
> > >>>
> > >>>
> > >
> > >
> > >
> > > ------------------------------------
> > >
> > > Please note that this group is for discussion between users
only.
> > >
> > > To get support from AmiBroker please send an e-mail directly to
> > > SUPPORT {at} amibroker.com
> > >
> > > For NEW RELEASE ANNOUNCEMENTS and other news always check
DEVLOG:
> > > http://www.amibroker.com/devlog/
> > >
> > > For other support material please check also:
> > > http://www.amibroker.com/support.html
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>
------------------------------------
Please note that this group is for discussion between users only.
To get support from AmiBroker please send an e-mail directly to
SUPPORT {at} amibroker.com
For NEW RELEASE ANNOUNCEMENTS and other news always check DEVLOG:
http://www.amibroker.com/devlog/
For other support material please check also:
http://www.amibroker.com/support.html
Yahoo! Groups Links
<*> To visit your group on the web, go to:
http://groups.yahoo.com/group/amibroker/
<*> Your email settings:
Individual Email | Traditional
<*> To change settings online go to:
http://groups.yahoo.com/group/amibroker/join
(Yahoo! ID required)
<*> To change settings via email:
mailto:amibroker-digest@xxxxxxxxxxxxxxx
mailto:amibroker-fullfeatured@xxxxxxxxxxxxxxx
<*> To unsubscribe from this group, send an email to:
amibroker-unsubscribe@xxxxxxxxxxxxxxx
<*> Your use of Yahoo! Groups is subject to:
http://docs.yahoo.com/info/terms/
|