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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@xxx> 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
> >>>
> >>>
> >>>
> >>>
> >>>
> >>> ------------------------------------
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> >>>
> >>>
> >
> >
> >
> > ------------------------------------
> >
> > 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:
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> > Yahoo! Groups Links
> >
> >
> >
> >
>
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