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Good morning Howard,
Thanks for your comments.
Indeed, I am not proposing that the various growth metrics are
suitable to use as Objective Functions, at this stage (I wouldn't do
that without some attendant controls on variance).
What I am doing is:
a) pointing out the relationship between expectancy($), as
popularised by Van Tharp, and ProfitFactor.
b) showing why, IMO, Profit Factor has limited uses (once again it
is quite a popular metric).
c) making some unequivocal objections to ProfitFactor and expectancy
(as $) (I have read commentators who say they don't, or won't, use
ProfitFactor but who then fail to give any valid reasons, which I
find very annoying - so I am doing my bit to set the record straight).
d) objecting to the use of expectancy(as %) since expectancy(as
$)/ProfitFactor are derived from summed P&L's whereas an equity curve
is the product of the % trades (expectancy as % also breaks the
mathematical relationships inherent in ProfitFactor) - in fact it
doesn't work at all (it is a mathematical dead end) and ProfitFactor
breaks down entirely if ave%W/ave%L is used.
(I take that to mean that expectancy($)/ProfitFactor are metrics that
apply to fixed contract trading whereas PowerFactor is the expectancy
of reinvesting (compounding)
e) doing my bit to get rid of ProfitFactor - I used the term
PowerFactor to delineate it from ProfitFactor which really needs to
be put to bed as far as a metric for compounded equity curves goes.
f) flagging the difficult issues that traders face when dealing with
back adjusted data (using relative measures overcomes some problems
but also invalidates some well known trading equations).
g) repeating my claim that focusing on equity curves is rather like
putting the cart before the horse.
What I am definitely saying is that PowerFactor (the geometric mean)
is the real expectancy (as %) that traders should use if they want to
establish that they have a valid system - it is a lot easier to
subtract commissions too.
I have some reservations about the equity curve metrics and in the
longer term I am looking to make some statements about effective
metrics that we can apply at the trade end i.e. using W/L and the
PayOff ratio as the key metrics, along with variance, to predict
equity curve smoothness.
One example of the problem with some of the equity curve metrics:
- if by RRR you mean Risk Reward Ratio == slope/standard error then
as standard error tends towards zero RRR tends towards infinity,
irrespective of what the slope is doing so RRR is a metric that
rewards smoothness in preference to growth (any metric that has
variance on the bottom line will do that won't it?).
Another potential problem, as I see it, is that the equity curve
comes after money management, so MM could be contributing to eq
smoothness, or lack of it (wouldn't it be better to measure
the 'systems' smoothness before position sizing is applied to the
trade series?).
I am not measuring the 'rightness' or 'wrongness' of what you are
saying - I am just letting you know that I am happy to share my
alternative thoughts on the subject with you and the forum.
brian_z
--- In amibroker@xxxxxxxxxxxxxxx, "Howard B" <howardbandy@xxx> wrote:
>
> Greetings all --
>
> It is possible to use a metric such as Power Factor, or the closely
related
> Terminal Relative Wealth, or Net Profit, as the objective function
when
> optimizing and choosing among alternatives.
>
> But beware.
>
> Optimizing to maximize any of these will very often reward a system
that has
> not only a high return, but also a high drawdown. I recommend
using one of
> the metrics that automatically rewards both high equity growth and
equity
> smoothness. The equity smoothness part minimizes drawdowns.
>
> Try RRR, KRatio, Ulcer Performance Index, CAR/MDD, or RAR/MDD.
>
> Thanks,
> Howard
>
>
>
>
> On Sat, Apr 5, 2008 at 6:49 PM, brian_z111 <brian_z111@xxx> wrote:
>
> > 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 <amibroker%40yahoogroups.com>,
> > "brian_z111" <brian_z111@> 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 <amibroker%40yahoogroups.com>,
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 <amibroker%
40yahoogroups.com>,
> > 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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> > > only.
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