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Thanks Howard. I entered this thread because someone posted:
> The K-ratio isn't worth the space it takes up: RRR is simpler.
I was wondering about the K-ratio bashing. This lead to me realising that I have difficulty in
really "feeling" what these metrics mean and how they differ. Would you normally start from visual
inspection of equity curves and then go to the stats?
Howard B 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@xxxxxxxxx
> <mailto:brian_z111@xxxxxxxxx>> 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
> <mailto:amibroker%40yahoogroups.com>, "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
> <mailto: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
> <mailto: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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