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@yahoogroups.com, "brian_z111" <[EMAIL PROTECTED]> 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@yahoogroups.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@yahoogroups.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 > > >>> > > >>> > > >>> > > >>> > > >>> > > >>> ------------------------------------ > > >>> > > >>> 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 > > > > > > > > > > > > > > >