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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@xxx> 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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> >
> >
>
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