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Hi Mike, and all --
There is a lot to like in Tharp's book, Definitive Guide to Position Sizing.
But it appears to me that he developed the concept of system quality number without using it as an objective function used in testing and validating trading systems. He describes several idealized trading systems that have a range of SQNs -- from negative to about 7. One on page 38 is described as:
Mean expectancy: 3.42
Standard deviation: 4.89
Win percentage: 90
Win/Loss Ratio: 2.35
Number Trades: 100
SQN: 6.99
Plugging those numbers into the formula for the t-test, which is (mean/stdev) * sqrt(N)
we get (3.42/4.89)*10 which equals 6.99 -- the same as the SQN.
While he does not call SQN t-test, for each of the examples I worked out, the two are the same.
So, one of my points is that SQN is equivalent to t-test where the hypothesis that is being tested is "is expectancy greater than 0?"
I like the idea that the statistical test is incorporated into the metric. I have been using that concept for some time, and I think it works well. I wish he had not called it SQN, and I wish he had not put a Service Mark next to it every time it appears in his book. But that concept is good.
I seriously doubt that he, or anyone else, has a series of truly out-of-sample closed trades where the t-test of expectancy is 7. It would take only a few weeks to turn $10,000 into enough to buy Manhattan with a system like that. Which goes to my point that I doubt that any of the idealized trading system he describes with large SQNs reflect real trading systems. Idealized, yes. In-sample, perhaps, but I doubt it. Out-of-sample, almost impossible and I very seriously doubt it.
As a basis for my comment, look at a table of t-test percentile values. I use a rule of thumb that the t-test should be above about 2.0, just for its ease of computation. With n=10 trades (9 degrees of freedom), 95% confidence comes with t-statistic of 1.83. With n=120, 99.5% confidence comes with a t-statistic of 2.62.
For sample sizes greater than about 60, the t-distribution and the normal distribution are essentially identical. Something 3 standard deviations away from the mean happens much much less than 1% of the time. Something 7 standard deviations away is so rare as to be essentially impossible on our time scale. It is nice to see the fantasy equity curve, but it will never happen.
If expectancy works as an objective function for a particular trader
and system, then by all means, use it. As the characteristics of the
trade returns change, the advantages and disadvantages of using
expectancy change.
All of that said, I think Tharp's book is good. It brings out many excellent points about the importance of positions sizing. Read it in conjunction with Ralph Vince's "The Leverage Space Trading Model." My own research and experience is in agreement with both of those.
There is an implication -- one that many people will not find comfortable and will argue strongly against. It is this: The only way to generate large increases in equity safely is to have a trading system that trades frequently, holds a short period of time, and carefully limits losing trades.
Yes, there are examples of people who have made a lot of money trading infrequently and holding long periods. My contention is that
1. we are hearing from those who were successful. Not many people who tried to do this succeeded. Most who tried and failed have not remained in the trading community and we are not hearing their stories of failure.
2. The period from 1982 to 2000, or even 2007, in US equities, is probably a once in a millenium event. I doubt that it will be repeated -- I am certain it will not be repeated in my lifetime. Long-only, buy-and-hold systems did very well during that period. At the risk of being flip, it was easy to confuse brains with a bull market.
The price earning ratio for the S&P 500 companies is now about 120 (per S&P's numbers on their website). The price earnings ratio at equity market bottoms is single digits, and in normal times is mid-teens. Excursions to an extreme tend to correct, and the correction seldom stops at the mean -- it makes an excursion to the other extreme. Can we expect fundamentals to improve enough so that earnings increase by a factor of 10? Or will prices decrease by a factor of 10? Or some of each? I expect that one or more of those events will be taking place in the next twelve months. In any event, 10 percent per year annual increases in stock prices seem extremely unlikely. We need trading systems that do not depend on a rising market.
I suggest that we read Tharp and Vince, use good modeling and simulation technique, test the significance of our out-of-sample results, and look for systems that have truly out-of-sample t-test scores of 2.0 or more -- they are hard enough to find -- forget 6.99. Then work on position sizing methods that use anti-martingale techniques (increase position size when winning, reduce it when losing) to determine what position size will produce the goal the trader wants while keeping the probability of bankruptcy at a low enough level so he or she is confortable trading.
There are two very distinct components to this:
1. Develop good trading systems that have positive expectancy, limiting the losing trades to small amounts, and trade frequently.
2. Apply aggressive position sizing when winning.
Thanks for listening,
Howard
On Thu, Oct 8, 2009 at 11:15 PM, Mike <sfclimbers@xxxxxxxxx> wrote:
Hi Howard,
I'm a bit confused by your remarks.
1. You have said that Definitive Guide To Positoin Sizing is an excellent book.
2. You have said that SQN is a t-test (of expectancy?).
3. You have said that a t-test of expectancy is functionally equivalent to CAR.
4. You have said that CAR is a poor fitness function.
Given that the book repeatedly promotes usage of SQN as a comparator (i.e. a fitness function) with which to measure two systems, how do you reconcile point 1 with points 2-4?
Just to pin it down without any indirection, are you saying that you consider SQN as poor a fitness function as CAR? Or, have I misunderstood something you've said?
Thanks,
> Hi Mike --
>
> CAR is compound annual rate of return. Expectancy is the percentage (or
> dollar amount, but not for this discussion) gain on the average trade. The
> final value of the trading account, Terminal Relative Wealth in some
> descriptions, is: (1 + expectancy) raised to the power of the number of
> trades. When there are a few large trades included, this relationship is
> slightly different, but not enough to worry this discussion. CAR is: (1 +
> annual gain) raised to the power of the number of years. These are both
> based on geometric means. Aren't they the same, or so close that they act
> the same when used as an objective function?
>
> Van Tharp defines System Quality Number on page 28 of "Definitive Guide to
> Position Sizing." SQN = (expectancy / standard deviation) times squareroot
> of number of trades. SQN decreases when a median trade is replaced by
> either a large win or a large loss. It is possible to redefine the metric
> so that large wins are not penalized, such as by using the semi-deviation
> instead of the standard deviation as the denominator. But without making
> that change, outliers, both good and bad, do affect SQN by reducing it.
>
> What happens with open (or potentially open) trades at the boundaries of
> walk forward periods is difficult to handle in both theory and practice.
> Tomasz' implementation is to close all open trades at the end of each WF
> period; and go into each WF period flat, not taking a new position until
> there is a new signal. This creates a potentially serious distortion of
> results when trades are typically held a long time (a large proportion of a
> WF period) or when there are a few large trades that comprise the majority
> of a system's profit or loss.
>
> I think this leads to a conclusion that we both agree on -- high quality
> trading systems that can benefit from position sizing are based on high
> frequency trading with very careful control over losses, and even control
> over gains.
>
> Thanks for listening,
> Howard
>
>
> On Wed, Oct 7, 2009 at 2:36 PM, Mike <sfclimbers@xxx> wrote:
>
> >
> >
> > Howard,
> >
> > Assuming that SQN is the t-test for expectancy, then optimizing on the
> > t-test of expectancy (i.e. SQN) is not the same as optimizing on CAR.
> >
> > The primary reason that CAR is a poor target for optimization is that
> > outliers can significantly improve the calculation. The exact opposite is
> > true for SQN.
> >
> > SQN rewards consistency and punishes outliers. Consistent winners with a
> > few large wins will improve CAR but hurt SQN, resulting in different
> > parameter combinations being selected during an optimization.
> >
> > As for writing a custom method, AmiBroker's stats are calculated based on
> > the assumption that all open trades are closed out at the backtest boundary
> > date. Many open trades, or even just a few large open trades, can skew these
> > values.
> >
> > For high frequency strategies or strategies using heavy position sizing,
> > creating a custom function is the only way to get reliable measurements.
> >
> > Mike
> >
> >
> > --- In amibroker@xxxxxxxxxxxxxxx <amibroker% 40yahoogroups.com>, Howard B
> > <howardbandy@> wrote:
> > >
> > > Greetings all --
> > >
> > > There has been a lot of activity on this thread. I'll not respond to each
> > > point individually, but will make a couple of general comments.
> > >
> > > I know David Aronson, speak with him regularly, and collaborate with him
> > on
> > > projects. I have a copy of his book, "Evidence-Based Technical Analysis."
> > > His book is excellent and I highly recommend it. I think David and I are
> > in
> > > pretty close agreement on most of the modeling, simulation, testing, and
> > > validation issues.
> > >
> > > I have spoken with Robert Pardo and have exchanged several emails and
> > forum
> > > postings with him. I think his earlier book was very good, particularly
> > at
> > > the time it was published. And his more recent book is not quite up to
> > > those standards. There are several important areas he did not cover and
> > > several areas where I see things considerably differently than Robert.
> > >
> > > I have spoken with and exchanged emails with Van Tharp, and I have copies
> > of
> > > his books "Trade Your Way to Financial Freedom" and "Definitive Guide to
> > > Position Sizing." Both are excellent, and I recommend them both highly.
> > Be
> > > sure to get the second edition of Trade Your Way to Financial Freedom --
> > it
> > > has some important corrections and clarifications.
> > >
> > > Permit me a short rant on my soapbox. I really dislike it when people
> > claim
> > > ownership of common terms. Tom DeMark, Robert Pardo, Van Tharp, and
> > others
> > > put Service Mark symbols on terms that they think are unique to them, but
> > > are not. I appreciate Tharp's enthusiasm over what he calls System
> > Quality
> > > Number, but I wish he would not put the Service Mark symbol next to every
> > > occurrence of it. And trying to Service Mark the term Position Sizing is
> > > like a dietician service marking "calorie counting." Robert Pardo claims
> > > "Walk Forward." I used exactly that term describing exactly that process
> > in
> > > research papers I delivered at conferences in the late 1960s. The mark
> > has
> > > been registered, not by Robert, but by a company I used to work for and
> > with
> > > which Robert was not associated, over my strong objection. End of rant.
> > >
> > > System quality number is equivalent to t-test. Systems with SQNs above 2
> > > work well for exactly the same reasons that systems with t-test scores
> > above
> > > 2 work well. In fact, it is possible to create a custom objective
> > function
> > > that Is the t-test and use it for optimization. Attendees at my workshops
> > > in Melbourne later this month will see that demonstrated. Optimizing for
> > > the t-test of expectancy is equivalent to optimizing for CAR, so don't
> > > bother creating the custom function unless you have a better candidate
> > for
> > > your objective function than CAR.
> > >
> > > Back to the topic at hand -----
> > >
> > > There is No rule of thumb to determine how long the in-sample period
> > should
> > > be. The Only way to determine that is by testing the model and the data
> > > together. And be prepared for that length to change over time. Some
> > > writers suggest a relationship between the number of free parameters and
> > the
> > > number of data points, or some proportional division of the available
> > data.
> > > Those techniques do work on industrial time-series data which is usually
> > > stationary, but they do not work on financial time-series data which is
> > > non-stationary and changes as trading systems become better at extracting
> > > inefficiencies from it.
> > >
> > > No matter how good the in-sample results look, no matter how high the
> > t-test
> > > score is, no matter how many closed trades are represented -- in-sample
> > > results have no value in estimating the future performance of the system.
> > > None. The only information you have that gives any indication of future
> > > performance are the out-of-sample results from testing on data that was
> > > never used at all -- not even once -- during system development.
> > >
> > > Tomorrow is out-of-sample. The only way to prepare for real-money trading
> > > tomorrow is to be rigorous during the system testing and validation
> > > process. Anything less will overestimate the probability of success.
> > >
> > > Thanks for listening,
> > > Howard
> > >
> >
> >
> >
>
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