OK, I read a few posts by Bill and I now understnad what he claims. He claims the following: let us assume that a trading system involves some random number generator for taking positions in ES with X ticks profit/stop. He then assumes that his system has a long streak of winning trades, 100 in number, a sequence of events of low probability but nevertheless other than zero. He than claims that the Van Tharp metric as you call it, will produce an infinite value, indicating a non-random system. It is clear that logic_man does not agree but the example Bill gave was a blow to Tharp's ratio. How can you claim that a system designed to be random was not random? It appears that the Van Tharp metric cannot distinguish between non-random/low variance and those low probability random systems that basically cause the highest damage to traders. Logic_man please provide your answer.
Please look at the link provided (scroll to the bottom to see the animation). This is one of the cases where a pure random game has positive expectations. This is the right angle to attack the problem. http://www.cut-the-knot.org/ctk/Parrondo.shtml
There are a few points that I think are important enough for me to butt in: 1. I was looking for a method to determine if my trading results were due to chance alone and not skill (i.e. Was I just lucky I did 7.5% during 3 difficult summer months?). Therefore any formula that incorporates std deviation I believe is the correct answer. I thank the several gentlemen who have provided what I think are good solutions to this question. 2. Although drawdowns are not included in van tharps formula (or any formula mentioned so far), it is not what I was looking for initially. Drawdowns are very important but with my drawdowns averaging from 0% - 10% (cost basis of trade in denominator not total trading capital), I am not too concerned about this. In fact, from what I've read the hedge fund, CTA, etc. pros have average drawdowns of about 8% with some going as high as 13% (but this was data in 2005). I assume my drawdowns are still not far off from from the pros. In the future and after I have determined the probability of my success as being due to a bunch of lucky guesses (or even dare I say due to skill), then I would like to incorporate drawdowns because that is a measurement of risk which I feel I need to minimize to improve trading...I'm not sure... Is it alpha? 3. Correct me if I'm wrong, but van tharps formula assumes a normal distribution of trading results. I have shown that trading results are in fact normally distributed in a previous post of mine. If the data being analyzed are not normally distributed, then van tharps formula probably would not be accurate. Therefore running a random trading simulation on ES to prove van tharps formula true doesn't seem to make sense to me. But then again I only have a few stats classes under my belt.
Oh, boy .. The good news is that you are willing to learn and analyze! I think you should start with the book I have posted below. I placed it on my server for a short time so that people who are interested could download it. Please do not abuse my server and treat it with respect. The book will be there for 2 days only. http://www.divitiaeconsulting.com/B... Distribution...Actuarial Sciences (2003).pdf Cheers, MAESTRO
I sincerely thank you for your time and generosity. I was lookong for something like this. Yes I am very willing to learn. So much too learn, not enough time! Now that my anesthesia oral board exam is out of the way (at least for the next 10 yrs), I now have to take the Transesophageal Echocardiogram boards, pass Series 63 exam, and read through this and many other books. And after all this flaming in recent posts, I still have to do van tharps number after I get back from vacation lol! I'm just glad we all seem to have something to positive contribute on this board and still remains for me a good source of ideas, bouncing ideas, and trader communication. If I can help you out in anyway within my powers, please don't hesitate to ask (pm) me Maestro.
Is this similar to this problem? I play a coin tossing game all summer. I have made over 100 calls and my P&L is positive. I ask myself, am I lucky or good? I believe that in the above case calculating if the coin is a fair coin with some degree of certainty (let's say 95%) should answer the question. If we calculate that the coin is fair then my result was based on luck. If we find that the coin is not fair than I might be good of guessing the unfairness.
I think you should realize that there are 2 distinct processes: 1 - flipping the coin; 2 - you guessing it. Regardless of their nature these processes (fair or unfair coin for example) will result in a game that will have distribution that is very close to Gaussian providing that these processes are independent and are not correlated and have no feed back. One of the core theorems in the probabilities theory states that the sum of multiple independent random processes with various distributions will have normal distribution. MAESTRO
This is not a game but a strategy that involves alternating between two games with the payoff of one game depended on its capital. I wonder, where you saw a connectiom between this paradox and what we are talking here. Actually, it is not even a paradox. It is a game setup. It does not apply to trading.