I'm having a bit of trouble because Bayes theorem is based on conditional probability, but we haven't established or assumed any reason to think the trades are or are not independent. In trying to see if I've just missed something, I've been playing around with the formula, and a table, but they seem to come up with the same 35%-65% probabilities (actually, I've used 1/3 and 2/3, hopefully this is not cheating). For another route, assuming independence, I took the long way and drew out a tree for sets of 3 trades. The goal is 2 wins out of 3, improve from 1/3 win to 2/3 or 3/3 win. In this case, if the first trade wins, there is a probability of 5/9 the set will have 2 or more wins. If the first one loses, there is only 1/9 probability of 2 wins. So, it would seem, if the first one wins, continue with 3 trades; if the first one loses, skip the next 2. But of course, in actual trading, things probably would not work out quite like this, and this approach probably misses the point. Next will look up WR Ashby.
If anyone else is following along, I've found these 2 links: http://en.wikipedia.org/wiki/Variety_(cybernetics) http://pespmc1.vub.ac.be/Books/AshbyReqVar.pdf second one is a 13 page pdf on applying Requisite Variety.
My take on this is that many of the posters in this thread are groping different parts of the elephant. Most of what I have read is right, but right under a set of assumptions that are not quite specified and may not apply. The gambler's fallacy is relevant when you have independent observations and a stationary edge - the coin doesn't change, and all the cards are put back in the deck between hands. Bayes is relevant when you think you have a stationary edge but aren't confident your past data is sufficient for a precise measurement, then you consider the latest set of trades to be new information that helps you measure it more precisely. A similar idea, tests for structural breaks, are where you think the edge might have changed and use the latest data to test this. The take every trade when you have an edge philosophy is for when you think the edge is unchanged and each trade is independent. Long story short you need to have some beliefs about your system to know which approaches to consider. I think the most interesting case to consider is whether there is memory because your trades are not really independent. There are lots of times when trades from a system do empirically have autocorrelation (positive or negative) and sometimes there is a good explanation. In lots of long term stock systems, this happens because investors chase hot funds and these funds tend to put more into the same stocks or the same style, or because of delayed reactions. Examples of this stuff are publicly documented and fairly well known. In shorter term systems I don't think things are as clear but the volatility cycles mentioned in a prior post or larger traders following a related system and breaking up their trades for liquidity reasons are pretty plausible.
+1 Bayes theorem and its Monty Hall application mentioned by a few uninformed here assume that new information that arrives in a deterministic game after the first choice is made, or trade, alters a posteriori the prior probability. For example, in the Monty Hall problem, the opening of a door immediatelly alters the prior probability due to new information it provides given that the outcome space is fixed. This is not true in trading, at least it cannot be assumed true. Any reference to a previous outcome in order to estimate the probability of future outcomes is gambler's fallacy.
Not necessarily. Consider the following imaginary case. A system measures the time (speed) with which a buy or a sell orders are filled. Let's assume a system places the buy order at the bid and the sell order at the ask. Then the timing to fill the order is measured and the next order to buy or sell is placed depending on the time difference of the previous fills but not necessarily whether or not the previous trade was successful or not. This creates a useful feed back loop (memory) that will add CONDITIONAL probability to the next trade's outcome thus creating a case for a Bayes's interpretation of the decision making rules. There are many useful feedback parameters that could be considered including the success rate of filled orders etc. to create a very useful feedback and add the outcome of the previous trade to the decision with regards to a new trade. Cheers, MAESTRO
Not entirely true. there are many ways to add "new information" to a decision making process to increase the Requisite Variety of a system. Cheers, MAESTRO
Let's see, maybe this is on the right track: reading that pdf on Requisite Variety, we'd want to reduce the number of possible outcomes. The formula, in simplified terms, is: outcomes >= possible disturbances / possible reactions so minimize the number of possible outcomes, hopefully to a set where more are "good" than "bad", we need several "reaction" techniques to cope with the possible disturbances we might see. Instead of "a system", with reactions of buy/sell/wait/skip/set stop/set limit/adjust stop/adjust limit to its signals, I'll go for a 2-in-1 system -- it can choose whether to use a trend-following system or range-bound system (let's call them "approach"). Then possible reactions are doubled, thus halving the minimum number of outcomes. So start the system with trend following approach, keep track of consecutive losses, and implement some logic as: if (consecutive losses < expected maximum) { continue with current approach (trend or range); } else { switch to opposite approach; } And, trade frequently enough to increase the probability the current market conditions still apply as indicated by the consecutive losses. For the expected maximum, backtesting should give some figures to plug into this formula (forgot where I got this): expected max losing streak = ln(1/number of trades) / ln(% of losers) Hmmm -- maybe the Bayes application is: what is the probability the market is in trend mode, given my trend approach has generated X consecutive losers/winners? and vice versa for range-bound. The risk -- by the time you get X consecutive losers to signal switching to opposite approach, market conditions change.
Very Good! You are digging in the right direction! There is a reward for you in the end, I promise! Cheers, MAESTRO
A Markov process such as the one you described is memoryless. http://en.wikipedia.org/wiki/Markov_process