If you read New Market Wizards, there's an interview with William Eckhardt, who was a mathematician before becoming a trader, then there's a passage in there that's really interesting. He said a colleague entered a trading contest which asked the contest to guess a price of a certain commodity at some X months in the future. So, as a joke, his friend used a "random walk" model to arrive at the price. Guess what? He was placed 4th out of like HUNDREDS of contestants. So, Eckhardt said that most people trade worst than random! Perhaps that a thought to think about and why 95% of traders lose $.... interesting... hmmm... -99
http://www.casino-help.com/systems/martingale http://www.roulette-systems.com/martingale-roulette.html I didn't know roulette was the vehicle of choice for the Martingale system until reading these links. They don't sound too high on it.
i think anti-martingale is where you bet 2*N if you win and N if you lose. so on a losing streak your bet is constant, and on a winning streak your bet is *increasing*.
There are literally an infinite number of ways to trade the market. In my own trading, I like to keep it simple. All I use is candle stick charts, volume, bollinger bands, some momentum type indicators, MACD histogram being my favorite and an assortment of sentiment type indicators (VIX, TICK, put/call ratio, etc). That's basically it. No fibonacci numbers for me. Trend lines, moving averages, etc aren't for me. In the first Market Wizards book, Larry Hite (the trader obsessed with controlling risk) described how his cousin had found "the holy grail" (for lack of a better word). He turned $5k playing options into $100 k. Not bad, 20x your money. His "secret" was to buy an option and if it went up, he would stay in, but if it went down, he wouldn't get out until at least he broke even. Long story short, the inevitable happens and he loses it all plus another $10k. To me, that was a really provacative strategy. Ridiculously simple and it worked quite well (up 20 fold). His goal wasn't to use the strategy forever, just to "make a million". I've certainly had those thoughts cross my mind at one time or another, "it doesn't have to work forever, just until I make XYZ dollars". The irony is that if you've got the discipline to quite while you're ahead (up $100 k), that's exactly the kind of disciple you need to be a great trader who has a sound methodology. The bottom line is that you've got to find a methodology that fits your personality. There is no way around it. And make sure your methodology is for the long term.
Martingale strategy is a money management or bet-sizing strategy of doubling the bet size after a loss (see also http://www.allcraps.com/sitemoneymanage.htm ). It comes from the gambling world (scary how many ideas about trading come from the gambling world, eh?). A great many trading books advise against doubling after losses because it increases risk. For a fair-game, like the coin-toss, a Martingale strategy WILL lead to gamblers ruin faster than other, better money management strategies (ones that tend to decrease bet size as the account drops in size during a drawdown). I know some people "believe" in streaks, but if the game is fair and the outcomes are independent, then the streaks are a total illusion (ya gotta work hard to rid your brain of a million years of evolved bad intuition). The coin does not know that it is "due" for a heads after being tails 10 times in a row. For a fair game, a Martingale strategy ONLY increases risk. A Martingale strategy can be profitable when trading returns are serially anti-correlated. This occurs when the price dynamics are mean reverting -- long runs of either price rises or drops are less likely than expected (think choppy, range-bound markets). But, a Martingale strategy is disastrously unprofitable if returns are serially correlated (or trending). Given that so many traders think the markets change character over time, a given trading system is bound to fall out sync with the markets and generate a long string of losses. This suggests that even if trading returns look serially anticorrelated, a Martingale strategy will only be profitable for a while and then will lead the trader to blow up their account when the markets change behavior. <b>Is coin toss model a valid model?</b> The bigger issue with this thread is whether the coin toss model is even a valid model of trading or the markets. If price movements in stocks are like coin tosses (being independent, identically distributed trials), then STOP TRADING because you are only being a gambler. If price moves are independent, that means that prior price action has NO influence on future price action. Each new day in the markets is an independent event that you cannot predict at all. Even if you argue that the markets are a biased coin-toss (with slightly better wins and than losses) the better strategy is long-term-buy-hold (but only if you have no means of predicting future price moves). And if the markets do not have independent, identically distributed price moves, then all this talk of converging to a normal distribution is a waste of time. That the distribution of market returns does NOT converge to a normal distribution is clear evidence that the markets violate key assumptions the underpin the central limit theorem. Me, I think the price moves in the markets are NOT independent and NOT identically distributed (I'm not even sure that the variance of returns is defined, but that's another issue entirely). The coin-toss model is a somewhat useful model for thinking about the behavior of stochastic systems, but is only a starting point for understanding markets and trading systems. Wishing everyone good & careful trading -Traden4Alpha
Oh, by the way, we weren't talking about if YOU had a positive expectation on a particular stock, but if EVERY stock has a positive expectation
Streaks are an almost certain statistical certainty. You don't have to believe in them. They are not just anecdotal. I gotta get back to work. After the close I will try to find the proof. It is all formulas, I don't understand them, but maybre somebody else will.
I couldn't find it. But here's one which theorizes my chances of making money on a streak are nil. If I flip a coin N times, then the odds that I will never flip a head are 1/(2^N). This is true no matter how high a value I give for N. So it seems plausible that, if I flip a coin a countably infinite number of times, then the odds that I will never flip a head are 1/(2^countable infinity)--in other words, one over an uncountable infinity. This result seems reasonable, since the problem can also be looked at as "If I somehow picked a random infinite string of coin flips from the set of all possible infinite strings of coin flips, what would be the odds that I would pick the set with all tails?" There are an uncountably infinite number of infinite strings of coin flips, and I'm looking for exactly one; so, assuming that I'm really picking randomly (so I'm no more or less likely to pick one string than another), the odds of picking the all-tails string should be 1 over that uncountable infinity. Now, _if_ I'm restricting myself to the real numbers, I then proceed to say "Well, any finite number over any infinity must be zero"--so I say that the probability is zero. If I'm allowing myself to use infinitesimals, then finite numbers _don't_ get zeroed out by infinities in this way, so I simply leave the result as it is--1 over an uncountable infinity. That's not a valid real number, but it's a valid infinitesimal. Yes, this is counterintuitive; but then, so is infinity itself. And think about this: If we exclude infinitesimals, then the odds that an infinite string of coin flips will contain at least one head are "1-but-just-maybe-it- won't-happen." The odds that an infinite string of coin flips will contain at least ten coin flips are "1-and-I-really-really-mean-it-this-time." We're using the exact same probability figure--1--to describe one event that's certain to happen, and another event that's not. Doesn't that defeat the whole purpose of probability figures? Doesn't that suggest that, in problems like this, we're making an error by restricting probability figures to real numbers? --------------------------------------------------------------------------------