Here is a statistical principle that, to me, works almost like magic when I looked at it the first time:
Regression to the Mean
According to an article on Wikipedia, if I know the mean or expected value of a random variable (coin flips, test results, etc), if I take a random result from the variable's sample space and it turns out to be far from the mean, (either beyond the 25-percentile on the distribution curve, or at a certain distance beyond the standard deviation), if I take another independent sample, the second value will be much closer to the mean, depending on how independent my second measurement is from the first.
Does regression to the mean occur in stock price movement? Or perhaps this is better applied to forex spot prices, due to its greater volatility which more closely approximates normal distributions (will have to find out whether this is true). If that's the case, one should simply go long when the price is far below the mean, and short when its above.
The key reason why this doesn't apply is because the range of values of the second price is almost always dependent on the first, since the price-time graph is continuous. But instead of being applied to the instrument price as a whole, we can use it to gauge the likelihood of more specific events which are more random, eg after the MACD crosses over and this indicator goes up and so-and-so, what is the average price behavior over the next 10 candlesticks? In this case we might simply open a position based on the average behavior, But if regression to the mean applies, we can also wait for a large deviation to occur in the negative direction, which according to the principle will increase the odds that this won't happen the next time.
This brings me to the question: what is the best way to model the price of a financial instrument as a random variable, and hence in a probability distribution graph?
Sunday, March 29, 2009
First Post
I'm not a gambler. I won't get excited at low-probability lotteries. I dislike betting on football, as it takes the fun out of supporting my favorite team (if someone offers me good odds for Spurs to lose against Arsenal, will I take it?). I like easy money as much as the next person, but I don't believe in casinos. All casino games are designed such that the dealer has the advantage, so no one can ever win in the long run, so the most you'll get is a short-term thrill from beating the odds, in which case you might as well go to the lotteries.
But financial markets are a different thing altogether. It's a matter of company and/or economic fundamentals, technical signals, and ultimately, how your fellow traders feel about the same stock. Are there millions of them, or is it only a few thousand traders whose large transactions matter? In any case, they are the cause of all price movements, and consequently the changes on your profit/loss statement. Do the laws of probability dictate that the odds are firmly set against day traders? Is it possible to retrieve sufficient parameters to calculate the probability of a making successful long trade?
And so, thinking that I know all there is to know about forex after reading a few Investopedia articles, I've put $3000 of my savings into a forex account. And so I've lost $3000 within a week. And I've allowed a unit trust to lose 30% of its value due to the recent downturn. That sums up my experience with the financial markets.
But I'm not giving up. You have charts, and all kinds of technical indicators out there which can allow you to predict future movements. The only thing is, there's no fixed rule saying how they should be used. An MACD crossover indicates a change in trend. Does that mean you can open your long position now? Or shall I wait for the Stochastic Oscillator to crossover in order to confirm the trend? How about RSI? Has it crossed 50, or is it already in the 70-80 range, which means you're probably too late to enter a long position. Or does it mean that there's a strong trend and that you should hop in? What about the ADX? What about the Aroon oscillator? Wait, what was I talking about?
The key questions to be asked, I feel, is:
1. Given the economic/technical/whatever signals, what is the probability that the price will move in a given direction, and that I will profit from this movement?
2. How will this probability be affected with different take-profit and stop-loss parameters?
Once a situation is arrived where the probability is known for certain, or perhaps a range of probabilities, or perhaps a situation where the probability is above 50%, we can conclude that consistently entering a trade whenever the given situation occurs will result in profits in the long run.
It'll be cool if this can be done mathematically. I've taken a couple of classes in probability and statistics, and was enthralled by how the theorems and distributions can be used to explain and even predict real-world events. Hopefully, perhaps in combination with technical analysis, perhaps it will be possible to predict future chart prices using these methodologies. Perhaps.
But financial markets are a different thing altogether. It's a matter of company and/or economic fundamentals, technical signals, and ultimately, how your fellow traders feel about the same stock. Are there millions of them, or is it only a few thousand traders whose large transactions matter? In any case, they are the cause of all price movements, and consequently the changes on your profit/loss statement. Do the laws of probability dictate that the odds are firmly set against day traders? Is it possible to retrieve sufficient parameters to calculate the probability of a making successful long trade?
And so, thinking that I know all there is to know about forex after reading a few Investopedia articles, I've put $3000 of my savings into a forex account. And so I've lost $3000 within a week. And I've allowed a unit trust to lose 30% of its value due to the recent downturn. That sums up my experience with the financial markets.
But I'm not giving up. You have charts, and all kinds of technical indicators out there which can allow you to predict future movements. The only thing is, there's no fixed rule saying how they should be used. An MACD crossover indicates a change in trend. Does that mean you can open your long position now? Or shall I wait for the Stochastic Oscillator to crossover in order to confirm the trend? How about RSI? Has it crossed 50, or is it already in the 70-80 range, which means you're probably too late to enter a long position. Or does it mean that there's a strong trend and that you should hop in? What about the ADX? What about the Aroon oscillator? Wait, what was I talking about?
The key questions to be asked, I feel, is:
1. Given the economic/technical/whatever signals, what is the probability that the price will move in a given direction, and that I will profit from this movement?
2. How will this probability be affected with different take-profit and stop-loss parameters?
Once a situation is arrived where the probability is known for certain, or perhaps a range of probabilities, or perhaps a situation where the probability is above 50%, we can conclude that consistently entering a trade whenever the given situation occurs will result in profits in the long run.
It'll be cool if this can be done mathematically. I've taken a couple of classes in probability and statistics, and was enthralled by how the theorems and distributions can be used to explain and even predict real-world events. Hopefully, perhaps in combination with technical analysis, perhaps it will be possible to predict future chart prices using these methodologies. Perhaps.
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