Well I must admit that you have me baffled... Baye's Theorem is usually used to figure out if a "test" is accurate or not. I think some computer programmers use it as well but I don't do that. I can't figure out what it has in common with trading...? Any chances you could give me a hint as to what you apply it to...?
Sure: A very simple (and a very abstract) example. The actual decision making tree is a lot more complex, nevertheless: Portfolio A has 100 securities in it. All the securities in this portfolio have an average daily range of X%. If any security in this portfolio is at 80% from its daily range (high or low) it has 90% chance of reaching its daily average high (or low). However, if the security 'fails" to reach its daily limit it has 70% chance of "retracing" to its daily open price. On a particular day one of the securities in portfolio A is within 10% of its average high. What is the chance for this security to hit its average high before the day is over. There are thousands of examples like this and they are all important to consider when creating an AI based decision making algo,
MAESTRO, Forgive me for jumping in. When we isolate a company doesn't it mean that the chances will be 50/50 on any given day? It seems that we also need to know what % of them on average hit the target. A number of days as a sample size would also help. Although I wouldn't know what formula to use here because I'm not a mathematician. Thank you.
Not necessarily. The good example is the Monty Hall paradox or a cancer screening phenomenon. Also, there is a solution for the example provided without any additional data.
Of course it does unless you know already the outcome of some other stocks. In the Monty Hall problem, you already know the outcome of the game presenter's choice. This is what changes the probability. But you are correct that at the start of the day, this has no meaning. So any reference to Monty Hall and Bayes is quite unfortunate at this point. Only if trading were that easy...
Reading the question above, I get: The particular security is at: 80% <= security price < 100% so: security has 90% chance of reaching high, and 10% chance not reaching high; Of the 10% that don't reach the high, 70% will retrace to open: 10% * 70% = 7% So, given the security is within 10% of the high (at 90%), it has the following probabilities: hitting high: 90% retracing back to open: 7% ending somewhere between high and open (exclusive): 3% Intuition tells me that's not illustrating the concept fully; I think we need the prior probability -- "what is the probability a security will hit its daily average high?" as estimated before the start of the trading day, one step before the conditional probability of 90% given it's at 80% from its daily range. Unless we can assume "average daily high" is distributed with kurtosis close to 1, then we could assume probability of hitting avg daily high = probability of not hitting avg daily high = 25% (half goes to daily high; half goes to daily low; but that's again with a big assumption of daily price distribution).
MAESTRO, In this example a piece of statistics was used to arrive at current probabilities. Looking at the point where the security is within 10% of it's high we need another set of statistics to calculate the most probable outcome. But you say the solution here doesn't require new data. The security now has covered half of the distance towards the potential target and still has 70% chance to retrace to its open price. At this point, I would just cheer them up by adding 5% more so they can reach the finish line that is so close. Although it feels like we are in the grey area and the chance of success is still 90%.
"if any security is at 80% from it daily range." so are you saying that if the distance from the high and low is greater than 80%? "it has 90% chance of reaching it daily average high (or low)". Are you saying it has 90% chance of reaching one or the other?
No, because each company will behave according to maestro's numbers in the long run (this is our "given" info). Sample size won't matter because our domain is all the companies within the portfolio for which we have the relevant statistics for. (remember this is a hypothetical example). In practice you would be dealing with distributions, so you deal with sample data by having qualified priors.