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Coin Toss Runs Calculator

The expected number of runs for two consecutive heads or tails is 3. Is there an edge if we place a progressive constant size bet(limited to 3 times)for consecutive appearance of H or T only after pattern HTH or THT appears, Or is prob=0.5 always?

Say Dow is on a daily bar chart 'uptrend', i.e. 50MA above 100&200MA, Is it a better to long (a day duration each time), e.g. mini-Dow futures until two days UP in a row the day after a 'Up,down,up' daily bar pattern occurred?

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Is the coin fair or you don't know? –  Alexey Kalmykov Oct 31 '12 at 16:55
    
Prob=0.5 means a fair coin. –  Shelagh Nov 1 '12 at 11:24
    
    
    

1 Answer 1

1) The probability of a H or T of any next coin toss (fair coin) is always 0.5 because coin tosses are independent of each other.

2) Stock markets, or for that matter any asset, are an entirely different game. First of all the expectancy is not 0.5 of, for example, experiencing an up or down day tomorrow in a stock simply because the distribution is different and because stock prices exhibit a drift component. Additionally, financial asset returns and especially their volatility exhibit co-integration properties of varying degrees. Thus, it does not pay to compare coin toss expectancy with asset return expectancy.

3) Changes in stock index levels as well as individual stock prices are the strict result of supply-demand imbalances and such imbalances are partly a function of varying and shifting sentiment on the macro side, industry sector side, and individual company side. Sometimes stock price imbalances can carry on for a prolonged period, at other times the market exhibits a strong drive to move the price back into what the market views as fair value regimes.

Such switches from momentum back to "mean reversion" and again back to momentum are what experienced traders are the most concerned with and attempt to assess in order to maximize the expectancy of their placed bets. I have not heard of long-term successful "market operators" to generate profits off the back of predicting what the next tick/bar/day is gonna be purely as a function of the up/down pattern of past returns. What I observed on the other hand makes a successful trader is the ability to assess as early as possible shifts in co-integration patterns after they occurred.

Just my 2 cents.

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Shifts in CoIntegration patterns sounds interesting. Please elaborate(with example). –  Shelagh Oct 31 '12 at 16:24
    
I'll throw a disagreement (only) on the pattern side (although I do agree few approach it successfully). As an example, please see Toby Crabel's work and accomplishments (he utilizes the conditional probabilities of simple 'coin toss' like experiments as a pattern based decision). There are other more complex ways to apply the logic as well. But the key, as you point out (IMO), is that markets have properties like drift and momentum that make such methods feasible –  pat Oct 31 '12 at 21:48
    
@pat, I am afraid I don't quite understand what point you try to make. Of course I can utilize any sort of pattern to base decisions on. It all comes down to the tracking error between the expected value and future realized value. I am happy to debate and defend the futility of using coin toss arithmetic and apply it to forecasting financial time series, or to be more precise, forecasting future returns. I do not even know where to start with even if I wanted to look at similarities simply because subsequent asset prices always exhibit co-integration, coin tosses never do. –  Matt Wolf Nov 1 '12 at 1:13
    
@Shelagh, all I tried to say was that sometimes subsequent returns are positively correlated, sometimes they are negatively correlated, mostly as a function of whether time series exhibit a trending property or reversion back to some sort of mean (however you want to define mean). The difficulty is to spot such shifts early, and especially how to filter out the false positives in the observation pool. –  Matt Wolf Nov 1 '12 at 1:20
    
@Freddy. You stated, "I have not heard of long-term successful "market operators" to generate profits off the back of predicting what the next tick/bar/day is gonna be as a function of the past couple observations, dictated by certain observed or quantified "patterns". " I gave one concrete illustration where that was the case. I agree with just about everything else. –  pat Nov 1 '12 at 7:59

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