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willsmith
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The problem with random walk theory

October 7th, 2009, 10:05 pm

I think it's fairer to say that under random walk, future RETURNS are independent of past RETURNS.I suppose you could say that returns and prices are two sides of a coin (differential / integral).
 
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beaker
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The problem with random walk theory

October 7th, 2009, 10:59 pm

Quote I think it's fairer to say that under random walk, future RETURNS are independent of past RETURNS.Absolutely, independent price increments. But I wouldn't say prices are independent under a random walk, e.g.P(GOOG = $700 tomorrow given GOOG = $505 today) = P(GOOG = $700 tomorrow) = P(GOOG = $700 tomorrow given GOOG = $700 today)
 
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Fermion
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The problem with random walk theory

October 8th, 2009, 12:28 am

Richyiee:Random walksYou can't reasonably talk about randomness without an implicit probability distribution. A random dice has a probability of 1/6 for each value turning up. If you are talking about future prices, then you would expect the probability density will likely peak in the region of the last price, unless you have a good reason to the contrary. In general, small returns will be more likely than large returns -- again unless you have a good reason to suspect otherwise. But by how much? The usual way to estimate the width of the density (and any other parameters that may affect its shape) is to look at historic data. If you need to do this to generate your predicted density of returns (and who doesn't) then returns cannot in any sense be independent of past data and, particularly, the statistical distribution of past returns.The only meaningful content in the term "random walk" then is that returns should be generated by some stochastic process and even a Markovian process will reflect the way history informs us how to generate its parameters.The sense in which randomness operates in a Markov process is that the parameters tell us how to generate returns in terms of a some parameter-free underlying process -- such as a standard Wiener process. It is only in this underlying process that increments are truly independent of history -- because of the absence of history-dependent parameters.Market efficiencyMarket efficiency is a completely different kettle of fish. It assumes that all relevant information that could determine the price (let's call that strong efficiency) or its density (let's call that weak efficiency) is instantly available to all market participants. Plainly, that includes all historic information.
 
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Richyiee
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The problem with random walk theory

October 8th, 2009, 8:36 pm

hi fermion,by specifying a probability distribution, you are determining the range within which returns will move. Then at the end of the day, although the movements are 'random' within this range, they are in a sense very 'deterministic' because this 'range' is completely specified. The whole motive for using random walk models is because markets are assumed efficient right => theres no point searching for 'technical patterns' => lets simplify the thing and abstract all returns together with this one distribution. But since this distribution is determined by historical data, why is it not possible finer structure lay within the data which may give us a better approximation than using the one distribution? For example:during market state a we adust our models so returns come from "distribution a" market state b we adust our models so returns come from "distribution b" .. and so forth, so we have many distributions depending on the "state" of the marketbut hang on, this is what chartists do in their heads right
 
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beaker
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The problem with random walk theory

October 8th, 2009, 9:09 pm

Quoteby specifying a probability distribution, you are determining the range within which returns will move. Then at the end of the day, although the movements are 'random' within this range, they are in a sense very 'deterministic' because this 'range' is completely specified.Just a note, you may want to consider the support of the logistic and normal distributions.
 
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quantmeh
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The problem with random walk theory

October 8th, 2009, 9:17 pm

QuoteOriginally posted by: Richyieebut hang on, this is what chartists do in their heads rightno. again, you're wrong. also you're getting far from your original post on Markovian properties, of course.in Fermion's example the "chartist" would be trying to predict next coin flip's side. so, if the last three coin flips were head, tail,head, then the chartist would rationalize that "they alternate in short term", so he'll bet on next tail.suppose that it wasn't tail, it was head again, i.e. head, tail, head, head"hm... maybe regime switched.... maybe it went into momentum!", then he bets one headsuppose that it came out as head - wohoooo!!!!! head, tail, head, head, headnow he's puzzled... "is it still momentum or maybe we're hitting resistance...." after some though, reading trading forums, talking to friends and watching Mad Money, he decides that momentum is over, time to retreat and he bets on tail now.....all this time, Mr Markov was looking at the chartist from his grave amused...
 
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Richyiee
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The problem with random walk theory

October 8th, 2009, 9:44 pm

"the "chartist" would be trying to predict next coin flip's side. so, if the last three coin flips were head, tail,head, then the chartist would rationalize that "they alternate in short term", so he'll bet on next tail."your viewing markets from a prejudiced perspective, if you assume they're 'random' then of course technical analysis is stupid. actually given enough data from a random walk generated on matlab, it may be possible to make better than 50-50 predictions on future increment directions using 'technical analysis'. Although im not completely sure how pseudorandom numbers are generated on matlab i remember somewhere of a mention of a period, if it has a period its definatly deterministic, im not proposing "record the sequence, next time it starts we have the numbers", but if the thing driving it is anything like a chaotic equation where attractors exist, then a type of 'technical analysis' may work
Last edited by Richyiee on October 7th, 2009, 10:00 pm, edited 1 time in total.
 
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quantmeh
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The problem with random walk theory

October 8th, 2009, 10:02 pm

QuoteOriginally posted by: Richyieeyour viewing markets from a prejudiced perspective, if you assume they're 'random' then of course technical analysis is stupid. i only was pointing the difference between approaches of chartist and Markovian guy in Fermion's example. Markovian dude would say that next coin flip outcome does NOT depend on previous ones. he may still look at the previous outcomes to compute probabilities. it's very very different from what simplistic chartist would do now, the complication's that you may realize that coin flips are NOT independent. maybe with every flip the probabilities change by some rule. then Markovian guy will reject the first simplistic model, and will build a new one. let's say he notices that probabilities of tails increase in the morning, and go down in evenings. etc. this doesn't change the Markovian guy's approach though! he'll look into past to find that rule, and will build another markovian model
 
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Beachcomber
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Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 8th, 2009, 10:07 pm

QuoteOriginally posted by: Richyiee"the "chartist" would be trying to predict next coin flip's side. so, if the last three coin flips were head, tail,head, then the chartist would rationalize that "they alternate in short term", so he'll bet on next tail."your viewing markets from a prejudiced perspective, if you assume they're 'random' then of course technical analysis is stupid. actually given enough data from a random walk generated on matlab, it may be possible to make better than 50-50 predictions on future increment directions using 'technical analysis'. Although im not completely sure how pseudorandom numbers are generated on matlab i remember somewhere of a mention of a period, if it has a period its definatly deterministic, im not proposing "record the sequence, next time it starts we have the numbers", but if the thing driving it is anything like a chaotic equation where attractors exist, then a type of 'technical analysis' may workI am not sure what your point is. Sure, if the underlying distribution isn't Markovian, than you can do better than using a Markovian model. Your initial question seemed to have to do with knowledge of or assumptions about the underlying distribution effecting the "Markovianness" (did I just coin a word there?) of the distribution. I do not know how much clearer, simpler, or straightforward of an example we can give. We know exactly what the distribution of a coin flip is, yet we can study history all we want and we will never come up with a better guess than 50% heads, 50% tails for the next flip.As far as viewing markets from a prejudiced perspective...economists and market makers will be debating what inefficiencies, if any, exist in the market until we all join Mr. Markov in the grave. Most of the time, when an ineffieciency is reported, it disappears rather quickly. Is the market getting more efficient or was the inefficiency not there in the first place?
 
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Beachcomber
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Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 8th, 2009, 10:16 pm

QuoteOriginally posted by: jawabeanQuoteOriginally posted by: Richyieeyour viewing markets from a prejudiced perspective, if you assume they're 'random' then of course technical analysis is stupid. i only was pointing the difference between approaches of chartist and Markovian guy in Fermion's example. Markovian dude would say that next coin flip outcome does NOT depend on previous ones. he may still look at the previous outcomes to compute probabilities. it's very very different from what simplistic chartist would do now, the complication's that you may realize that coin flips are NOT independent. maybe with every flip the probabilities change by some rule. then Markovian guy will reject the first simplistic model, and will build a new one. let's say he notices that probabilities of tails increase in the morning, and go down in evenings. etc. this doesn't change the Markovian guy's approach though! he'll look into past to find that rule, and will build another markovian modelReminds me of a story from grad school...First econometrics class, prof walks in, gives us a series of numbers and asks us to analyze the data noting trends, patterns, etc. We (the students) all found underlying trends and patterns, some quite profound. The prof then announced that he was just fooling around the other day and generated a bunch of random numbers.Richyiee, if you think you have found something non-Markovian that the rest of the market hasn't found, good luck; it could be very profitable...or not.
 
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quantmeh
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The problem with random walk theory

October 8th, 2009, 11:34 pm

QuoteOriginally posted by: BeachcomberRichyiee, if you think you have found something non-Markovian that the rest of the market hasn't found, good luck; it could be very profitable...or not. i think that our last class on portfolio management (after finals) was on persistent anomalies in markets. overall, i remember she wasn't discarding tech analysis on wholesale basis. but again this has nothing to do with Richyiee's original question
 
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Richyiee
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The problem with random walk theory

October 9th, 2009, 11:12 am

"Richyiee, if you think you have found something non-Markovian that the rest of the market hasn't found, good luck; it could be very profitable...or not. " Well im sure theres plenty of people making plenty of money out there one way or another , and I gotta feeling its not because they followed the preachings of financial mathematics, maybe im wrong tho. Perhaps they preach financial mathematics then benefit?
 
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Beachcomber
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Joined: May 25th, 2004, 5:56 pm

The problem with random walk theory

October 9th, 2009, 12:06 pm

QuoteOriginally posted by: Richyiee"Richyiee, if you think you have found something non-Markovian that the rest of the market hasn't found, good luck; it could be very profitable...or not. " Well im sure theres plenty of people making plenty of money out there one way or another , and I gotta feeling its not because they followed the preachings of financial mathematics, maybe im wrong tho. Perhaps they preach financial mathematics then benefit?I do not disagree except to say that some people are making money because they understand how to interpret the "preachings of financial mathematics".
 
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Richyiee
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The problem with random walk theory

October 9th, 2009, 12:35 pm

" some people are making money because they understand how to interpret the "preachings of financial mathematics". "Sure, i like this sentence. Although im not sure we share same views on the "how" in the "how to interpret" bit
 
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TitanPartners
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The problem with random walk theory

October 9th, 2009, 12:52 pm

I have seen this type of argument (what I currently believe to be sophistry) before on Wilmott regarding Markov Processes, where it seems to me that quant finance has managed to totally deviate from "the thing in itself".In my mind, a Markov process is by definition independent of historical data, period. For example a coin toss or a dice throw. This assumption in finance then has implications for the application of the Central Limit theorem, which you then derive the Gauss distbn function of the returns from.Implying from the market appears to be perhaps implying from historical data, or perhaps it is not, perhaps from some level of fear in the masses, as reflected in current prices of implied volatility, where traders books are facing etc. This is where in my mind the whole thing becomes quite deep philosophically (although still totally shallow in comparison to science).The original response by Jawabean of simply "no" to these questions, is quite simply, pathetic. But then I guess you are getting paid to be so shallow, so each to their own.