Behavioral Finance Lecture 05: Fractal & Inefficient Markets

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Lecture 5: Market Behavior--Stock Markets II. (Slides: CfESI Subscribers  Part 1Part 2; Debtwatch Subscribers Part 1 Part 2)

The Fractal Markets Hypothesis and the Inefficient Markets Hypothesis are two of several attempts to provide a realistic theory of how finance markets actually behave. In this first half of the lecture, I explain what fractals aew, and discuss their basic characteristics.

In the second half of the lecture, I outline the Fractal Markets Hypothesis and the Inefficient Markets Hypothesis (IEH). The IEH suggests precisely the opposite investment strategy to the EMH on how to maximize returns on the stock market: invest in low volatility, high Book to Market stocks.

The videos can be watched by anyone; Powerpoint files can be downloaded by members of the Center for Economic Stability

About Steve Keen

I am a professional economist and a long time critic of conventional economic thought. As well as attacking mainstream thought in Debunking Economics, I am also developing an alternative dynamic approach to economic modelling. The key issue I am tackling here is the prospect for a debt-deflation on the back of the enormous debts accumulated in Australia, and our very low rate of inflation.
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12 Responses to Behavioral Finance Lecture 05: Fractal & Inefficient Markets

  1. sj says:

    Mr Keen
    I did watch the lec­ture as a teacher you are too kind , very few of your stu­dents even knew what a frac­tal is infact it was bit of a joke.
    Well Mr Keen may I make a hum­ble sug­gested next class you have if a stu­dent does not bring a frac­tal object exam­ples are many tree branches, leaves,sea shells,maps,stock charts, you should failed them.
    The lazy stu­dents can point to their DNA or blood ves­sels for a frac­tal.
    This will make them think in eco sys­tems and away from a nar­row minded sta­ble class envirnoment.

  2. TruthIsThereIsNoTruth says:

    The fail­ure of CAPM implies that stocks don’t fol­low the strictly defined CAPM model. To say the fail­ure of CAPM implies that stocks are not ran­dom is sim­ply false. To say that the fail­ure of CAPM implies that stocks are not ran­dom is sim­ply false does not imply that stocks are random…

    The com­mon mis­con­cep­tion being employed here is that ran­dom­ness nec­es­sar­ily means a ran­dom walk, coin toss style process. This is one spe­cific type of ran­dom process and I would not go as far as to say that this is the truly ran­dom process.

    There are at least sev­eral processes that describe the extreme tails in stock returns. FMH is intu­itive and inter­est­ing, there is noth­ing wrong with teach­ing that but as you say it is hard to use, it’s very com­plex. There are more prac­ti­cal mod­els that fit the data equally well if not bet­ter. I think if I was your stu­dent again you would find me to be a great pain.

  3. enorlin says:

    If stu­dents of eco­nom­ics don’t know about frac­tals (or even com­plex num­bers!), I wouldn’t hold that against them — I guess noone thus far both­ered to teach them.

  4. Steve Keen says:

    Pre­cisely Enor­lin! It’s their teach­ers who are at fault primarily.

  5. Attitude_Check says:


    There is a spe­cific tech­ni­cal def­i­n­i­tion of ran­dom­ness and ran­dom behav­ior. Dr. Keen is using the tech­ni­cal def­i­n­i­tion and shows quite con­vinc­ingly that the mar­ket does not behave that way. You seem to be using a col­lo­quial def­i­n­i­tion (e.g. not pre­dictable), which is also true about the mar­ket, but it is math­e­mat­i­cally incor­rect to call it ran­dom. It does appear to be com­plex, which is deter­min­is­tic, but unpre­dictable at most times scales.

    The truth is there is truth, and we all argue what it is. You do real­ize your han­dle is inher­ently con­tra­dic­tory and illog­i­cal. I assume that was an inten­tional jab at mod­ern rel­a­tivis­tic philosophy.

  6. TruthIsThereIsNoTruth says:

    The spe­cific ‘tech­ni­cal’ def­i­n­i­tion in the lec­ture is exactly that, it is spe­cific. There is also a more gen­eral tech­ni­cal def­i­n­i­tion of ran­dom­ness. Would you say a sto­chas­tic volatil­ity model is less ran­dom than geo­met­ric brown­ian motion? Even the most sim­ple sto­chas­tic model can repro­duce empir­i­cal behav­iour of stock returns given the appro­pri­ate prob­a­bil­ity distribution.

    I don’t assume this is some­thing that is well under­stood out­side quan­ti­ta­tive finance cir­cles, I expect that for you a ran­dom process is a geo­met­ric brown­ian motion, that is what you think is a ‘tech­ni­cal’ def­i­n­i­tion of randomness.

    My post was aimed to bring atten­tion to the fact that there is a well refined field of research which deals with the topic of the lec­ture in a dif­fer­ent and defi­nately more prac­ti­cal way.

    Good pick up on the handle’s para­dox, well done!

  7. TruthIsThereIsNoTruth says:

    but it is math­e­mat­i­cally incor­rect to call it random”

    All I have to say to that, is that to learn more, you first need to come to terms with the fact that you know very little.

  8. TruthIsThereIsNoTruth says:

    Don’t get me wrong though. I think FMH is a fan­tas­tic and insight­ful idea, well worth teach­ing. How­ever the approach of teach­ing it to naive stu­dents in this sort of THIS IS THE TRUTH way, results in mis­guided opin­ions such as you demon­strate. Sorry for my reac­tion, I do appre­ci­ate the debate, please realise there is another way of thinking.

  9. Attitude_Check says:

    The clear def­i­n­i­tion of terms and the math that fol­lows is impor­tant. The impor­tant issue of ran­dom­ness — par­tic­u­larly mod­eled as noise, is often treated as a process of zero infor­ma­tion. In par­tic­u­lar the mutual infor­ma­tion of the noise and the “sig­nal” is zero. In the case of a chaotic sys­tem, that assump­tion is false, and many typ­i­cal math­e­mat­i­cal “proofs” regard­ing noisy behav­ior of a sys­tem are no longer valid. I am deal­ing with this exact prob­lem as an engi­neer. A ran­dom error process for a spe­cific prob­lem is not inde­pen­dent of the para­me­ter being esti­mated. at least 50+ years of aca­d­e­mic the­ory regard­ing this is flat wrong. I am exploit­ing this fact to achieve “impos­si­ble” results accord­ing to clas­sic the­ory that treats this ran­dom error sig­nal as noise.

  10. Attitude_Check says:


    I actu­ally under­stand quite a bit about ran­dom­ness as ysed in the con­text Dr. Keen is using it.

    These excerpts from Wikipedia cap­ture the salient points.

    The fields of math­e­mat­ics, prob­a­bil­ity, and sta­tis­tics use for­mal def­i­n­i­tions of ran­dom­ness. In math­e­mat­ics, a ran­dom vari­able is a way to assign a value to each pos­si­ble out­come of an event. In prob­a­bil­ity and sta­tis­tics, a ran­dom process is a repeat­ing process whose out­comes fol­low no describ­able deter­min­is­tic pat­tern, but fol­low a prob­a­bil­ity dis­tri­b­u­tion, such that the rel­a­tive prob­a­bil­ity of the occur­rence of each out­come can be approx­i­mated or cal­cu­lated. For exam­ple, the rolling of a fair six-sided die in neu­tral con­di­tions may be said to pro­duce ran­dom results, because one can­not know, before a roll, what num­ber will show up. How­ever, the prob­a­bil­ity of rolling any one of the six rol­lable num­bers can be calculated.

    In the 19th cen­tury, sci­en­tists used the idea of ran­dom motions of mol­e­cules in the devel­op­ment of sta­tis­ti­cal mechan­ics in order to explain phe­nom­ena in ther­mo­dy­nam­ics and the prop­er­ties of gases.

    Accord­ing to sev­eral stan­dard inter­pre­ta­tions of quan­tum mechan­ics, micro­scopic phe­nom­ena are objec­tively random.[6] That is, in an exper­i­ment where all causally rel­e­vant para­me­ters are con­trolled, there will still be some aspects of the out­come which vary ran­domly. An exam­ple of such an exper­i­ment is plac­ing a sin­gle unsta­ble atom in a con­trolled envi­ron­ment; it can­not be pre­dicted how long it will take for the atom to decay; only the prob­a­bil­ity of decay within a given time can be calculated.[7] Thus, quan­tum mechan­ics does not spec­ify the out­come of indi­vid­ual exper­i­ments but only the prob­a­bil­i­ties. Hid­den vari­able the­o­ries are incon­sis­tent with the view that nature con­tains irre­ducible ran­dom­ness: such the­o­ries posit that in the processes that appear ran­dom, prop­er­ties with a cer­tain sta­tis­ti­cal dis­tri­b­u­tion are some­how at work “behind the scenes” deter­min­ing the out­come in each case.

    Algo­rith­mic infor­ma­tion the­ory stud­ies, among other top­ics, what con­sti­tutes a ran­dom sequence. The cen­tral idea is that a string of bits is ran­dom if and only if it is shorter than any com­puter pro­gram that can pro­duce that string (Kol­mogorov randomness)—this means that ran­dom strings are those that can­not be com­pressed. Pio­neers of this field include Andrey Kol­mogorov and his stu­dent Per Martin-Löf, Ray Solomonoff, and Gre­gory Chaitin.

    In math­e­mat­ics, there must be an infi­nite expan­sion of infor­ma­tion for ran­dom­ness to exist. This can best be seen with an exam­ple. Given a ran­dom sequence of three-bit num­bers, each num­ber can have one of only eight pos­si­ble values:

    In infor­ma­tion sci­ence, irrel­e­vant or mean­ing­less data is con­sid­ered to be noise. Noise con­sists of a large num­ber of tran­sient dis­tur­bances with a sta­tis­ti­cally ran­dom­ized time distribution.

    In com­mu­ni­ca­tion the­ory, ran­dom­ness in a sig­nal is called “noise” and is opposed to that com­po­nent of its vari­a­tion that is causally attrib­ut­able to the source, the signal.

    In terms of the devel­op­ment of ran­dom net­works, for com­mu­ni­ca­tion ran­dom­ness rests on the two sim­ple assump­tions of Paul Erd?s and Alfréd Rényi who said that there were a fixed num­ber of nodes and this num­ber remained fixed for the life of the net­work, and that all nodes were equal and linked ran­domly to each other.

    The ran­dom walk hypoth­e­sis con­sid­ers that asset prices in an orga­nized mar­ket evolve at random.

    Other so-called ran­dom fac­tors inter­vene in trends and pat­terns to do with supply-and-demand dis­tri­b­u­tions. As well as this, the ran­dom fac­tor of the envi­ron­ment itself results in fluc­tu­a­tions in stock and bro­ker markets.

    Note the empha­sis of infor­ma­tion con­tent through­out. The ran­dom walk hypoth­e­sis of finance is taken from Brown­ian motion of mol­e­cules (dis­cov­ered by Ein­stein, and actu­ally what he was awarded the Nobel prize for). It rests upon the assump­tion that the veloc­ity of indi­vid­ual atoms in a ther­mo­dy­namic equi­lib­rium of a 3D gas are ran­dom and com­pletely inde­pen­dent of each other and the mol­e­cule being dri­ven. The pre­vi­ous his­tory of the path of the mol­e­cule pro­vides NO INFORMATION about the future path. The under­ly­ing dynam­ics are assumed to be com­pletely ran­dom and tem­po­rally and spa­tially inde­pen­dent. This is clearly a very bad model for the finan­cial mar­kets. Gauss­ian Cop­ula the­ory applied to risk man­age­ment clearly shows that in detail.

    The truth is you need to study a bit more on ran­dom process the­ory, infor­ma­tion the­ory, dynamic sys­tems, and com­plex­ity, and how those relate — or don’t, to the finan­cial mar­ket and economics.

  11. Attitude_Check says:


    I should have read a lit­tle far­ther. This describes pseudo-random process.

    Some math­e­mat­i­cally defined sequences, such as the dec­i­mals of pi men­tioned above, exhibit some of the same char­ac­ter­is­tics as ran­dom sequences, but because they are gen­er­ated by a describ­able mech­a­nism, they are called pseudo­ran­dom. To an observer who does not know the mech­a­nism, a pseudo­ran­dom sequence is unpredictable.

    A process may appear to be ran­dom, but as we learn more infor­ma­tion about it (the algo­rithm used and the seed value for exam­ple) it becomes fully pre­dictable, and no longer ran­dom. Ran­dom­ness is only then a quan­tifi­ca­tion of our igno­rance of the under­ly­ing dynam­ics vice a descrip­tion of the dynam­ics itself.

  12. TruthIsThereIsNoTruth says:

    Thanks for the reply.

    In finance I take a slightly dif­fer­ent view. I don’t actu­ally believe there exists a model which truly cap­tures mar­ket behav­iour. Mar­ket behav­iour is nei­ther ran­dom or deter­min­is­tic but can be described by both, par­tic­u­larly with ideas such as frac­tal­ity. That’s why I find a big flaw in the engi­neer­ing approach to under­stand­ing mar­kets, how­ever at the same time the engi­neer­ing approach is nec­es­sary as long as you don’t start think­ing it gives you a monop­oly to the truth.

    The funny thing about this spe­cific topic, com­ing back to my orig­i­nal point, that by the same cri­te­ria which ‘proves’ that mar­kets are frac­tal, you can prove that mar­ket are ran­dom, if you apply the cor­rect process (not GBM obvi­ously). The def­i­n­i­tion of ran­dom­ness you pro­vide only has a brief men­tion of finan­cial math­e­mat­ics, if you want insight and cut­ting edge research the most appro­pri­ate author on this topic is E. Platen.

    The most impor­tant prac­ti­cal appli­ca­tion of mod­els in mod­ern finance is man­ag­ing risk, some­thing which has been done very poorly recently by for­merly large invest­ment banks. It is not as implied by the lec­ture, asset allo­ca­tion… When peo­ple find out what I do, they auto­mat­i­cally think I should know where they should invest, I think the more you know about mar­kets the more you realise that there is no objec­tive answer to that ques­tion (again as sug­gested by lec­ture 5). For man­ag­ing risk the most appro­pri­ate mod­els are based on ran­dom­ness, this doesn’t mean that mar­kets are ran­dom, but nei­ther are they deter­min­is­tic or com­plex or chaotic. Mar­kets are some­times all those things, nei­ther of those things, one or more of those things or some­thing else all­to­gether, but unlike moun­tains, they are always chang­ing (well moun­tains do erode, what­ever). Also unlike moun­tains, they are not gov­erned by a force of grav­ity in over­whelm­ingly one direction.

    What is really inter­est­ing about frac­tals and mar­kets is the ques­tion why? Or even just frac­tals in gen­eral, why are things frac­tal. Why would mar­kets fol­low this law? Get the stu­dents think­ing about that, instead bom­bard­ing them with deriva­tions that leave them con­fused or worst in a com­mon state of being con­vinced “by expo­sure to infor­ma­tion they don’t understand”.

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