Am gasit pe YouTube un documentar interesant desprea Marea Depresiune din 1929. Sunt 6 parti care explica pentru publicul larg cam ce a insemnat criza din 1929 (violenta si amplitudinea cu care s-a manifestat), si evident daca am reusit sa invatam ceva din ea.

Exista oare vreo asemanare cu ceea ce se intampla in zilele noastre, sau…. this time is different?

Se vor demonstra a fi eficiente masurile luate pana acum?

To big to fail?

Probabil ca nu vom afla foarte curand raspunsul la aceste intrebari, insa din punctul meu de vedere increderea populatiei in economie este cea mai importanta veriga a sistemului. In momente de criza este extrem de important sa controlezi (daca poti) panica si sa restaurezi optimismul, increderea.

In momente de panica, datele fundamentale nu mai conteaza absolut deloc, si normal aici apare statul. Evident, acum apare urmatoarea intrebare… este corecta si sanatoasa interventia statului? Stim din manualele de economie ca interventia statului poate distorsiona grav economia si ca normal ar fi sa lasam piata sa se regleze singura, fiindca are aceasta capacitate (chiar are?).

Este un cerc vicios de care nu cred ca avem cum sa scapam, insa instoria ne invata ca ea se repeta (si putem sa invatam din asta) si ca un sistem bazat pe controlul absolut al pietei si al preturilor este sortit esecului inca de la inceput.

Update: Daca tot vorbim despre criza financiara, despre increderea populatiei in economie, si despre finante comportamentale… va las sa urmariti urmatorul clip. Enjoy!

It seems that testing is the flavour of the month in business these days. All the presentations I go to talk about A/B split testing and multivariate Taguchi methods. Of course the guiding principle of testing is a good one; but I think it gives some  the misguided notion that business is a purely deterministic process and that persistent testing  provides an algorithm for success (or quick, cheap failure, which is also good). There are some useful parallels between empiricism and its critics.

What am I actually testing? The process seems pretty simple; do A/B tests on your google ads, your landing pages, your email blasts, your automated workflows etc etc. Eke out success one word change at a time. How do you know you are isolating the one thing you want to test? How do you know you are not just locally optimising in totally the wrong place.

The empiricists and positivists thought the only source of knowledge is experience. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world, rather than resting solely on a priori reasoning, intuition, or revelation. Sounds reasonable. Quine illustrated problems with this view in the “Two Dogmas of Empiricism”. Quine argued for a holistic theory of testing; he thought that you cannot understand a particular thing without looking at its place in a larger whole. Holism about testing says that we cannot test a single hypothesis in isolation; instead we can only test complex networks of claims and assumptions. To test one claim you need to make assumptions about many other things e.g. measurement equipment, data quality etc. So whenever you think you are testing a single idea, what you are really testing is a long, complicated conjunction of statements. If a test has an unexpected result, then something in that conjunction is false, but the failure of the test itself does not tell you where the error is.

Take an example of ‘test the business model over a period of one year’, the background assumptions and  conjunction of interdependencies are legion. Two things can happen; you can say it doesn’t work when there is a simple element, which can be changed easily, in the web of dependencies that is the cause of failure  i.e. you get a false negative. A wrong pricing decision for example. You can also ‘forgive’ a fundamental problem by saying that something else in the chain is the cause i.e. a false positive. For any complex business decision the theory is always underdetermined by the available evidence i.e. there will always be a range of possible alternative theories compatible with the set of evidence. So what good is my test if it doesn’t tell us something definitive?

It didn’t work this time is different from it doesn’t work. People are also very keen with the notion of failing fast and failing cheap. Once again admirable but how do you know when you have failed? Karl Popper thought science progressed by a process of falsification; from the problem of induction you could never say that a general statement was true from a handful of observations but you could say the statement was false if an observation contradicted it. The issue of underdetermination rears its head again; you could never force someone to logical conclude that a theory was false because it may be a background assumption that is at fault. Falsification also struggles with probabilistic statements; take the example of proton decay – some grand unified theories predict that a proton should decay into new X bosons. During the 80’s there were a lot of experiments and they never saw a proton decay. They were able to put a lower limit of the proton half-life of 6.6×10^33 years but were not able  to say that it doesn’t decay. Most people may conclude that it doesn’t decay but the key thing is that they have to make a choice to believe so, it does not follow logically from observation. Doing a split test on a low volume search term feels a bit like waiting for proton decay.

Now take an example like James Dyson – he made 5,126 prototypes of his vacuum cleaner before hitting the big time. Why did he not declare that he had failed quickly and cheaply after the first 10 tries? Often it is difficult to know if you have the admirable quality of persistence or whether you are just a nutter.

Putting things to the test is a good idea but it only really works in a very well bounded context; most of the success stories come from web-based business that have a large enough user base to derive useful conclusions. For the majority of businesses there will be other things that matter a great deal more.  A business has a huge amount of knobs that you can turn, the only problem is that you can’t turn them all independently of each other. Basically I don’t think people should spend a lot of their time obsessing with analytics. Doing things intuitively has served a lot of people well for a very long time. If anyone can figure out how to do an A/B split test on the ‘cut of your jib’ please let me know.

Take a look at this 5 min video about Dollar Cost Averaging by Professor Kenneth French.

Dollar (UK investors should read Pound) Cost Averaging, in this case refers to lump sums available for  investment which, instead of  immediately being fully invested in the markets, are allocated over a series of months. The objective is to avoid being caught out by sudden market falls shortly after making the investment. In the UK we call this ‘Phased Investment’.

Interestingly, Prof French  reinforces the academically accepted view that Dollar Cost Averaging does not optimise returns, given the level of risk that an investor wishes to take. When considered purely from a finance perspective, if the right thing to do, in order to deliver a set of goals, is to invest in an equity portfolio, then it should be implemented in full, immediately. Market timing has been shown to contribute very little to returns and as a consequence there is no good reason to delay.

But, is this always right? Well ,Prof French observed that, from a behavioural finance point of view, it may be a good thing. People apparently feel worse about the negative outcomes from acts of comission (things they did) than they do about acts of ommission (things they didn’t do). Hence an investor feels a lot worse about the fact that his portfolio plummeted shortly after investing the money that he does about the returns which he failed to make because he didn’t invest the money.

On balance, Prof French concludes that, even with his finance professor’s hat on, the damage to prospective returns caused by Dollar Cost Averaging is very little, so it makes little difference whether investors use it or not. However, he observed that it may give them an experience that they feel better about.

Ultimately as investment professionals and, especially as financial planners, we do need to step outside of the theoretical world of optimised portfolios and look at things more closely from our client’s point of view. If doing things that are theoretically sub-optimal but not actually damaging makes our clients feel better about what they are doing then there is no good reason not to facilitate this. After all we are not on some kind of Evangelical mission to convert the pagan unwashed. Oh, and it is their money…. not ours.

Interesting huh!

Bayes’ theorem in its common form describes the way in which one’s beliefs about observing ‘A’ are updated by having observed ‘B’. Bayes’ theorem relates the conditional and marginal probabilities of events A and B, where B has a non-vanishing probability.

Each term in Bayes’ theorem has a conventional name:

P(A) is the prior probability or marginal probability of A. It is “prior” in the sense that it does not take into account any information about B.

P(A|B) is the conditional probability of A, given B. It is also called the posterior probability because it is derived from or depends upon the specified value of B.

P(B|A) is the conditional probability of B given A.

P(B) is the prior or marginal probability of B, and acts as a normalizing constant.

Bayesian belief updating is the model we use for learning. We in effect already use it when we sit in meetings, discussing best options, as we will have individually modified belief over time as we receive new information – the problem is that it is difficult for others to see what evidence corroborates this belief, which opens up the door for our cognitive biases and simple heuristics.

Jeffrey’s Rule

During product selection and development we acquire and learn new information, which allows us to update our belief about how to make future investment. However, we know that some information is of a higher quality e.g. let’s say two people make exactly the same statement; one is a lead customer and the other is a stranger on the street, we know which is of a higher quality with a higher information content. Bayes’ rule relies on learning a definitive new truth to revise our belief. Most new knowledge we acquire during product development cannot be classed as definitively true e.g. one customer may say one thing and another may say something totally different. Jeffrey’ rule allows us to deal with opinion, rumor and weakly supporting evidence.

We can formulate a partition of hypothesis Ho and ~Ho

Ho = We will sell 10 products to customer x this year

We are at a trade show talking to a distributor who tells us he has heard that customer x is currently trialing our competitors products. We will call this new piece of evidence E

E = Customer x is currently trialing our competitors products

Before we had heard this we may have been quite bullish about the prospects of selling to customer x because we have had several meetings where they expressed interest and have been talking about using some demo equipment.

Pr(Ho)=0.8

However if it is true that customer x is currently trialing the competitor products then I figure that is bad news as they need to commit resource to testing and are further down the line with our competitors.

Pr(Ho/E)=0.1

If what I’ve heard is not true then I have no other reason to revise my prior belief

Pr(Ho/~E)=0.8

I represent my belief in light of the new rumor as Pr*, so that Pr*(Ho) stands for my belief in Ho in light of the new information E.

When talking to the distributor he can’t remember who he heard it from but is pretty sure that he is right. I might assign a probability that the information is right to 0.75.

Pr*(E)=0.75    Pr*(~E)=0.25

Jeffrey’s revision of Bayes’ rule is reminiscent of the rule for total probability

Pr*(Ho) =Pr(Ho/E)Pr*(E)+Pr(Ho/~E)Pr*(~E)

Jeffrey tells us to conclude that Pr*(Ho)=0.275. Before we heard the rumor we thought it was quite probable that we would sell to customer x, but things are looking a bit more bleak.

Dashboard representation

We can put together a dashboard that allows a user to start with a prior belief and update using Jeffrey’s rule. Two sliders are used to input Pr(Ho/E) and Pr*(E). The numeric inputs are augmented with descriptive labels.

Examples

If we receive a new piece of information that definitively refutes our hypothesis, but we know the source is completely unreliable then we would have no reason to update our belief e.g. if a stranger in the street says he wouldn’t buy our chemical detection equipment, this has no relevance or impact on my belief that the US Army will.

If we receive a new piece of information that we know is definitely true but is doesn’t add much to support our hypothesis then our posterior belief will be unchanged. For example, two people from one company tell me a piece of information separately. When I hear it from the first person I update my belief accordingly, when I hear it for the second time is gives me no new knowledge even though I believe the source completely.

Potential problems with the application of Jeffrey’s rule

Prior Belief

We can look at what happens if we start out with very different prior beliefs. If we are rationally updating with new evidence and agree on the impact and quality we should eventually converge on a common belief.

Table 1 Change in belief from a starting belief of 1

Table 2 change in belief from a starting belief of 0

The tables above and graph below illustrate the sequential application of Jeffrey’s rule. We start with differing prior beliefs and as new evidence arrives we update our belief. The dataset for Pr(Ho/E) and Pr*(E) are randomly generated number between 0 and 1. We can see that after 3-4 pieces of evidence we are starting to converge on a common belief. While not rigorous, inspection of simulated cases supports the idea that beliefs will converge irrespective of the staring belief.

Applying the principle of insufficient reason to prior belief

What happens if we start with no evidence at all for a hypothesis? We may be inclined to say that there is nothing to choose between the alternatives, true or false, so they should be treated as equally probable- this is the principle of insufficient reason or the principle of indifference. However we can look at a simple example; I state a hypothesis, “your car is red”. Initially without any evidence it doesn’t seem that the partition “your car is red” and “your car is not red” would have an equal probability.

In most business examples I can think of it is usually more likely for a specific hypothesis to be false; “this product will be successful” vs “this product will fail”. There are usually many more ways to fail than to be successful. We may be happy to assign a personal probability to the prior belief as opposed to assuming indifference. However this may allow certain hypothesis an ‘easy ride’ without forcing us to find evidence to corroborate or falsify. I prefer to operate the maxim ‘guilty until proven innocent’; assume the hypothesis is false until proven otherwise. This forces me to find evidence so I can justify my belief position – just because I think it is obvious that something is true doesn’t mean that others do. If I already have a high prior belief it should be easy for me to find the supporting evidence. This also means that I will be operating conservatively in the early stages as my belief is ‘dragged down’ by the memory of initial belief up to the point of convergence.

Order of discovery

It would also seem intuitively obvious that the order in which we uncover new evidence should make no difference to our eventual beliefs. We have generated 20 discrete pieces of evidence and updated belief at each stage. We have then reordered the evidence (re-sampling without replacement) and calculate the new belief trajectory. Interestingly we can have marked differences in belief at the end of the process. The results are presented without further discussion, but this may pose a significant problem in the application of this belief updating methodology.

The above re-sampling example assumes that we would actually assign the same ‘marginal belief change’ irrespective of the order of discovery. This may not be a valid assumption and we can look at an example from history. In 1818 Siméon Poisson deduced from Augustin Fresnel’s theory the necessity of a bright spot at the centre of the shadow of a circular opaque obstacle. With his counterintuitive result Poisson hoped to disprove the wave theory; however Dominique Arago experimentally verified the prediction and today the demonstration goes by the name “Poisson’s (or Arago’s) spot.” Since the spot occurs within the geometrical shadow, no particle theory of light could account for it, and its discovery in fact provided weighty evidence for the wave nature of light, much to Poisson’s chagrin. If I believed in the corpuscular theory of light I would be extremely surprised to see a Poisson spot. However once I have seen it and adjusted my belief accordingly, seeing it again would only have a very small impact on my belief; the new experiment contains very little information. This is the same as saying that the marginal belief change for a particular piece of evidence depends on my current belief and the history of how I arrived here. It doesn’t therefore seem valid to resample, as we deal with marginal change in belief, not absolute values as new evidence arrives.

Introduction

Disruptive platform technologies usually have a broad base of application. During early stage development, before there is a developed market, the selection of a particular product is usually a ‘high risk, low data’ decision. There are a large number of unknowns, both the known unknowns and the unknown unknowns; we seek the resolve these over time. In this type of situation it is difficult to make the initial portfolio selection decision and to effectively monitor the resolution of uncertainty, and determine the ultimate ‘chance of success’ for the product.

Problems in portfolio selection and project monitoring

The portfolio selection process, even when highly structured, often reduces to persuasion by advocates and champions. When a lot of data is being presented it is easy to forget ‘how we arrived’ at a particular position, assigning a higher importance to things that we heard recently (or long ago, depending on how your mind works). Soaring rhetoric can outweigh sober analysis and dispassionate appraisal of risk. It can be difficult to judge the ‘quality’ of a piece of information, which may find itself as a lynchpin in an argument to take a particular course of action. With a lot of unknowns it can be difficult to formulate go/no-go metrics and not relax the criteria when you get to the decision point.

Cognitive biases

The field of behavior economics examines some of the less rational beliefs of Homo economicus. Work by Tversky and Kahneman illustrate cases of overconfidence in our abilities, the desire to go with the herd and a propensity for rolling rationalization. Here is a list of cognitive biases that you can easily imagine arise in portfolio selection processes.

Objectives

1. Develop a simple methodology and toolset that allows us to :-
   
2. Reduce complex business decisions to specific and testable hypothesis, which can be definitively refuted.
   
3. Systematically revise our ‘belief’ in a hypothesis as we receive new information.
   
4. Integrate new information of many types and forms, of varying degrees of ‘quality’.
   
5. Maintain a history of how we arrived at a particular belief to provide an ‘audit trial’ or ‘memory’ to support future decisions and actions.
   
6. Integrate and logically connect hypothesis to create a ‘belief network’ that supports complex decision making.
   
7. Avoid cognitive biases and increase objectivity
   

Logic and Probability

There are three main modes of argument, deduction, induction and abduction (inference to best explanation IBE). Inductive logic analyses risky arguments using probability ideas. There are however different interpretations of what ‘a probability is’.

Frequentists talk about probabilities only when dealing with experiments that are random and well-defined. The probability of a random event denotes the relative frequency of occurrence of an experiment’s outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency “in the long run” of outcomes.

Bayesians, however, assign probabilities to any statement whatsoever, even when no random process is involved. Probability, for a Bayesian, is a way to represent an individual’s degree of belief in a statement, given the evidence.

Logical Probability is thought of as a logical relation between a hypothesis and the evidence for it. J.M. Keynes and Rudolf Carnap both favored a logical theory of probability. Personal probabilities are a private matter, they are up to the individual and anything goes so long as be basic rules of coherency are obeyed. Logical probability maintains that there are uniquely correct, uniquely rational judgments of the probability of a hypothesis in the light of evidence.

For the purposes of decision making in a business context there are very few cases where a Frequentists approach can be used. We tend to use the Bayesian notion of probability where belief allows us to make investment decisions.

It is plausible to connect personal degrees of belief and personal betting rates

You would not pay more than $1 to win $2 on the flip of a coin. If you have some domain specific business knowledge that allows you to exploit an opportunity, your betting rate would be markedly different from someone without that knowledge. During product development as uncertainty is resolved our beliefs are updated and we revise the level of investment we are willing to make. People have always used this ‘managerial flexibility’ and there is now a move to formalize this type of ‘real option’ thinking in investment and portfolio selection.

Verificationism and Falsifiability

There are two common problems in portfolio decision making, how do we extrapolate experience to the future? And how can we provide definitive go/no-go criteria when we do not know the problem well? The former is the problem of induction, and is the question of whether inductive reasoning leads to truth. That is, what is the justification for presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold). If we cannot assume uniformity of nature for physical laws we definitely cannot do so in a business context where we know that the landscape changes very quickly.

Often a go/no-go criteria is framed in a way that allows it to get out of jail down the line. A criteria such as, “show interest from a customer” is quite broad. If in a month’s time if we hear a statement “Fred and Jeff seem quite interested”, this adds practically no new useful knowledge upon which to base a decision – “A difference that makes no difference is no difference”. It also allows us to introduce an ad hoc revisions to ‘pass’ the criteria. If we set criteria such as “one sale made by the end of the quarter”, then we have something that is definitively testable. This is a criterion that puts itself at risk, which can be refuted or falsified – falsification adds new knowledge as it allows us to eliminate options and make definite investment decisions i.e. don’t invest. Falsifiability was put forward as solution to the problem of induction by Karl Popper.

This is related to the Logical Positivist view of the verifiability theory of meaning: the meaning of a sentence consists in its method of verification. In other words, if a sentence or statement has no possible method of verification, it has no meaning. It is pointless to make a go/no-go goal such as, “demonstrate our value proposition and facilitate end to end knowledge transfer”, as there is no possible way to test this and it therefore falls into the category of a nonsensical statement (also known as bullshit bingo).

In return for your hard work at an Investment Bank, your company decides to reward you with a sizable bonus. You’re given two options:

(A) Take a sure $1 million. Or,

(B) Play a lottery where you get $1 million with 89% probability, $5 million with 10% probability, and nothing ($0) with 1% probability.

Given the emotionless genius that you are, you calculate that the expected value of option B is $390,000 higher than option A, and pick option B without any hesitation whatsoever.

Most people, however, (emotionless geniuses are still a minority in the population) would pick option A, if real money were at stake. This type of behaviour (Allais paradox) is very puzzling from an economic point view as it violates expected utility maximization, one of the central tenets of rational decision-making. 

Regret avoidance is a plausible explanation for such behaviour: By picking option B, you are exposed to the unlikely (1%) event where you get nothing. That would lead to a deep feeling of regret “If only I had picked A, I could have walked away with a sure $1 million”. Regret is indeed a strong emotion (more songs have been written about the road not taken than about love), and people would give up expected utility in order to not experience it in the future. 

This can account for other irrational behaviour such as buying lotto tickets, and not getting examined for a health-related disorder. Even though people are aware that the expected value of a lotto ticket is negative, they still buy them since if their lucky numbers were chosen, they’d feel regret (and the Lotto company plasters the happy faces of the winners everywhere). In fact, a regular lotto-player in Liverpool committed suicide in 1996 after he came to know that he missed out on £2 million prize: his lucky combination (14,17,22,24,42,47) won out, and he had incidentally not renewed his ticket for that week!

This is also an issue in healthcare. People avoid going for a check-up, even when they know that the information can only help them, since finding out that they have a disease would lead to the experience of regret afterwards.

So if regret makes us inefficient decision-makers, why did this emotion evolve in humans? Would we be better off if we could somehow remove this emotion? 

No, since regret is a very useful component of learning. Learning through rewards and punishment developed quite early on the evolutionary path. Rats and birds learn through pleasure and pain as well, but they learn slowly. Regret on the other hand, is learning after the fact: comparing “what is” with “what might have been” (counterfactual learning). Compared to disappointment, which is felt when a negative outcome occurs which had nothing to do with our decision, regret is strongly associated with a feeling of responsibility. This provides more signal than just rewards and punishment alone, and learning is much faster.

If perfect knowledge of outcomes were available, a genius would be able to compute the long-term values of all their actions, and choose the most utile one. However, most decisions are made under incomplete information, and knowledge of the better outcome arises after the event. So even geniuses need to feel regret to learn! 

This was demonstrated in a recent Neuroeconomics study, published in PNAS May 2007, by Lohrenz and Montague. 20 subjects were asked to play a stock-market game inside a MRI scanner. The initial price of the stock was $100, and players could bet a percentage (0 to 100%) of their earnings at every round. They would get to keep all their earnings at the end. Unbeknownst to the players, these “simulated” price movements were actually taken from “famous” days in stock markets, like the great crashes of the 80s and 90s. Players experienced regret when they bet on stocks whose prices went down, or when they didn’t make a bet and the prices went up. These regret signals correlated strongly with the neural activity in the ventral caudate area (where a horizontal line through your eyes, and through your ears, would intersect).

In fact the activity in the ventral caudate strongly predicted how players learned from these errors, and their actions in the future stages of the game. A tragic result however, was that when the market was booming, as in a bubble, there were no regret signals available. Players only received positive reinforcement for their actions, and kept reinvesting (sometimes 100% of) their earnings back into the stock. When the bubble finally burst, these players lost their earnings (and, of course, received a big regret signal from their brain). 

The beneficial role of regret in learning was also shown by Camille et al. in Science magazine in May 2004. Normal subjects and patients with damage to the orbitofrontal cortex played a gambling task. Some gambles offered higher amounts but the payoffs were given out with lower probabilities, whereas some gambles had lower payoffs but paid off more consistently. Players would learn if they won the gamble, and occasionally receive feedback on how well the other gambles would have paid off, had they chosen it.

Normal players reported satisfaction and disappointment when they won and lost, but also felt regret (as measured by skin conductance tests) when an alternate gamble paid off more. Through counterfactual learning, they were able to pick the most advantageous gambles.

Patients with damage to the orbitofrontal cortex area show poor decision-making skills in their social and personal lives. In this game, the OFC patients felt satisfaction or disappointment when their gambles did or did not pay off. But they never felt regret when they learned about the outcomes of the other gambles! Moreover, they did not learn to avoid the gambles which had a low probability of paying off. 

So, only omniscient gods, operating under complete information, can do without regret. A genius has to take actions that maximize expected utility, and embrace the possible regret afterwards!

A recent article in Nature magazine by Jean-Philippe Bouchaud titled “Economics Needs a Scientific Revolution” grabbed my attention. Prof. Bouchaud, who heads research at a hedge fund and teaches physics in Paris, blames the recent (and ongoing) financial crisis on the economists’ lack of changing their theories in light of empirical evidence. 

He argues for a physicist’s approach to Economics: the ability to observe and probe (human) nature, and modify our theories to accord to empirical evidence. He states that “Reliance on models based on incorrect axioms has clear and large effects” and he goes on to question the assumptions of rationality and profit maximization (covered in previous topics in this blog).

Another simplifying assumption that has been used in Economics is that prices deviate from their mean according to a Normal (Guassian) distribution. This was highlighted in a recent bestseller by Nasim Taleb titled “Fooled by Randomness“. A lot of variability in nature can be explained by a Normal distribution. The mean height of an adult male is around 170 cms, and a height of 185 cm will be observed in less than 10% of adults. One would not find someone who’s 1000 cm tall, for example. But the Normal distribution is not so good at explaining variability in social phenomenon, such as wealth, number of relationships etc. Although the mean income might be $35,000 with a standard deviation of $25,000, there would many people with incomes of $500,000, $1 billion etc. That’s like people being 170cms tall on average and occasionally finding someone who’s 10m or even 1km tall!!

This type of wrong assumption led to the collapse of Long Term Capital Management, the biggest hedge fund in the 1990s, and required a Fed bailout of $4 billion (miniscule in today’s numbers). The models created by their team of Economists, which included 2 Nobel Prize winners, and thus considered “too smart to fail“, never predicted the kinds of price fluctuations that were seen in the market. According to their models, such craziness could have occurred only once in the lifetime of 2 universes!. Many social phenomenon, including price of assets, are better modeled as Fractals or Power distributions that Physicists use regularly. Incorporating power laws into the financial models would predict large price fluctuations more regularly, and prescribe more conservative strategies for risk management.

But before we all hail Physicists and let them take charge of the Fed, we should realize that modeling Economic phenomenon is far more complex than modeling many natural phenomenon. Imagine how complex nature would be if particles could also think!

Perhaps a promising direction is to marry the complex models of decision-making from Robotics and Computational Neuroscience, with notions of game theory, to account for some of the phenomenon observed in financial markets. Then we can simulate a market with interacting agents equipped with different cognitive abilities, utilities, and emotional biases (such as risk aversion, loss aversion, regret avoidance etc). This can account for phenomenon that still lack reasonable explanations from economic theory, such as financial bubbles, herding, collapses etc. Hedge funds can then have better predictions of how the markets will react to their strategies, and those with less sinister and more paternalistic aspirations could simulate the effects of policies and regulations, to curb bubbles and collapses.

Finally, a silly joke at the expense of (classical) Economists:

Q. How many economists does it take to change  a lightbulb?

A. None. If the lightbulb needed changing, then the market forces should have already changed it!

  John Maynard Keynes, the most brilliant economist after Adam Smith (and a very mysterious character), likened the stock market to a newspaper beauty contest. Keynes was also a highly successful investor and married a  beauty  queen (perhaps the analogy was inspired by his personal life). To quote Keynes directly:

   “professional investment may be likened to those newspaper contests in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view.

 It is not a case of choosing those which, to the best of one’s judgement, are the really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.”

The Beauty Contest game, described below, creates a simple abstraction of this phenomenon:

The Beauty-Contest game: Every player is asked to pick a (whole) number between 0 and 100 (and write it down on a paper). The prize goes to the one who picks a number that’s closest to 2/3-rd of the average of the numbers picked by everyone.

So what number would a Game Theorist pick? He or she would reason that a naive approach would be to randomly pick a number between 0 and 100 (say, based on the last 2 digits of one’s social security number). Thus the average using the naive approach would be 50, so reasonable players ought to pick at most 2/3-rd of that, i.e. 33. Reasoning one step further, one ought to choose 2/3-rd of 33, i.e. 22. By carrying this iterated reasoning all the way, the rational answer would be 0 (the only Nash equilibrium).

The Nash equilibrium solution predicts that all players would pick 0 (and share the prize equally). But what happens when this game is conducted with human subjects? It seems that most people choose numbers between 22 and 33 (they are doing just 1 or 2 steps of iterated thinking). This game was played across a wide cross-section of the population: CEOs, Investment bankers, Educators, PhDs in Engineering, and numbers close to 0 are rarely picked. Even reasoning upto 3-4 levels is rare. While these experimental results should not seem too surprising, it contains a prescription for the emotionless genius: do not engage in too many steps of strategic thinking. Clearly, acting according to Game Theory (and choosing 0) would not win her the prize in the Beauty contest game.

In everyday social interactions, people do engage in strategic thinking, but not to arbitrarily high levels. The 0-level thinkers (duds) would interpret all actions as random. The 1-level thinkers (naive) accept everything at face value “she gave me a gift since she likes me”. The 2-level thinkers would reason “she gave me a gift so that I’d think she likes me”. A 5-level thinker reasons “she gave me a gift so that she could think that I’d think that she’d think that I’d think that she likes me”; but most people do not perform their actions with such in-depth thinking. In fact thinking beyond 2 or 3 levels is over-mentalizing and ascribing intentions to people that they may not have (strategic people have a tendency to be more cynical!).

How can we figure out the “strategic level” of one’s partner or opponent? One can probe their partner to figure it out, but that is a hard task since a strategic opponent knows that their partner is trying to figure out their level. An opponent with a higher strategic level would already figure out your strategies and also intentionally act naive in order not to reveal their strategic-ness. Thus, the actions of a higher-level player remain mysterious: “One cannot figure out the mind of god“.

Some of the lowest numbers in the beauty contest game, roughly 9 to 14 (corresponding to 3 to 4 steps) were picked by Caltech students (who get the highest average scores on standardized quantitative tests among all US universities). So IQ could be a strong determinant of strategic level, although I think this is neither necessary nor sufficient: there are many people with high levels of intelligence who might not be adept at strategic thinking, and vice versa. It would be great to create a verbal version of the Beauty contest game to take away some of the emphasis on quantitative reasoning (although most people should be able to take averages and fractions). An aim of cognitive neuroscience is to identify the regions of the brain that are involved in strategic thinking; then we can have a test for strategic thinking ability: an increased activity in those regions would correlate with more strategic ability. As far as I know, this has not yet been done successfully.

Social interaction involves figuring out dyadic relationships which makes the task even more difficult: “I think that Tom thinks that Jane thinks that Rob would like to buy an iPhone since Tom thinks that Jane thinks that Rob thinks that buying an iPhone would impress Mary”. That is the basis of the Social Brain hypothesis: the reason that humans developed such a big brain was to handle the complex computations that are required for living in a society! 

I’ll discuss my opinions on the consequences of over-mentalizing (or doing too much strategic thinking) in financial decision-making, and its effects on stock markets in a later post. 

Those of you who were misled to this post by the title, can see the right video here: http://in.youtube.com/watch?v=WALIARHHLII